[[[[750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 620700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 100 beta4 - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 < 0 /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 + 182550 nu + 3651 /= 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 + 182550 nu + 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]] \/ [2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2463750000 beta4^2 nu^2 + 66711050000 beta4^2 nu + 1333235500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2463750000 beta4^2 nu^2 + 66711050000 beta4^2 nu + 1333235500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1332250000 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 1999105050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 1332250000 beta4 + 9127500 nu^2 + 365100 nu + 3651 /= 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [5000 beta4^2 nu + 985600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 2190200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 1460200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] \/ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 985600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 100 beta4 - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 < 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1551250000 beta4^2 nu^2 + 133287050000 beta4^2 nu + 2665120500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1332250000 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 133287050000 beta4^2 nu + 2665120500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 7994230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1551250000 beta4^2 nu^2 + 133287050000 beta4^2 nu + 2665120500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1332250000 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 < 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 + 182550 nu + 3651 /= 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 + 182550 nu + 3651 /= 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [85775000 beta4^2 nu + 1715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1149750000 beta4^2 nu + 323759745000 beta4^2 - 212975000 beta4 nu^2 - 119943869000 beta4 nu - 2398792190 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1750 beta4^2 nu + 985535 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1750 beta4 nu + 985535 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3285000000 beta4^2 nu + 323802450000 beta4^2 - 608500000 beta4 nu^2 - 119959690000 beta4 nu - 2398950400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [85775000 beta4^2 nu + 7195865500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 85775000 beta4 nu + 7195865500 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [407668500000 beta4^2 - 135482525000 beta4 nu - 2709650500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1241000 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1113250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1113250 beta4 - 182550 nu - 3651 = 0 ]]] /\ [563541750000 beta4^2 - 164355850000 beta4 nu - 3287117000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1715500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [3686500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 3686500 beta4 - 547650 nu - 10953 = 0 ]]]] \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [4375000 beta4^2 nu^3 + 1277762500 beta4^2 nu^2 + 69994230250 beta4^2 nu + 1399373535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [958125000 beta4^2 nu^2 + 93295825000 beta4^2 nu + 1703814908250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1916250000 beta4^2 nu^2 + 93334150000 beta4^2 nu - 3402032833500 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [85775000 beta4^2 nu + 1715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [407668500000 beta4^2 - 135482525000 beta4 nu - 2709650500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1241000 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1113250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1113250 beta4 - 182550 nu - 3651 = 0 ]]] /\ [563541750000 beta4^2 - 164355850000 beta4 nu - 3287117000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1715500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [3686500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 3686500 beta4 - 547650 nu - 10953 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [809341875000000 beta4^2 nu^2 + 15349918050000000 beta4^2 nu + 306674624250000 beta4^2 - 299838375000000 beta4 nu^3 - 2855349740000000 beta4 nu^2 - 113854183550000 beta4 nu - 1137342482000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2463750000 beta4^2 nu^2 + 23412925000 beta4^2 nu + 467273000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 49275000 beta4 nu + 467273000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [809341875000000 beta4^2 nu^2 + 43796786175000000 beta4^2 nu + 875611986750000 beta4^2 - 299838375000000 beta4 nu^3 - 8124731552500000 beta4 nu^2 - 324629456050000 beta4 nu - 3245095207000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1565886500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [24637500 beta4 nu + 1565886500 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [87500 beta4^2 nu^2 + 25553500 beta4^2 nu + 1399373535 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 - 93231950000 beta4^2 nu - 10213561144500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 7298731807350 beta4 nu + 145947991149 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [47906250000 beta4^2 nu^3 + 4665749375000 beta4^2 nu^2 + 85284041237500 beta4^2 nu + 1703814908250 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 >= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2445500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [2682750000 beta4^2 nu + 65333905000 beta4^2 - 1916775000 beta4 nu^2 - 93359721000 beta4 nu - 1866427710 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 3042500 nu^2 - 444326700 nu - 8885317 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1596875000 beta4^2 nu^2 + 81664187500 beta4^2 nu + 852607332500 beta4^2 - 684562500 beta4 nu^3 - 25027605000 beta4 nu^2 - 1000282725 beta4 nu - 10000089 beta4 < 0 \/ 63875000 beta4 nu + 933852500 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 3042500 nu^2 - 444326700 nu - 8885317 = 0 ]]] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1596875000 beta4^2 nu^2 + 81664187500 beta4^2 nu + 852607332500 beta4^2 - 684562500 beta4 nu^3 - 25027605000 beta4 nu^2 - 1000282725 beta4 nu - 10000089 beta4 < 0 \/ 63875000 beta4 nu + 933852500 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]]]] \/ [1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 466389700000 beta4^2 nu + 13624921772000 beta4^2 - 1369125000 beta4 nu^3 - 199974397500 beta4 nu^2 - 7997332950 beta4 nu - 79967853 beta4 < 0 \/ 51100000 beta4 nu + 1866172000 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 >= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 >= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]] \/ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 1022070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 1022070 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4^2 nu + 511210 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 1241070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 1022070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 1022070 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [10500 beta4^2 nu + 511210 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 10500 beta4 nu + 511210 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]] \/ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 1022070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 1022070 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [10500 beta4^2 nu + 511210 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 10500 beta4 nu + 511210 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 1241070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 1022070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4^2 nu + 511210 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]]] \/ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [3500 beta4^2 nu + 1241070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 1022140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1533140 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1533140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 1241070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 1022070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 1022070 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4^2 nu + 511210 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]]] \/ [6022500000 beta4^2 nu^2 + 246707150000 beta4^2 nu + 2436287984000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 /\ 1916250000 beta4^2 nu^2 - 93180850000 beta4^2 nu - 3405763133500 beta4^2 - 1369125000 beta4 nu^3 + 66548602500 beta4 nu^2 + 2434685962050 beta4 nu + 48667088847 beta4 < 0 /\ 2250000 beta4^2 nu^2 + 147915000 beta4^2 nu + 2267782400 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [95812500000 beta4^2 nu^3 + 9331498750000 beta4^2 nu^2 + 170568082475000 beta4^2 nu + 3407629816500 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [95812500000 beta4^2 nu^3 - 4657126250000 beta4^2 nu^2 - 170381337525000 beta4^2 nu - 3405763133500 beta4^2 - 68456250000 beta4 nu^4 + 3326061000000 beta4 nu^3 + 121800846705000 beta4 nu^2 + 4868040404400 beta4 nu + 48667088847 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [10128750000 beta4^2 nu^2 + 446708900000 beta4^2 nu + 4871642626500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [239531250000 beta4^2 nu^3 + 9340121875000 beta4^2 nu^2 + 85470786187500 beta4^2 nu + 1705681591250 beta4^2 - 68456250000 beta4 nu^4 - 1671245250000 beta4 nu^3 - 100110420000 beta4 nu^2 - 2001113100 beta4 nu - 13337103 beta4 < 0 \/ 652802500000000 beta4^2 nu^2 + 11939757725000000 beta4^2 nu + 238534033500000 beta4^2 - 583019062500000 beta4 nu^3 - 8547059456250000 beta4 nu^2 - 341182755375000 beta4 nu - 3409495477500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 31937500 beta4 nu + 466926250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [262500 beta4^2 nu^2 + 25560500 beta4^2 nu + 466798605 beta4^2 - 9127500 beta4 nu^2 - 222467600 beta4 nu - 4445701 beta4 < 0 \/ 2682750000 beta4^2 nu + 130614155000 beta4^2 - 1916775000 beta4 nu^2 - 140001246000 beta4 nu - 2799258210 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 127785 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 < 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2445500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [163200625000000 beta4^2 nu^2 + 35747464900000000 beta4^2 nu + 714884017750000 beta4^2 - 233207625000000 beta4 nu^3 - 25550227395000000 beta4 nu^2 - 1021729246650000 beta4 nu - 10216359636000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [319375000 beta4^2 nu^2 + 46641525000 beta4^2 nu + 932702750 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [6387500 beta4 nu + 932702750 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2190000000 beta4^2 nu^2 + 46716350000 beta4^2 nu + 933451000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 139937350000 beta4^2 nu + 2798236000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 2798236000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 933597000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 51100000 beta4 nu + 933597000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [1277500000 beta4^2 nu^2 + 139937350000 beta4^2 nu + 2798236000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4^2 nu + 933597000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 5000 nu^2 - 127550 nu - 2553 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [2190000000 beta4^2 nu^2 + 46716350000 beta4^2 nu + 933451000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 547400 nu - 10949 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5000 nu^2 - 127550 nu - 2553 > 0 \/ 100 nu - 2553 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 139937350000 beta4^2 nu + 2798236000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 2798236000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 933597000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 51100000 beta4 nu + 933597000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 >= 0 /\ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 < 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 >= 0 /\ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 >= 0 /\ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 < 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 >= 0 /\ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 620570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [3102500000 beta4^2 nu + 385082300000 beta4^2 - 912750000 beta4 nu^2 - 226581060000 beta4 nu - 4531256100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [49275000 beta4^2 nu + 4530635500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 49275000 beta4 nu + 4530635500 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [2171750000 beta4^2 nu + 385063685000 beta4^2 - 638925000 beta4 nu^2 - 226570107000 beta4 nu - 4531146570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1750 beta4^2 nu + 620535 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1750 beta4 nu + 620535 beta4 - 182550 nu - 3651 = 0 ]]] /\ [203834250000 beta4^2 - 97725100000 beta4 nu - 1954502000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2226500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 2226500 beta4 - 547650 nu - 10953 = 0 ]]] /\ [181186000000 beta4^2 - 91062025000 beta4 nu - 1821240500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [748250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 748250 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 620570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [4375000 beta4^2 nu^3 + 1277762500 beta4^2 nu^2 + 69994230250 beta4^2 nu + 1399373535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1916250000 beta4^2 nu^2 + 93334150000 beta4^2 nu - 3402032833500 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [958125000 beta4^2 nu^2 + 93295825000 beta4^2 nu + 1703814908250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 46690800000 beta4^2 nu + 933195500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 5000 nu^2 - 127550 nu - 2553 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [203834250000 beta4^2 - 97725100000 beta4 nu - 1954502000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2226500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 2226500 beta4 - 547650 nu - 10953 = 0 ]]] /\ [181186000000 beta4^2 - 91062025000 beta4 nu - 1821240500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [748250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 748250 beta4 - 182550 nu - 3651 = 0 ]]] /\ [962550625000000 beta4^2 nu^2 + 41371558275000000 beta4^2 nu + 827046145250000 beta4^2 - 566361375000000 beta4 nu^3 - 12194093557500000 beta4 nu^2 - 487084108650000 beta4 nu - 4868575641000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 899579000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [15512500 beta4 nu + 899579000 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [962550625000000 beta4^2 nu^2 + 28971641400000000 beta4^2 nu + 579047807750000 beta4^2 - 566361375000000 beta4 nu^3 - 8546059995000000 beta4 nu^2 - 341162766150000 beta4 nu - 3409362216000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 23376425000 beta4^2 nu + 466908000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 31025000 beta4 nu + 466908000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 5000 nu^2 - 127550 nu - 2553 > 0 /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1551250000 beta4^2 nu^2 + 46690800000 beta4^2 nu + 933195500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 - 93231950000 beta4^2 nu - 10213561144500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 7298731807350 beta4 nu + 145947991149 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [87500 beta4^2 nu^2 + 25553500 beta4^2 nu + 1399373535 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [47906250000 beta4^2 nu^3 + 4665749375000 beta4^2 nu^2 + 85284041237500 beta4^2 nu + 1703814908250 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2920000000 beta4^2 nu^2 + 46745550000 beta4^2 nu + 933743000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1095000000 beta4^2 nu^2 + 46672550000 beta4^2 nu + 933013000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 21900000 beta4^2 nu + 933013000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [21900000 beta4^2 nu + 1865588000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [21900000 beta4 nu + 1865588000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7300000 beta4^2 nu + 932721000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 7300000 beta4 nu + 932721000 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2372500000 beta4^2 nu^2 + 46723650000 beta4^2 nu + 933524000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 47450000 beta4 nu + 933524000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [250000 beta4^2 nu^2 + 27385000 beta4^2 nu + 547600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 1277600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 547600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 25 nu - 1277 <= 0 /\ [5000 beta4^2 nu + 912600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 63885000 beta4^2 nu + 1277600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1277600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 27395000 beta4^2 nu + 547700 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 547700 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 182600 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 5000 beta4 nu + 182600 beta4 - 60850 nu - 1217 = 0 ]]]] \/ [68437500000 beta4^2 nu^3 + 1669418750000 beta4^2 nu^2 - 364636742875000 beta4^2 nu - 8881743714577500 beta4^2 - 68456250000 beta4 nu^4 - 1671245250000 beta4 nu^3 + 364703245830000 beta4 nu^2 + 8891471801886900 beta4 nu + 177683541380397 beta4 > 0 /\ 9581250000 beta4^2 nu^2 + 433364500000 beta4^2 nu + 4871375957500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7117500000 beta4^2 nu^2 + 313363450000 beta4^2 nu + 3410163172000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 27375000 beta4^2 nu + 666672500 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 < 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [750000 beta4^2 nu^2 + 45655000 beta4^2 nu + 667037800 beta4^2 - 9127500 beta4 nu^2 - 222467600 beta4 nu - 4445701 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 60850 nu - 1217 = 0 ] /\ [9375000 beta4^2 nu^3 + 1597437500 beta4^2 nu^2 + 83329511250 beta4^2 nu + 1217344076325 beta4^2 - 456375000 beta4 nu^3 - 44447882500 beta4 nu^2 - 812451492650 beta4 nu - 16231254351 beta4 > 0 \/ 1368750000 beta4^2 nu + 66639875000 beta4^2 - 1369125000 beta4 nu^2 - 100000890000 beta4 nu - 1999470150 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1250 beta4 nu + 91275 beta4 - 60850 nu - 1217 = 0 ] /\ [8554687500000 beta4^2 nu^4 + 958239062500000 beta4^2 nu^3 + 27410231625000000 beta4^2 nu^2 + 222956517464375000 beta4^2 nu + 4448173921181250 beta4^2 - 3422812500000 beta4 nu^5 - 333496031250000 beta4 nu^4 - 6106721928750000 beta4 nu^3 - 365603199075000 beta4 nu^2 - 7306730783250 beta4 nu - 48693763053 beta4 > 0 \/ 333062500000000 beta4^2 nu^2 + 6091713125000000 beta4^2 nu + 121701037500000 beta4^2 - 416442187500000 beta4 nu^3 - 6105042468750000 beta4 nu^2 - 243701968125000 beta4 nu - 2435353912500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 22812500 beta4 nu + 333518750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [22812500000 beta4^2 nu^3 + 4997306250000 beta4^2 nu^2 - 121367947625000 beta4^2 nu - 26625780295192500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 + 121301225610000 beta4 nu^2 + 26635503053502300 beta4 nu + 532661500590399 beta4 < 0 /\ 365000000 beta4^2 nu^2 + 126578350000 beta4^2 nu + 10214227671000 beta4^2 - 152125000 beta4 nu^3 - 33324502500 beta4 nu^2 - 1332797550 beta4 nu - 13327367 beta4 > 0 /\ 250000 beta4^2 nu^2 + 118635000 beta4^2 nu + 13990997600 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [3125000 beta4^2 nu^3 + 2053312500 beta4^2 nu^2 + 383104003750 beta4^2 nu + 18242833133775 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 > 0 \/ 456250000 beta4^2 nu + 133234125000 beta4^2 - 456375000 beta4 nu^2 - 166595130000 beta4 nu - 3331720050 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1250 beta4 nu + 456275 beta4 - 182550 nu - 3651 = 0 ] /\ [570312500000 beta4^2 nu^4 + 208209687500000 beta4^2 nu^3 + 21286858400000000 beta4^2 nu^2 + 666434997940125000 beta4^2 nu + 13320186881028750 beta4^2 - 380312500000 beta4 nu^5 - 111089281250000 beta4 nu^4 - 6088941558750000 beta4 nu^3 - 365069909675000 beta4 nu^2 - 7299621069250 beta4 nu - 48658216917 beta4 > 0 \/ 166531250000000 beta4^2 nu^2 + 18241833125000000 beta4^2 nu + 364770050000000 beta4^2 - 249865312500000 beta4 nu^3 - 18255159731250000 beta4 nu^2 - 729906550875000 beta4 nu - 7298066047500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 4562500 beta4 nu + 333153750 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3421875000000 beta4^2 nu^4 + 916195625000000 beta4^2 nu^3 + 30446916650000000 beta4^2 nu^2 - 1329950769534250000 beta4^2 nu - 26611186828327500 beta4^2 - 3422812500000 beta4 nu^5 - 916515093750000 beta4 nu^4 - 30473587203750000 beta4 nu^3 + 1329706034442675000 beta4 nu^2 + 53224780356606750 beta4 nu + 532369551288897 beta4 > 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [5000 beta4^2 nu + 1277600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 < 0 /\ [250000 beta4^2 nu^2 + 27385000 beta4^2 nu + 547600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 /\ [25000000 beta4^2 nu^3 + 4107750000 beta4^2 nu^2 + 166695530000 beta4^2 nu + 3332267700 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 912700 beta4 - 182550 nu - 3651 = 0 ]]] /\ [5000 beta4^2 nu + 547600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 547600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 82145000 beta4^2 nu + 3332267700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ [250000 nu^3 + 13702500 nu^2 - 332514700 nu - 6655773 < 0 /\ 25 nu - 912 = 0 ]] /\ [5000 beta4^2 nu + 912600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 118645000 beta4^2 nu + 5997497700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 10000 beta4 nu + 1642700 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 27395000 beta4^2 nu + 547700 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 547700 beta4 - 182550 nu - 3651 = 0 /\ [50000000 beta4^2 nu^3 + 5934250000 beta4^2 nu^2 + 166768560000 beta4^2 nu + 3332997900 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [20000 beta4 nu + 912900 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [2053125000 beta4^2 nu^2 + 141633687500 beta4^2 nu + 2434188102500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 866875000 beta4^2 nu^2 + 54989987500 beta4^2 nu + 852074140500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 4562500 beta4^2 nu + 166622500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [228125000 beta4^2 nu^2 + 8335687500 beta4^2 nu + 166622500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 22822500 beta4^2 nu + 500050100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 547700 beta4 - 182550 nu - 3651 = 0 ] /\ [228125000 beta4^2 nu^2 + 24988812500 beta4^2 nu + 608338747500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu + 66630750000 beta4^2 - 912750000 beta4 nu^2 - 99982635000 beta4 nu - 1999287600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [3125000 beta4^2 nu^3 + 684562500 beta4^2 nu^2 + 45823472500 beta4^2 nu + 912674789400 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 2500 beta4 nu + 273800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [249796875000000 beta4^2 nu^2 + 6088382500000000 beta4^2 nu + 121667731250000 beta4^2 - 333153750000000 beta4 nu^3 - 6100045162500000 beta4 nu^2 - 243602022000000 beta4 nu - 2434687605000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [1140625000000 beta4^2 nu^4 + 145806093750000 beta4^2 nu^3 + 5327337425000000 beta4^2 nu^2 + 55678233019312500 beta4^2 nu + 1111434891682500 beta4^2 - 570468750000 beta4 nu^5 - 62523375000000 beta4 nu^4 - 1525013572500000 beta4 nu^3 - 91350803887500 beta4 nu^2 - 1826016160125 beta4 nu - 12170108313 beta4 > 0 \/ 18250000 beta4 nu + 333427500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[182500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[182500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [228125000 beta4^2 nu^2 + 24988812500 beta4^2 nu + 608338747500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [182500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [1095000000 beta4^2 nu^2 + 253171300000 beta4^2 nu + 13620657988000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 155145000 beta4^2 nu + 11993352700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 82135000 beta4^2 nu + 6662892600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 4997306250000 beta4^2 nu^2 + 243335489875000 beta4^2 nu + 4864711057500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 /= 0 ] /\ [456250000 beta4^2 nu + 99927875000 beta4^2 - 456375000 beta4 nu^2 - 133279755000 beta4 nu - 2665412550 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [3125000 beta4^2 nu^3 + 1597062500 beta4^2 nu^2 + 233207628750 beta4^2 nu + 9730088513775 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ 1250 beta4 nu + 365025 beta4 - 182550 nu - 3651 = 0 ]]] /\ [166531250000000 beta4^2 nu^2 + 12163442500000000 beta4^2 nu + 243202237500000 beta4^2 - 249865312500000 beta4 nu^3 - 12175103793750000 beta4 nu^2 - 486704313375000 beta4 nu - 4866043672500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [1710937500000 beta4^2 nu^4 + 458097812500000 beta4^2 nu^3 + 36497825512500000 beta4^2 nu^2 + 888904394607875000 beta4^2 nu + 17763492426461250 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 - 12180105663750000 beta4 nu^3 - 730206480525000 beta4 nu^2 - 14600130852750 beta4 nu - 97320877101 beta4 > 0 \/ 13687500 beta4 nu + 666398750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [[182500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[182500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 + 99937000000 beta4^2 nu + 4864711057500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ [182500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1368750000 beta4^2 nu^2 + 166586000000 beta4^2 nu + 4866043672500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [68437500000 beta4^2 nu^3 + 8330668750000 beta4^2 nu^2 + 243468769625000 beta4^2 nu + 4866043672500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [125000 nu^3 - 9117500 nu^2 - 1332614850 nu - 26648649 > 0 \/ 50 nu - 3649 /= 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [68437500000 beta4^2 nu^3 + 11661293750000 beta4^2 nu^2 + 486737619625000 beta4^2 nu + 9730088422500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 27375000 beta4 nu + 2665047500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2281250000 beta4^2 nu^2 + 233235000000 beta4^2 nu + 4867376287500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1095000000 beta4^2 nu^2 + 126607550000 beta4^2 nu + 3406430463000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 45635000 beta4^2 nu + 1999287600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu + 66621625000 beta4^2 - 456375000 beta4 nu^2 - 99964380000 beta4 nu - 1999105050 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [1250 beta4^2 nu + 273775 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1250 beta4 nu + 273775 beta4 - 182550 nu - 3651 = 0 ]]] /\ [166531250000000 beta4^2 nu^2 + 6085051875000000 beta4^2 nu + 121634425000000 beta4^2 - 249865312500000 beta4 nu^3 - 6095047856250000 beta4 nu^2 - 243502075875000 beta4 nu - 2434021297500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [684375000 beta4^2 nu^2 + 16680500000 beta4^2 nu + 333336250 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 13687500 beta4 nu + 333336250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 182500 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1095000000 beta4^2 nu^2 + 46672550000 beta4^2 nu + 933013000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 21900000 beta4^2 nu + 1865588000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 21900000 beta4^2 nu + 933013000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1095000000 beta4^2 nu^2 + 93301300000 beta4^2 nu + 1865588000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 1095100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4^2 nu + 365300 beta4^2 - 182550 beta4 nu - 3651 beta4 <= 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]]] \/ [250000 beta4^2 nu^2 + 27385000 beta4^2 nu + 547600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 1277600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 547600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 25 nu - 1277 <= 0 /\ [5000 beta4^2 nu + 912600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [250000 beta4^2 nu^2 + 63885000 beta4^2 nu + 1277600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 ]] /\ [500000 beta4^2 nu^2 + 27395000 beta4^2 nu + 547700 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4^2 nu + 182600 beta4^2 - 60850 beta4 nu - 1217 beta4 <= 0 /\ 10000 beta4 nu + 547700 beta4 - 182550 nu - 3651 = 0 ]]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 < 0 /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 1998740000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1998740000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu + 666855000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 < 0 /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 3333362500000 beta4^2 nu^2 + 60917186000000 beta4^2 nu + 1217010740000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 999917600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 187500 beta4 nu^3 + 11417500 beta4 nu^2 + 166987725 beta4 nu + 3335189 beta4 < 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 1095100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [15000 beta4^2 nu + 365300 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 9329582500000 beta4^2 nu^2 + 340762981650000 beta4^2 nu + 6811528311000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 13992457500000 beta4^2 nu^2 + 681339371650000 beta4^2 nu + 13621190961000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 279874700000 beta4^2 nu + 6813393972000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [25000000 beta4^2 nu^3 + 3651500000 beta4^2 nu^2 + 133371030000 beta4^2 nu + 2665960200 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 109520000 beta4^2 nu + 5331190200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [50000000 beta4^2 nu^3 + 5478000000 beta4^2 nu^2 + 133444060000 beta4^2 nu + 2666690400 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 < 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 3405764155500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [21900000000 beta4^2 nu + 533338000000 beta4^2 - 5476500000 beta4 nu^2 - 266742060000 beta4 nu - 5332650600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [219000000 beta4^2 nu + 5333380000 beta4^2 - 27382500 beta4 nu^2 - 1333710300 beta4 nu - 26663253 beta4 < 0 \/ 219000000 beta4 nu + 5333380000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 ]]] /\ [2131600000000 beta4^2 - 666307500000 beta4 nu - 13326150000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2920000 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2920000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 3672500 beta4 nu^2 - 133078550 beta4 nu - 2663037 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 999917600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 999917600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu - 1215011270000 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 45725 nu - 1664399 < 0 ]]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 3750 beta4 nu^2 + 228275 beta4 nu + 3335189 beta4 < 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [750000 beta4 nu^3 + 4607500 beta4 nu^2 - 332879100 beta4 nu - 6659419 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 < 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [250000 beta4 nu^3 + 13702500 beta4 nu^2 - 332514700 beta4 nu - 6655773 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [136875000000 beta4^2 nu^3 + 3338837500000 beta4^2 nu^2 - 729273485750000 beta4^2 nu - 17763487429155000 beta4^2 - 68456250000 beta4 nu^4 - 1671245250000 beta4 nu^3 + 364703245830000 beta4 nu^2 + 8891471801886900 beta4 nu + 177683541380397 beta4 > 0 /\ 10950000000 beta4^2 nu^2 + 466725500000 beta4^2 nu + 4872042630000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 8486250000 beta4^2 nu^2 + 346724450000 beta4^2 nu + 3410829844500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 54750000 beta4^2 nu + 1333345000 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [375000 beta4^2 nu^2 + 36515000 beta4^2 nu + 666855150 beta4^2 - 9127500 beta4 nu^2 - 222467600 beta4 nu - 4445701 beta4 > 0 \/ 2500 beta4 nu + 182550 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [18750000 beta4^2 nu^3 + 3194875000 beta4^2 nu^2 + 166659022500 beta4^2 nu + 2434688152650 beta4^2 - 456375000 beta4 nu^3 - 44447882500 beta4 nu^2 - 812451492650 beta4 nu - 16231254351 beta4 > 0 \/ 5475000000 beta4^2 nu + 266559500000 beta4^2 - 2738250000 beta4 nu^2 - 200001780000 beta4 nu - 3998940300 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 2500 beta4 nu + 182550 beta4 - 60850 nu - 1217 = 0 ] /\ [17109375000000 beta4^2 nu^4 + 1916478125000000 beta4^2 nu^3 + 54820463250000000 beta4^2 nu^2 + 445913034928750000 beta4^2 nu + 8896347842362500 beta4^2 - 3422812500000 beta4 nu^5 - 333496031250000 beta4 nu^4 - 6106721928750000 beta4 nu^3 - 365603199075000 beta4 nu^2 - 7306730783250 beta4 nu - 48693763053 beta4 > 0 \/ 1332250000000000 beta4^2 nu^2 + 24366852500000000 beta4^2 nu + 486804150000000 beta4^2 - 832884375000000 beta4 nu^3 - 12210084937500000 beta4 nu^2 - 487403936250000 beta4 nu - 4870707825000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 45625000 beta4 nu + 667037500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 - 242735895250000 beta4^2 nu - 53251560590385000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 + 121301225610000 beta4 nu^2 + 26635503053502300 beta4 nu + 532661500590399 beta4 < 0 /\ 1551250000 beta4^2 nu^2 + 479672050000 beta4^2 nu + 30644681570500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 127760000 beta4^2 nu + 15989555100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 9993335050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 912550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [6250000 beta4^2 nu^3 + 4106625000 beta4^2 nu^2 + 766208007500 beta4^2 nu + 36485666267550 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 > 0 \/ 1825000000 beta4^2 nu + 532936500000 beta4^2 - 912750000 beta4 nu^2 - 333190260000 beta4 nu - 6663440100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 2500 beta4 nu + 912550 beta4 - 182550 nu - 3651 = 0 ] /\ [1140625000000 beta4^2 nu^4 + 416419375000000 beta4^2 nu^3 + 42573716800000000 beta4^2 nu^2 + 1332869995880250000 beta4^2 nu + 26640373762057500 beta4^2 - 380312500000 beta4 nu^5 - 111089281250000 beta4 nu^4 - 6088941558750000 beta4 nu^3 - 365069909675000 beta4 nu^2 - 7299621069250 beta4 nu - 48658216917 beta4 > 0 \/ 666125000000000 beta4^2 nu^2 + 72967332500000000 beta4^2 nu + 1459080200000000 beta4^2 - 499730625000000 beta4 nu^3 - 36510319462500000 beta4 nu^2 - 1459813101750000 beta4 nu - 14596132095000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [6843750000000 beta4^2 nu^4 + 1832391250000000 beta4^2 nu^3 + 60893833300000000 beta4^2 nu^2 - 2659901539068500000 beta4^2 nu - 53222373656655000 beta4^2 - 3422812500000 beta4 nu^5 - 916515093750000 beta4 nu^4 - 30473587203750000 beta4 nu^3 + 1329706034442675000 beta4 nu^2 + 53224780356606750 beta4 nu + 532369551288897 beta4 > 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 1369125000 beta4^2 nu^2 + 91646945000 beta4^2 nu + 1825349578800 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2281250000000 beta4^2 nu^4 + 291612187500000 beta4^2 nu^3 + 10654674850000000 beta4^2 nu^2 + 111356466038625000 beta4^2 nu + 2222869783365000 beta4^2 - 570468750000 beta4 nu^5 - 62523375000000 beta4 nu^4 - 1525013572500000 beta4 nu^3 - 91350803887500 beta4 nu^2 - 1826016160125 beta4 nu - 12170108313 beta4 > 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [1551250000 beta4^2 nu^2 + 319802050000 beta4^2 nu + 13621990420500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 164270000 beta4^2 nu + 13325785200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 + 486670979750000 beta4^2 nu + 9729422115000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 3194125000 beta4^2 nu^2 + 466415257500 beta4^2 nu + 19460177027550 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3421875000000 beta4^2 nu^4 + 916195625000000 beta4^2 nu^3 + 72995651025000000 beta4^2 nu^2 + 1777808789215750000 beta4^2 nu + 35526984852922500 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 - 12180105663750000 beta4 nu^3 - 730206480525000 beta4 nu^2 - 14600130852750 beta4 nu - 97320877101 beta4 > 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3407096770500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 1999105050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 < 0 ] \/ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2190000000 beta4^2 nu^2 + 46716350000 beta4^2 nu + 933451000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 547600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 < 0 /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 2798236000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 2798236000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 46730950000 beta4^2 nu + 933597000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 933597000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 833203800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 187500 beta4 nu^3 + 11417500 beta4 nu^2 + 166987725 beta4 nu + 3335189 beta4 < 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [2463750000 beta4^2 nu^2 + 453063550000 beta4^2 nu + 13624655285500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 912600 beta4 nu + 79953251 beta4 < 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]] \/ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 9329582500000 beta4^2 nu^2 + 340762981650000 beta4^2 nu + 6811528311000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 13992457500000 beta4^2 nu^2 + 681339371650000 beta4^2 nu + 13621190961000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 279874700000 beta4^2 nu + 6813393972000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 < 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 666490050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 3405764155500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [949000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [2044000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2044000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [38325000 beta4^2 nu + 933341500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [76650000 beta4^2 nu + 1866683000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [25550000 beta4^2 nu + 511000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4 - 60850 nu - 1217 = 0 ]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4 - 60850 nu - 1217 = 0 ]]] \/ [50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3832500000 beta4^2 nu^2 + 93410800000 beta4^2 nu + 1866683000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [5000 nu^2 - 127550 nu - 2553 > 0 \/ 100 nu - 2553 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [14600000000 beta4^2 nu + 533192000000 beta4^2 - 3651000000 beta4 nu^2 - 266669040000 beta4 nu - 5331920400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ]] \/ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 20000 beta4^2 nu + 912900 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 2553 < 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [14600000000 beta4^2 nu + 533192000000 beta4^2 - 3651000000 beta4 nu^2 - 266669040000 beta4 nu - 5331920400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [30000 beta4^2 nu + 730600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [10000 beta4^2 nu + 547700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 547700 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3832500000 beta4^2 nu^2 + 93410800000 beta4^2 nu + 1866683000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1095000000 beta4^2 nu^2 + 253171300000 beta4^2 nu + 13620657988000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 155145000 beta4^2 nu + 11993352700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 82135000 beta4^2 nu + 6662892600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ 50 nu - 3649 <= 0 /\ [166531250000000 beta4^2 nu^2 + 12163442500000000 beta4^2 nu + 243202237500000 beta4^2 - 249865312500000 beta4 nu^3 - 12175103793750000 beta4 nu^2 - 486704313375000 beta4 nu - 4866043672500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [456250000 beta4^2 nu + 99927875000 beta4^2 - 456375000 beta4 nu^2 - 133279755000 beta4 nu - 2665412550 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 16655862500000 beta4^2 nu^2 + 1459479929750000 beta4^2 nu + 29182936615000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 91272500 beta4 nu^2 + 2002025450 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 226581050000 beta4^2 nu + 3408429385500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 3998210100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 1460200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 3730811000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 2463750000 beta4^2 nu^2 + 226581050000 beta4^2 nu + 3408429385500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 3998210100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2920000000 beta4^2 nu^2 + 259905550000 beta4^2 nu + 3409095693000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 82135000 beta4^2 nu + 4664517600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [2497968750000000 beta4^2 nu^2 + 30491871875000000 beta4^2 nu + 608838250000000 beta4^2 - 916172812500000 beta4 nu^3 - 6135026306250000 beta4 nu^2 - 244301644875000 beta4 nu - 2439351757500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 733029500000 beta4^2 nu + 14602795170000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ [146000000 beta4 nu + 3999670000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2281250000 beta4^2 nu + 999233125000 beta4^2 - 456375000 beta4 nu^2 - 366487380000 beta4 nu - 7329565050 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 1095050 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [136875000000 beta4^2 nu^3 + 36645087500000 beta4^2 nu^2 + 1946550639250000 beta4^2 nu + 38916355845000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 < 0 \/ 54750000 beta4 nu + 10659095000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [45625000 beta4^2 nu + 3331537500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [3746953125000000 beta4^2 nu^2 + 121717690625000000 beta4^2 nu + 2432855031250000 beta4^2 - 1166038125000000 beta4 nu^3 - 24390186037500000 beta4 nu^2 - 974208195750000 beta4 nu - 9737417805000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[82125000 beta4 nu + 2666142500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [3193750000 beta4^2 nu^2 + 299884000000 beta4^2 nu + 4868708902500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 63875000 beta4 nu + 1333527500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2281250000 beta4^2 nu^2 + 166622500000 beta4^2 nu + 3331537500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000 beta4^2 nu + 3331537500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 912500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2281250000 beta4^2 nu^2 + 166622500000 beta4^2 nu + 3331537500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 912500 beta4 - 182550 nu - 3651 = 0 ]] /\ [9125000000 beta4^2 nu + 1498963750000 beta4^2 - 1825500000 beta4 nu^2 - 466488270000 beta4 nu - 9329035200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 1642700 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [12500000 beta4^2 nu^3 + 4107000000 beta4^2 nu^2 + 233308015000 beta4^2 nu + 4664517600 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 1277600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 226581050000 beta4^2 nu + 3408429385500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 3998210100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [5475000000 beta4^2 nu^2 + 533119000000 beta4^2 nu + 9736085190000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [12500000 beta4^2 nu^3 + 3650750000 beta4^2 nu^2 + 199983515000 beta4^2 nu + 3998210100 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 453063550000 beta4^2 nu + 13624655285500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [[730000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ [2500 beta4 nu + 1095050 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 19461509095000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [12500000 beta4^2 nu^3 + 5475750000 beta4^2 nu^2 + 533119015000 beta4^2 nu + 10660190100 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 5000 beta4 nu + 1460100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 999917600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [12500000 beta4^2 nu^3 + 1825750000 beta4^2 nu^2 + 50032390000 beta4^2 nu + 999917600 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 547700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 < 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [2007500000 beta4^2 nu^2 + 193256550000 beta4^2 nu + 3407763078000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 100395000 beta4^2 nu + 4664882700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [333062500000000 beta4^2 nu^2 + 6091713125000000 beta4^2 nu + 121701037500000 beta4^2 - 194339687500000 beta4 nu^3 - 2038345693750000 beta4 nu^2 - 81300620125000 beta4 nu - 812228842500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [4562500000 beta4^2 nu^2 + 466470000000 beta4^2 nu + 9734752575000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [456250000 beta4^2 nu + 133234125000 beta4^2 - 152125000 beta4 nu^2 - 77741960000 beta4 nu - 1554778350 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [91250000000 beta4^2 nu^3 + 23319850000000 beta4^2 nu^2 + 1216610809500000 beta4^2 nu + 24322888980000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 < 0 \/ 36500000 beta4 nu + 6661980000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [416328125000000 beta4^2 nu^2 + 12173434375000000 beta4^2 nu + 243302156250000 beta4^2 - 222102500000000 beta4 nu^3 - 4066696775000000 beta4 nu^2 - 162401348000000 beta4 nu - 1623125070000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [1825000000 beta4^2 nu^2 + 166604250000 beta4^2 nu + 2434687605000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [912500000 beta4^2 nu + 166549500000 beta4^2 - 304250000 beta4 nu^2 - 88853170000 beta4 nu - 1776941700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [6250000 beta4^2 nu^3 + 2281625000 beta4^2 nu^2 + 133316257500 beta4^2 nu + 2665412550 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 < 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 1095400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1095400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [5000 beta4^2 nu + 912600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 1825200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 1825200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 54770000 beta4^2 nu + 1095200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]]] \/ [1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3407096770500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2434021297500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 1825375000 beta4^2 nu^2 + 99991757500 beta4^2 nu + 1999105050 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 319802050000 beta4^2 nu + 13621990420500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 164270000 beta4^2 nu + 13325785200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ [2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 266504750000 beta4^2 nu + 9730754547500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 2737875000 beta4^2 nu^2 + 266559507500 beta4^2 nu + 5330095050 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 500000 beta4^2 nu^2 + 45645000 beta4^2 nu + 1000100200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 912875000 beta4^2 nu^2 + 25016195000 beta4^2 nu + 499958800 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3407096770500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 < 0 /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 532900000000 beta4^2 - 155471750000 beta4 nu - 3109435000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 304250000 beta4 nu^2 - 133273670000 beta4 nu - 2665351700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu + 399748000000 beta4^2 - 608500000 beta4 nu^2 - 133285840000 beta4 nu - 2665473400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3407096770500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [45625000000 beta4^2 nu^3 + 2737500000 beta4^2 nu^2 - 243135570250000 beta4^2 nu - 4862712135000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 4862712135000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2434021297500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 1825375000 beta4^2 nu^2 + 99991757500 beta4^2 nu + 1999105050 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu - 4860046905000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 150 nu - 3647 = 0 ]]]] \/ [1000000 beta4^2 nu^2 + 54790000 beta4^2 nu + 1095400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 1825200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 1277700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 100 nu - 2553 < 0 /\ [10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 54770000 beta4^2 nu + 1095200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 666125000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 532900000000 beta4^2 - 155471750000 beta4 nu - 3109435000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 365000 beta4 - 60850 nu - 1217 /= 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 304250000 beta4 nu^2 - 133273670000 beta4 nu - 2665351700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu + 399748000000 beta4^2 - 608500000 beta4 nu^2 - 133285840000 beta4 nu - 2665473400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ]] \/ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [3193750000 beta4^2 nu + 1632070125000 beta4^2 - 456375000 beta4 nu^2 - 466433505000 beta4 nu - 9328487550 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 1277550 beta4 - 182550 nu - 3651 = 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 9327210000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 73000000 beta4 nu + 9327210000 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [1865150000000 beta4^2 - 499730625000 beta4 nu - 9994612500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1460000 beta4 - 182550 nu - 3651 = 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [4015000 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 4015000 beta4 - 547650 nu - 10953 = 0 ]]] /\ [63875000 beta4^2 nu + 1277500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [699431250000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1277500 beta4 - 182550 nu - 3651 = 0 \/ 547500 beta4 - 60850 nu - 1217 = 0 ] /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2564581250000 beta4^2 - 599676750000 beta4 nu - 11993535000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2007500 beta4 - 182550 nu - 3651 = 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [547500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 547500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [63875000 beta4^2 nu + 1277500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4 - 182550 nu - 3651 = 0 ]] /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4 - 182550 nu - 3651 = 0 ]] /\ [6387500000 beta4^2 nu + 1632134000000 beta4^2 - 912750000 beta4 nu^2 - 466451760000 beta4 nu - 9328670100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1277600 beta4 - 182550 nu - 3651 = 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4^2 nu + 1277550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 1277550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000000 beta4^2 nu + 1632261750000 beta4^2 - 1825500000 beta4 nu^2 - 466488270000 beta4 nu - 9329035200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 1277700 beta4 - 182550 nu - 3651 = 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 1277600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1277600 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 100 nu - 2553 < 0 /\ [10000 beta4^2 nu + 1825200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1825200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 127790000 beta4^2 nu + 2555400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 20000 beta4 nu + 2555400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1000000 beta4^2 nu^2 + 54790000 beta4^2 nu + 1095400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1095400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 1095800 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 40000 beta4 nu + 1095800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [10000 beta4^2 nu + 1277700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 1277700 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 54770000 beta4^2 nu + 1095200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 1095400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 1606000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 365000 beta4 - 60850 nu - 1217 /= 0 /\ 50 nu - 3649 <= 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [1825000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [932575000000 beta4^2 - 222102500000 beta4 nu - 4442050000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [2555000 beta4 - 182550 nu - 3651 = 0 /\ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3650000000 beta4^2 nu + 399748000000 beta4^2 - 608500000 beta4 nu^2 - 133285840000 beta4 nu - 2665473400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [7300000000 beta4^2 nu + 399821000000 beta4^2 - 1217000000 beta4 nu^2 - 133310180000 beta4 nu - 2665716800 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [20000 beta4 nu + 1095400 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [3376250000 beta4^2 nu^2 + 293230050000 beta4^2 nu + 3409762000500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [[365000 beta4 - 60850 nu - 1217 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 60850 nu - 1217 = 0 \/ 50 nu - 3649 = 0 ] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu - 4860046905000 beta4^2 - 456375000 beta4 nu^3 - 22237632500 beta4 nu^2 + 809785167350 beta4 nu + 16204594749 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 \/ 150 nu - 3647 = 0 ]]] /\ [125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 4664335050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 1277550 beta4 - 182550 nu - 3651 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 24366852500000000 beta4^2 nu + 486804150000000 beta4^2 - 388679375000000 beta4 nu^3 - 4076691387500000 beta4 nu^2 - 162601240250000 beta4 nu - 1624457685000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [3193750000 beta4^2 nu^2 + 266577750000 beta4^2 nu + 2436686527500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 63875000 beta4 nu + 667402500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1665312500000000 beta4^2 nu^2 + 48693737500000000 beta4^2 nu + 973208625000000 beta4^2 - 444205000000000 beta4 nu^3 - 8133393550000000 beta4 nu^2 - 324802696000000 beta4 nu - 3246250140000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[91250000 beta4 nu + 2666325000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [3650000000 beta4^2 nu^2 + 333208500000 beta4^2 nu + 4869375210000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [45625000000 beta4^2 nu^3 + 2737500000 beta4^2 nu^2 - 243135570250000 beta4^2 nu - 4862712135000 beta4^2 - 7606250000 beta4 nu^4 - 608500000 beta4 nu^3 + 40533687995000 beta4 nu^2 + 1621348006600 beta4 nu + 16213481283 beta4 > 0 \/ 365000 beta4 - 60850 nu - 1217 /= 0 ] /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 4862712135000 beta4^2 - 152125000 beta4 nu^3 - 9127500 beta4 nu^2 + 810673942450 beta4 nu + 16213481283 beta4 > 0 \/ 365000 beta4 - 60850 nu - 1217 /= 0 ] /\ [1825000000 beta4^2 nu + 532936500000 beta4^2 - 304250000 beta4 nu^2 - 155483920000 beta4 nu - 3109556700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[5000 beta4 nu + 1460100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [6250000 beta4^2 nu^3 + 3650375000 beta4^2 nu^2 + 233289757500 beta4^2 nu + 4664335050 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 1277550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3650000000 beta4^2 nu + 666198000000 beta4^2 - 608500000 beta4 nu^2 - 177706340000 beta4 nu - 3553883400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1825200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [12500000 beta4^2 nu^3 + 4563250000 beta4^2 nu^2 + 266632515000 beta4^2 nu + 5330825100 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 1460100 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1022000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 511000 beta4 - 60850 nu - 1217 = 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3407096770500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3407096770500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 399821000000 beta4^2 nu + 9733419960000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [5000 nu^2 - 127550 nu - 2553 > 0 \/ 100 nu - 2553 = 0 ] /\ [1551250000 beta4^2 nu^2 + 46690800000 beta4^2 nu + 933195500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 3730811000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 2553 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] /\ [10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 2920400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 2920400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 1460800 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 3405764155500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [2463750000 beta4^2 nu^2 + 226581050000 beta4^2 nu + 3408429385500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 3998210100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [182500000000 beta4^2 nu^3 + 39978450000000 beta4^2 nu^2 + 1946683919000000 beta4^2 nu + 38917688460000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 799642000000 beta4^2 nu + 19466839920000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [146000000 beta4 nu + 5331920000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 1460200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 3730811000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 3405764155500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 < 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [91250000 beta4^2 nu + 1825000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 60850 nu - 1217 = 0 ]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 60850 nu - 1217 = 0 ]] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [532900000000 beta4^2 - 155471750000 beta4 nu - 3109435000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1460000 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 304250000 beta4 nu^2 - 133273670000 beta4 nu - 2665351700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 beta4^2 nu + 1095050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 1095050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3650000000 beta4^2 nu + 399748000000 beta4^2 - 608500000 beta4 nu^2 - 133285840000 beta4 nu - 2665473400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [91250000 beta4^2 nu + 7995325000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 91250000 beta4 nu + 7995325000 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [666125000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1825000 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [4015000 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 4015000 beta4 - 547650 nu - 10953 = 0 ]]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ] /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3407096770500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [45625000000 beta4^2 nu^3 + 2737500000 beta4^2 nu^2 - 243135570250000 beta4^2 nu - 4862712135000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 4862712135000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2434021297500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 1825375000 beta4^2 nu^2 + 99991757500 beta4^2 nu + 1999105050 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu - 4860046905000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 150 nu - 3647 = 0 ]]]] \/ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 < 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 54770000 beta4^2 nu + 1095200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 365400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 20000 beta4 nu + 365400 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 511000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1022000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 399821000000 beta4^2 nu + 9733419960000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3407096770500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 2553 <= 0 /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 1460800 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 2920400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 2920400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]] \/ [50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [1551250000 beta4^2 nu^2 + 46690800000 beta4^2 nu + 933195500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 3730811000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [5000 nu^2 - 127550 nu - 2553 > 0 \/ 100 nu - 2553 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 3405764155500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] \/ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 2553 < 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1065800000000 beta4^2 - 399784500000 beta4 nu - 7995690000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [7300000000 beta4^2 nu + 533046000000 beta4^2 - 1825500000 beta4 nu^2 - 266596020000 beta4 nu - 5331190200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 304250000 beta4 nu^2 - 133273670000 beta4 nu - 2665351700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [73000000 beta4^2 nu + 7994960000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 73000000 beta4 nu + 7994960000 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [532900000000 beta4^2 - 155471750000 beta4 nu - 3109435000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1460000 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [3650000 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 3650000 beta4 - 547650 nu - 10953 = 0 ]]] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [666125000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1825000 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 60850 nu - 1217 = 0 ]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 60850 nu - 1217 = 0 ]] /\ [3650000000 beta4^2 nu + 399748000000 beta4^2 - 608500000 beta4 nu^2 - 133285840000 beta4 nu - 2665473400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 2553 < 0 /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 109540000 beta4^2 nu + 2190400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 20000 beta4 nu + 2190400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 730800 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 40000 beta4 nu + 730800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ] /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [730000 beta4 - 60850 nu - 1217 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [14600000000 beta4^2 nu + 533192000000 beta4^2 - 3651000000 beta4 nu^2 - 266669040000 beta4 nu - 5331920400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 226581050000 beta4^2 nu + 3408429385500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [[730000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [5475000000 beta4^2 nu^2 + 266669000000 beta4^2 nu - 9720093810000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 \/ 150 nu - 3647 = 0 ]]] /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 3998210100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 5475000000 beta4^2 nu^2 - 486271140500000 beta4^2 nu - 9725424270000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu^2 + 73000000 beta4^2 nu - 9725424270000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [12500000 beta4^2 nu^3 + 3650750000 beta4^2 nu^2 + 199983515000 beta4^2 nu + 3998210100 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 3405764155500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [7300000000 beta4^2 nu + 533046000000 beta4^2 - 1825500000 beta4 nu^2 - 266596020000 beta4 nu - 5331190200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [1065800000000 beta4^2 - 399784500000 beta4 nu - 7995690000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]] \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [511000 beta4 - 182550 nu - 3651 = 0 /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1022000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]] \/ [949000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [38325000 beta4^2 nu + 933341500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [76650000 beta4^2 nu + 1866683000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [25550000 beta4^2 nu + 511000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4 - 60850 nu - 1217 = 0 ]] /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [2044000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2044000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4 - 60850 nu - 1217 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 833203800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1022000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [14600000000 beta4^2 nu + 533192000000 beta4^2 - 3651000000 beta4 nu^2 - 266669040000 beta4 nu - 5331920400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ]]] /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[730000 beta4 - 60850 nu - 1217 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]]]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [125000 beta4 nu^3 + 2288750 beta4 nu^2 - 83174225 beta4 nu - 1664399 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 833203800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu - 1215011270000 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 45725 nu - 1664399 < 0 ]]]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 3750 beta4 nu^2 + 228275 beta4 nu + 3335189 beta4 < 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [750000 beta4 nu^3 + 4607500 beta4 nu^2 - 332879100 beta4 nu - 6659419 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 < 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [250000 beta4 nu^3 + 13702500 beta4 nu^2 - 332514700 beta4 nu - 6655773 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [3193750000 beta4^2 nu^2 + 66740250000 beta4^2 nu + 1333527500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 1332797500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 27375000 beta4^2 nu + 1332797500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [27375000 beta4^2 nu + 2665047500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 2665047500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [63875000 beta4 nu + 1333527500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 438070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 1168070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 438070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 693570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 47457000 beta4^2 nu + 949070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 949070 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 21914000 beta4^2 nu + 438140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 /\ [3500 beta4^2 nu + 146070 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 3500 beta4 nu + 146070 beta4 - 60850 nu - 1217 = 0 ]]]] \/ [68437500000 beta4^2 nu^3 + 1669418750000 beta4^2 nu^2 - 364636742875000 beta4^2 nu - 8881743714577500 beta4^2 - 68456250000 beta4 nu^4 - 1671245250000 beta4 nu^3 + 364703245830000 beta4 nu^2 + 8891471801886900 beta4 nu + 177683541380397 beta4 > 0 /\ 9581250000 beta4^2 nu^2 + 433364500000 beta4^2 nu + 4871375957500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 27375000 beta4^2 nu + 666672500 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 < 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [525000 beta4^2 nu^2 + 34696000 beta4^2 nu + 533593710 beta4^2 - 9127500 beta4 nu^2 - 222467600 beta4 nu - 4445701 beta4 > 0 \/ 3500 beta4 nu + 146070 beta4 - 60850 nu - 1217 = 0 ] /\ [9375000 beta4^2 nu^3 + 1597437500 beta4^2 nu^2 + 83329511250 beta4^2 nu + 1217344076325 beta4^2 - 456375000 beta4 nu^3 - 44447882500 beta4 nu^2 - 812451492650 beta4 nu - 16231254351 beta4 > 0 \/ 1368750000 beta4^2 nu + 66639875000 beta4^2 - 1369125000 beta4 nu^2 - 100000890000 beta4 nu - 1999470150 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1250 beta4 nu + 91275 beta4 - 60850 nu - 1217 = 0 ] /\ [8554687500000 beta4^2 nu^4 + 958239062500000 beta4^2 nu^3 + 27410231625000000 beta4^2 nu^2 + 222956517464375000 beta4^2 nu + 4448173921181250 beta4^2 - 3422812500000 beta4 nu^5 - 333496031250000 beta4 nu^4 - 6106721928750000 beta4 nu^3 - 365603199075000 beta4 nu^2 - 7306730783250 beta4 nu - 48693763053 beta4 > 0 \/ 333062500000000 beta4^2 nu^2 + 6091713125000000 beta4^2 nu + 121701037500000 beta4^2 - 416442187500000 beta4 nu^3 - 6105042468750000 beta4 nu^2 - 243701968125000 beta4 nu - 2435353912500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 22812500 beta4 nu + 333518750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [22812500000 beta4^2 nu^3 + 4997306250000 beta4^2 nu^2 - 121367947625000 beta4^2 nu - 26625780295192500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 + 121301225610000 beta4 nu^2 + 26635503053502300 beta4 nu + 532661500590399 beta4 < 0 /\ 456250000 beta4^2 nu^2 + 166549500000 beta4^2 nu + 14591468307500 beta4^2 - 152125000 beta4 nu^3 - 33324502500 beta4 nu^2 - 1332797550 beta4 nu - 13327367 beta4 > 0 /\ 250000 beta4^2 nu^2 + 118635000 beta4^2 nu + 13990997600 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 85782000 beta4^2 nu + 10393265570 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 949070 beta4 - 182550 nu - 3651 = 0 ] /\ [3125000 beta4^2 nu^3 + 2053312500 beta4^2 nu^2 + 383104003750 beta4^2 nu + 18242833133775 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 > 0 \/ 456250000 beta4^2 nu + 133234125000 beta4^2 - 456375000 beta4 nu^2 - 166595130000 beta4 nu - 3331720050 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1250 beta4 nu + 456275 beta4 - 182550 nu - 3651 = 0 ] /\ [570312500000 beta4^2 nu^4 + 208209687500000 beta4^2 nu^3 + 21286858400000000 beta4^2 nu^2 + 666434997940125000 beta4^2 nu + 13320186881028750 beta4^2 - 380312500000 beta4 nu^5 - 111089281250000 beta4 nu^4 - 6088941558750000 beta4 nu^3 - 365069909675000 beta4 nu^2 - 7299621069250 beta4 nu - 48658216917 beta4 > 0 \/ 166531250000000 beta4^2 nu^2 + 18241833125000000 beta4^2 nu + 364770050000000 beta4^2 - 249865312500000 beta4 nu^3 - 18255159731250000 beta4 nu^2 - 729906550875000 beta4 nu - 7298066047500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 4562500 beta4 nu + 333153750 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3421875000000 beta4^2 nu^4 + 916195625000000 beta4^2 nu^3 + 30446916650000000 beta4^2 nu^2 - 1329950769534250000 beta4^2 nu - 26611186828327500 beta4^2 - 3422812500000 beta4 nu^5 - 916515093750000 beta4 nu^4 - 30473587203750000 beta4 nu^3 + 1329706034442675000 beta4 nu^2 + 53224780356606750 beta4 nu + 532369551288897 beta4 > 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [3500 beta4^2 nu + 1168070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 438070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 438070 beta4 - 182550 nu - 3651 = 0 /\ [17500000 beta4^2 nu^3 + 3012300000 beta4^2 nu^2 + 126684221000 beta4^2 nu + 2532479640 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 693640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3500 beta4^2 nu + 438070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 438070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 438070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [350000 beta4^2 nu^2 + 60239000 beta4^2 nu + 2532479640 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 3500 beta4 nu + 438070 beta4 - 182550 nu - 3651 = 0 ]] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ [437500 nu^3 + 20557500 nu^2 - 831834475 nu - 16644909 < 0 /\ 350 nu - 18243 = 0 ]] /\ [3500 beta4^2 nu + 693570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 85789000 beta4^2 nu + 4398140640 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 7000 beta4 nu + 1204640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 21914000 beta4^2 nu + 438140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 /\ [35000000 beta4^2 nu^3 + 4290850000 beta4^2 nu^2 + 126735342000 beta4^2 nu + 2532990780 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [14000 beta4 nu + 693780 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [2053125000 beta4^2 nu^2 + 141633687500 beta4^2 nu + 2434188102500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1140625000 beta4^2 nu^2 + 74984687500 beta4^2 nu + 1217177362500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 4562500 beta4^2 nu + 166622500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [228125000 beta4^2 nu^2 + 8335687500 beta4^2 nu + 166622500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 17344500 beta4^2 nu + 400021820 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 ] /\ [228125000 beta4^2 nu^2 + 24988812500 beta4^2 nu + 608338747500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu + 66630750000 beta4^2 - 912750000 beta4 nu^2 - 99982635000 beta4 nu - 1999287600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [3125000 beta4^2 nu^3 + 684562500 beta4^2 nu^2 + 45823472500 beta4^2 nu + 912674789400 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 2500 beta4 nu + 273800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [249796875000000 beta4^2 nu^2 + 6088382500000000 beta4^2 nu + 121667731250000 beta4^2 - 333153750000000 beta4 nu^3 - 6100045162500000 beta4 nu^2 - 243602022000000 beta4 nu - 2434687605000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [1140625000000 beta4^2 nu^4 + 145806093750000 beta4^2 nu^3 + 5327337425000000 beta4^2 nu^2 + 55678233019312500 beta4^2 nu + 1111434891682500 beta4^2 - 570468750000 beta4 nu^5 - 62523375000000 beta4 nu^4 - 1525013572500000 beta4 nu^3 - 91350803887500 beta4 nu^2 - 1826016160125 beta4 nu - 12170108313 beta4 > 0 \/ 18250000 beta4 nu + 333427500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[182500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[182500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [228125000 beta4^2 nu^2 + 24988812500 beta4^2 nu + 608338747500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [182500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [1368750000 beta4^2 nu^2 + 333117250000 beta4^2 nu + 19457511797500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 155145000 beta4^2 nu + 11993352700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 60232000 beta4^2 nu + 5063754570 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 4997306250000 beta4^2 nu^2 + 243335489875000 beta4^2 nu + 4864711057500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 /= 0 ] /\ [456250000 beta4^2 nu + 99927875000 beta4^2 - 456375000 beta4 nu^2 - 133279755000 beta4 nu - 2665412550 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [3125000 beta4^2 nu^3 + 1597062500 beta4^2 nu^2 + 233207628750 beta4^2 nu + 9730088513775 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ 1250 beta4 nu + 365025 beta4 - 182550 nu - 3651 = 0 ]]] /\ [166531250000000 beta4^2 nu^2 + 12163442500000000 beta4^2 nu + 243202237500000 beta4^2 - 249865312500000 beta4 nu^3 - 12175103793750000 beta4 nu^2 - 486704313375000 beta4 nu - 4866043672500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [1710937500000 beta4^2 nu^4 + 458097812500000 beta4^2 nu^3 + 36497825512500000 beta4^2 nu^2 + 888904394607875000 beta4^2 nu + 17763492426461250 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 - 12180105663750000 beta4 nu^3 - 730206480525000 beta4 nu^2 - 14600130852750 beta4 nu - 97320877101 beta4 > 0 \/ 13687500 beta4 nu + 666398750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [[182500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[182500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 + 99937000000 beta4^2 nu + 4864711057500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ [182500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1368750000 beta4^2 nu^2 + 166586000000 beta4^2 nu + 4866043672500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [68437500000 beta4^2 nu^3 + 8330668750000 beta4^2 nu^2 + 243468769625000 beta4^2 nu + 4866043672500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [125000 nu^3 - 9117500 nu^2 - 1332614850 nu - 26648649 > 0 \/ 50 nu - 3649 /= 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [68437500000 beta4^2 nu^3 + 11661293750000 beta4^2 nu^2 + 486737619625000 beta4^2 nu + 9730088422500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 27375000 beta4 nu + 2665047500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2281250000 beta4^2 nu^2 + 233235000000 beta4^2 nu + 4867376287500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1368750000 beta4^2 nu^2 + 166586000000 beta4^2 nu + 4866043672500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 34682000 beta4^2 nu + 1599393570 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 438070 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu + 66621625000 beta4^2 - 456375000 beta4 nu^2 - 99964380000 beta4 nu - 1999105050 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [1250 beta4^2 nu + 273775 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1250 beta4 nu + 273775 beta4 - 182550 nu - 3651 = 0 ]]] /\ [166531250000000 beta4^2 nu^2 + 6085051875000000 beta4^2 nu + 121634425000000 beta4^2 - 249865312500000 beta4 nu^3 - 6095047856250000 beta4 nu^2 - 243502075875000 beta4 nu - 2434021297500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [684375000 beta4^2 nu^2 + 16680500000 beta4^2 nu + 333336250 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 13687500 beta4 nu + 333336250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 182500 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 1332797500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 27375000 beta4^2 nu + 2665047500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 27375000 beta4^2 nu + 1332797500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [175000 beta4^2 nu^2 + 38332000 beta4^2 nu + 766570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4^2 nu + 255710 beta4^2 - 182550 beta4 nu - 3651 beta4 <= 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]]] \/ [175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 438070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 1168070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 438070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 693570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [175000 beta4^2 nu^2 + 47457000 beta4^2 nu + 949070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 21914000 beta4^2 nu + 438140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4^2 nu + 146070 beta4^2 - 60850 beta4 nu - 1217 beta4 <= 0 /\ 7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 ]]] \/ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 < 0 /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 1998740000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1998740000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu + 666855000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 < 0 /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 3333362500000 beta4^2 nu^2 + 60917186000000 beta4^2 nu + 1217010740000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 31032000 beta4^2 nu + 899889320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 187500 beta4 nu^3 + 11417500 beta4 nu^2 + 166987725 beta4 nu + 3335189 beta4 < 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 38332000 beta4^2 nu + 766570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [10500 beta4^2 nu + 255710 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [91250000000 beta4^2 nu^3 + 13327975000000 beta4^2 nu^2 + 486804259500000 beta4^2 nu + 9730754730000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 399821000000 beta4^2 nu + 9733419960000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [17500000 beta4^2 nu^3 + 2556050000 beta4^2 nu^2 + 93359721000 beta4^2 nu + 1866172140 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 76664000 beta4^2 nu + 3731833140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [35000000 beta4^2 nu^3 + 3834600000 beta4^2 nu^2 + 93410842000 beta4^2 nu + 1866683280 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 < 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 933086070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4^2 nu + 1095050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 730050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [7500 beta4^2 nu + 365150 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7500 beta4 nu + 365150 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [228125000 beta4^2 nu^2 + 8335687500 beta4^2 nu + 166622500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 4562500 beta4^2 nu + 166622500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [249796875000000 beta4^2 nu^2 + 6088382500000000 beta4^2 nu + 121667731250000 beta4^2 - 333153750000000 beta4 nu^3 - 6100045162500000 beta4 nu^2 - 243602022000000 beta4 nu - 2434687605000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [684375000 beta4^2 nu^2 + 41660187500 beta4^2 nu + 608671992500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [912500000 beta4^2 nu + 66630750000 beta4^2 - 912750000 beta4 nu^2 - 99982635000 beta4 nu - 1999287600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [11406250000 beta4^2 nu^3 + 1249668750000 beta4^2 nu^2 + 30441926187500 beta4^2 nu + 608338747500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [500000 beta4^2 nu^2 + 41082500 beta4^2 nu + 833477700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 912900 beta4 - 182550 nu - 3651 = 0 ] /\ [866875000 beta4^2 nu^2 + 54989987500 beta4^2 nu + 852074140500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [228125000 beta4^2 nu^2 + 8335687500 beta4^2 nu + 166622500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 4562500 beta4^2 nu + 166622500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [249796875000000 beta4^2 nu^2 + 6088382500000000 beta4^2 nu + 121667731250000 beta4^2 - 333153750000000 beta4 nu^3 - 6100045162500000 beta4 nu^2 - 243602022000000 beta4 nu - 2434687605000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [684375000 beta4^2 nu^2 + 41660187500 beta4^2 nu + 608671992500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [912500000 beta4^2 nu + 66630750000 beta4^2 - 912750000 beta4 nu^2 - 99982635000 beta4 nu - 1999287600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [11406250000 beta4^2 nu^3 + 1249668750000 beta4^2 nu^2 + 30441926187500 beta4^2 nu + 608338747500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [866875000 beta4^2 nu^2 + 54989987500 beta4^2 nu + 852074140500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 41082500 beta4^2 nu + 833477700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 912900 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 2553 <= 0 /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ [60000 beta4^2 nu + 1461200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [60000 beta4 nu + 1461200 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [20000 beta4^2 nu + 912900 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 912900 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 146080000 beta4^2 nu + 2920800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 40000 beta4 nu + 2920800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 1460800 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [14600000000 beta4^2 nu + 533192000000 beta4^2 - 3651000000 beta4 nu^2 - 266669040000 beta4 nu - 5331920400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ]] \/ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 20000 beta4^2 nu + 912900 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 2553 <= 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [14600000000 beta4^2 nu + 533192000000 beta4^2 - 3651000000 beta4 nu^2 - 266669040000 beta4 nu - 5331920400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] \/ [474500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [4562500000 beta4^2 nu + 832747500000 beta4^2 - 912750000 beta4 nu^2 - 333190260000 beta4 nu - 6663440100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [54750000 beta4^2 nu + 3331720000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 54750000 beta4 nu + 3331720000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ]]] /\ [1165718750000 beta4^2 - 399784500000 beta4 nu - 7995690000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1277500 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [1003750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1003750 beta4 - 182550 nu - 3651 = 0 ]]] /\ [45625000 beta4^2 nu + 912500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [2164906250000 beta4^2 - 599676750000 beta4 nu - 11993535000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2372500 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [547500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 547500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000 beta4^2 nu + 912500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 912500 beta4 - 182550 nu - 3651 = 0 ]] /\ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 912500 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000000 beta4^2 nu + 833021250000 beta4^2 - 3651000000 beta4 nu^2 - 333299790000 beta4 nu - 6664535400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 912900 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 912700 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 912700 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 2553 < 0 /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 109580000 beta4^2 nu + 2190800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 40000 beta4 nu + 2190800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ [60000 beta4^2 nu + 731200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 60000 beta4 nu + 731200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [20000 beta4^2 nu + 912900 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 20000 beta4 nu + 912900 beta4 - 182550 nu - 3651 = 0 ] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4^2 nu + 730800 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1496500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [2131600000000 beta4^2 - 666307500000 beta4 nu - 13326150000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [2920000 beta4 - 182550 nu - 3651 = 0 /\ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [21900000000 beta4^2 nu + 533338000000 beta4^2 - 5476500000 beta4 nu^2 - 266742060000 beta4 nu - 5332650600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ [15000 beta4^2 nu + 730300 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 15000 beta4 nu + 730300 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [[730000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu - 1215011270000 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 \/ 100 nu - 1823 = 0 ]]] /\ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 833203800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 ] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 1368750000 beta4^2 nu^2 - 30391925750000 beta4^2 nu - 607838880000 beta4^2 - 5704687500 beta4 nu^4 - 456375000 beta4 nu^3 + 7600056230625 beta4 nu^2 + 304002614325 beta4 nu + 3040027056 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [456250000 beta4^2 nu^2 + 18250000 beta4^2 nu - 607838880000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [12500000 beta4^2 nu^3 + 1825750000 beta4^2 nu^2 + 50032390000 beta4^2 nu + 999917600 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [50 nu - 3649 <= 0 /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 511420 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [21000 beta4 nu + 511420 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [7000 beta4^2 nu + 438140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1368750000 beta4^2 nu^2 + 333117250000 beta4^2 nu + 19457511797500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 155145000 beta4^2 nu + 11993352700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 60232000 beta4^2 nu + 5063754570 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ 50 nu - 3649 <= 0 /\ [166531250000000 beta4^2 nu^2 + 12163442500000000 beta4^2 nu + 243202237500000 beta4^2 - 249865312500000 beta4 nu^3 - 12175103793750000 beta4 nu^2 - 486704313375000 beta4 nu - 4866043672500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [456250000 beta4^2 nu + 99927875000 beta4^2 - 456375000 beta4 nu^2 - 133279755000 beta4 nu - 2665412550 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 16655862500000 beta4^2 nu^2 + 1459479929750000 beta4^2 nu + 29182936615000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 91272500 beta4 nu^2 + 2002025450 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 62057000 beta4^2 nu + 3598316070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 62057000 beta4^2 nu + 3598316070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3193750000 beta4^2 nu^2 + 299884000000 beta4^2 nu + 4868708902500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 175000 beta4^2 nu^2 + 71182000 beta4^2 nu + 4264623570 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [2497968750000000 beta4^2 nu^2 + 30491871875000000 beta4^2 nu + 608838250000000 beta4^2 - 916172812500000 beta4 nu^3 - 6135026306250000 beta4 nu^2 - 244301644875000 beta4 nu - 2439351757500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 733029500000 beta4^2 nu + 14602795170000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ [146000000 beta4 nu + 3999670000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2281250000 beta4^2 nu + 999233125000 beta4^2 - 456375000 beta4 nu^2 - 366487380000 beta4 nu - 7329565050 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 1095050 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [136875000000 beta4^2 nu^3 + 36645087500000 beta4^2 nu^2 + 1946550639250000 beta4^2 nu + 38916355845000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 < 0 \/ 54750000 beta4 nu + 10659095000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [45625000 beta4^2 nu + 3331537500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [3746953125000000 beta4^2 nu^2 + 121717690625000000 beta4^2 nu + 2432855031250000 beta4^2 - 1166038125000000 beta4 nu^3 - 24390186037500000 beta4 nu^2 - 974208195750000 beta4 nu - 9737417805000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [63875000 beta4 nu + 1333527500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [82125000 beta4 nu + 2666142500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2281250000 beta4^2 nu^2 + 166622500000 beta4^2 nu + 3331537500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000 beta4^2 nu + 3331537500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 912500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2281250000 beta4^2 nu^2 + 166622500000 beta4^2 nu + 3331537500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 912500 beta4 - 182550 nu - 3651 = 0 ]] /\ [9125000000 beta4^2 nu + 1498963750000 beta4^2 - 1825500000 beta4 nu^2 - 466488270000 beta4 nu - 9329035200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 1642700 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [12500000 beta4^2 nu^3 + 4107000000 beta4^2 nu^2 + 233308015000 beta4^2 nu + 4664517600 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 1277600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 175000 beta4^2 nu^2 + 62057000 beta4^2 nu + 3598316070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [5475000000 beta4^2 nu^2 + 533119000000 beta4^2 nu + 9736085190000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [12500000 beta4^2 nu^3 + 3650750000 beta4^2 nu^2 + 199983515000 beta4^2 nu + 3998210100 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 19461509095000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [[730000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ [2500 beta4 nu + 1095050 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [12500000 beta4^2 nu^3 + 5475750000 beta4^2 nu^2 + 533119015000 beta4^2 nu + 10660190100 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 5000 beta4 nu + 1460100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 175000 beta4^2 nu^2 + 31032000 beta4^2 nu + 899889320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [12500000 beta4^2 nu^3 + 1825750000 beta4^2 nu^2 + 50032390000 beta4^2 nu + 999917600 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5000 nu^2 - 127550 nu - 2553 > 0 \/ 100 nu - 2553 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2007500000 beta4^2 nu^2 + 213240300000 beta4^2 nu + 4866976503000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 94920000 beta4^2 nu + 4265098200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [226482500000000 beta4^2 nu^2 + 4871771800000000 beta4^2 nu + 97344843000000 beta4^2 - 161024312500000 beta4 nu^3 - 2036346771250000 beta4 nu^2 - 81260641675000 beta4 nu - 811962319500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [3741250000 beta4^2 nu^2 + 386502150000 beta4^2 nu + 8274339796500 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ [74825000 beta4 nu + 2266321500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [365000000 beta4^2 nu + 90600300000 beta4^2 - 152125000 beta4 nu^2 - 64415810000 beta4 nu - 1288255350 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [77562500000 beta4^2 nu^3 + 19322278750000 beta4^2 nu^2 + 997628860575000 beta4^2 nu + 19944848920500 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 < 0 \/ 31025000 beta4 nu + 5462845500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [7300000 beta4^2 nu + 533046000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [365000000 beta4^2 nu^2 + 26659600000 beta4^2 nu + 533046000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [7300000 beta4^2 nu + 533046000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 146000 beta4 - 60850 nu - 1217 = 0 ]] /\ [365000000 beta4^2 nu^2 + 26659600000 beta4^2 nu + 533046000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 146000 beta4 - 60850 nu - 1217 = 0 ]] /\ [511000000 beta4^2 nu + 101261220000 beta4^2 - 212975000 beta4 nu^2 - 68860294000 beta4 nu - 1377120690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [4375000 beta4^2 nu^3 + 1734012500 beta4^2 nu^2 + 103318730250 beta4^2 nu + 2065681035 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 565785 beta4 - 182550 nu - 3651 = 0 ]]] /\ [253127500000000 beta4^2 nu^2 + 6817922600000000 beta4^2 nu + 136257201000000 beta4^2 - 172129437500000 beta4 nu^3 - 2847687203750000 beta4 nu^2 - 113700932825000 beta4 nu - 1136320810500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [1414375000 beta4^2 nu^2 + 126620325000 beta4^2 nu + 1704481215750 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 28287500 beta4 nu + 466853250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [5000 nu^2 - 127550 nu - 2553 > 0 /\ 50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3193750000 beta4^2 nu^2 + 93385250000 beta4^2 nu + 1866427500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [63875000 beta4 nu + 1866427500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 3731066500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 3731066500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 93334150000 beta4^2 nu + 1865916500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 766780 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 766780 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [3500 beta4^2 nu + 693570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 63889000 beta4^2 nu + 1277640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 1277640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 766640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 186591650000 beta4^2 nu + 3407629816500 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1277762500 beta4^2 nu^2 + 69994230250 beta4^2 nu + 1399373535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 93295825000 beta4^2 nu + 1703814908250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ [2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1916512500 beta4^2 nu^2 + 186591655250 beta4^2 nu + 3731066535 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 186553325000 beta4^2 nu + 6811528183250 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 639012500 beta4^2 nu^2 + 17511336500 beta4^2 nu + 349971160 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 34997112500 beta4^2 nu + 426187030500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1715500 beta4 - 182550 nu - 3651 = 0 ] /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1149750000 beta4^2 nu + 323759745000 beta4^2 - 212975000 beta4 nu^2 - 119943869000 beta4 nu - 2398792190 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ] /\ [3285000000 beta4^2 nu + 323802450000 beta4^2 - 608500000 beta4 nu^2 - 119959690000 beta4 nu - 2398950400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ] /\ [407668500000 beta4^2 - 135482525000 beta4 nu - 2709650500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ] /\ [563541750000 beta4^2 - 164355850000 beta4 nu - 3287117000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 1715500 beta4 - 182550 nu - 3651 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 170194899175000 beta4^2 nu - 3403898494500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 3403898494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1277762500 beta4^2 nu^2 + 69994230250 beta4^2 nu + 1399373535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 93295825000 beta4^2 nu + 1703814908250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1916250000 beta4^2 nu^2 + 93334150000 beta4^2 nu - 3402032833500 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 150 nu - 3647 = 0 ]]]] \/ [1000000 beta4^2 nu^2 + 49315000 beta4^2 nu + 985900 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 1715700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 1168200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 < 0 /\ [10000 beta4^2 nu + 985700 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 49295000 beta4^2 nu + 985700 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 nu^2 - 127550 nu - 2553 > 0 \/ 100 nu - 2553 = 0 ]] \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 563541750000 beta4^2 - 164355850000 beta4 nu - 3287117000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 328500 beta4 - 60850 nu - 1217 /= 0 /\ 50 nu - 3649 <= 0 /\ [1149750000 beta4^2 nu + 323759745000 beta4^2 - 212975000 beta4 nu^2 - 119943869000 beta4 nu - 2398792190 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ] /\ [3285000000 beta4^2 nu + 323802450000 beta4^2 - 608500000 beta4 nu^2 - 119959690000 beta4 nu - 2398950400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ] /\ [407668500000 beta4^2 - 135482525000 beta4 nu - 2709650500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ]] \/ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2920000000 beta4^2 nu + 1364282400000 beta4^2 - 456375000 beta4 nu^2 - 426455055000 beta4 nu - 8528918550 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 1168050 beta4 - 182550 nu - 3651 = 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [67525000 beta4^2 nu + 8527750500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 67525000 beta4 nu + 8527750500 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [1577384000000 beta4^2 - 459752175000 beta4 nu - 9195043500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1350500 beta4 - 182550 nu - 3651 = 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [3686500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 3686500 beta4 - 547650 nu - 10953 = 0 ]]] /\ [58400000 beta4^2 nu + 1168000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [2216864000000 beta4^2 - 559698300000 beta4 nu - 11193966000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [511000 beta4 - 60850 nu - 1217 = 0 /\ [1898000 beta4 - 182550 nu - 3651 = 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [58400000 beta4^2 nu + 1168000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [67525000 beta4^2 nu + 1350500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1168000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1168000 beta4 - 182550 nu - 3651 = 0 ]] /\ [4088000000 beta4^2 nu + 1364305760000 beta4^2 - 638925000 beta4 nu^2 - 426462357000 beta4 nu - 8528991570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 1168070 beta4 - 182550 nu - 3651 = 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [1750 beta4^2 nu + 1168035 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1750 beta4 nu + 1168035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [11680000000 beta4^2 nu + 1364457600000 beta4^2 - 1825500000 beta4 nu^2 - 426509820000 beta4 nu - 8529466200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 1168200 beta4 - 182550 nu - 3651 = 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 1168100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1168100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [554216000000 beta4^2 - 157692775000 beta4 nu - 3153855500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1168000 beta4 - 182550 nu - 3651 = 0 \/ 474500 beta4 - 60850 nu - 1217 = 0 ] /\ [1295750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1295750 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [10000 beta4^2 nu + 985700 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 < 0 /\ [10000 beta4^2 nu + 1715700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 122315000 beta4^2 nu + 2445900 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 20000 beta4 nu + 2445900 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1000000 beta4^2 nu^2 + 49315000 beta4^2 nu + 985900 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 985900 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 986300 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 40000 beta4 nu + 986300 beta4 - 182550 nu - 3651 = 0 ]]] /\ [10000 beta4^2 nu + 1168200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 1168200 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 49295000 beta4^2 nu + 985700 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 985900 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 nu^2 - 127550 nu - 2553 > 0 \/ 100 nu - 2553 = 0 ]] \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 328500 beta4 - 60850 nu - 1217 /= 0 /\ 50 nu - 3649 <= 0 /\ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1350500 beta4 - 182550 nu - 3651 = 0 ] /\ [803346750000 beta4^2 - 208776350000 beta4 nu - 4175527000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [2445500 beta4 - 182550 nu - 3651 = 0 /\ 1715500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2299500000 beta4^2 nu + 323782740000 beta4^2 - 425950000 beta4 nu^2 - 119952388000 beta4 nu - 2398877380 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [7000 beta4 nu + 985640 beta4 - 182550 nu - 3651 = 0 /\ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ]]] /\ [6570000000 beta4^2 nu + 323868150000 beta4^2 - 1217000000 beta4 nu^2 - 119984030000 beta4 nu - 2399193800 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [20000 beta4 nu + 985900 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 985700 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ]]] /\ [491600250000 beta4^2 - 151029700000 beta4 nu - 3020594000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [1496500 beta4 - 182550 nu - 3651 = 0 /\ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [3376250000 beta4^2 nu^2 + 313213800000 beta4^2 nu + 4868975425500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [[328500 beta4 - 60850 nu - 1217 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[328500 beta4 - 60850 nu - 1217 = 0 \/ 50 nu - 3649 = 0 ] /\ [2463750000 beta4^2 nu^2 + 120001050000 beta4^2 nu - 4374042214500 beta4^2 - 456375000 beta4 nu^3 - 22237632500 beta4 nu^2 + 809785167350 beta4 nu + 16204594749 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 \/ 150 nu - 3647 = 0 ]]] /\ [125000 beta4^2 nu^2 + 67530000 beta4^2 nu + 4264550550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 1168050 beta4 - 182550 nu - 3651 = 0 ] /\ [1408854375000000 beta4^2 nu^2 + 43820766675000000 beta4^2 nu + 875851791750000 beta4^2 - 410889625000000 beta4 nu^3 - 8131394627500000 beta4 nu^2 - 324762717550000 beta4 nu - 3245983617000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [41062500000 beta4^2 nu^3 + 2463750000 beta4^2 nu^2 - 218822013225000 beta4^2 nu - 4376440921500 beta4^2 - 7606250000 beta4 nu^4 - 608500000 beta4 nu^3 + 40533687995000 beta4 nu^2 + 1621348006600 beta4 nu + 16213481283 beta4 > 0 \/ 328500 beta4 - 60850 nu - 1217 /= 0 ] /\ [821250000 beta4^2 nu^2 + 32850000 beta4^2 nu - 4376440921500 beta4^2 - 152125000 beta4 nu^3 - 9127500 beta4 nu^2 + 810673942450 beta4 nu + 16213481283 beta4 > 0 \/ 328500 beta4 - 60850 nu - 1217 /= 0 ] /\ [1149750000 beta4^2 nu + 407691495000 beta4^2 - 212975000 beta4 nu^2 - 135491044000 beta4 nu - 2709735690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [4375000 beta4^2 nu^3 + 3102762500 beta4^2 nu^2 + 203292230250 beta4^2 nu + 4064603535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 1113285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3285000000 beta4^2 nu + 563607450000 beta4^2 - 608500000 beta4 nu^2 - 164380190000 beta4 nu - 3287360400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [12500000 beta4^2 nu^3 + 4289500000 beta4^2 nu^2 + 246637815000 beta4^2 nu + 4931040600 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 1350600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1019171250000000 beta4^2 nu^2 + 15358311225000000 beta4^2 nu + 306758556000000 beta4^2 - 338706312500000 beta4 nu^3 - 2857681816250000 beta4 nu^2 - 113900825075000 beta4 nu - 1137653425500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2783125000 beta4^2 nu^2 + 226593825000 beta4^2 nu + 1706480138250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 55662500 beta4 nu + 467400750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [63875000000 beta4^2 nu^3 + 13992457500000 beta4^2 nu^2 + 681339371650000 beta4^2 nu + 13621190961000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2555000000 beta4^2 nu^2 + 279874700000 beta4^2 nu + 6813393972000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] /\ [10000 beta4^2 nu + 985700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 2920400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 2920400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 1460800 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 62057000 beta4^2 nu + 3598316070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [182500000000 beta4^2 nu^3 + 39978450000000 beta4^2 nu^2 + 1946683919000000 beta4^2 nu + 38917688460000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 799642000000 beta4^2 nu + 19466839920000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [146000000 beta4 nu + 5331920000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 933086070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [85775000 beta4^2 nu + 1715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1149750000 beta4^2 nu + 323759745000 beta4^2 - 212975000 beta4 nu^2 - 119943869000 beta4 nu - 2398792190 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1750 beta4^2 nu + 985535 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1750 beta4 nu + 985535 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3285000000 beta4^2 nu + 323802450000 beta4^2 - 608500000 beta4 nu^2 - 119959690000 beta4 nu - 2398950400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [85775000 beta4^2 nu + 7195865500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 85775000 beta4 nu + 7195865500 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [407668500000 beta4^2 - 135482525000 beta4 nu - 2709650500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1241000 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1113250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1113250 beta4 - 182550 nu - 3651 = 0 ]]] /\ [563541750000 beta4^2 - 164355850000 beta4 nu - 3287117000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1715500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [3686500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 3686500 beta4 - 547650 nu - 10953 = 0 ]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1715500 beta4 - 182550 nu - 3651 = 0 ] /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]]] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 170194899175000 beta4^2 nu - 3403898494500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 3403898494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1277762500 beta4^2 nu^2 + 69994230250 beta4^2 nu + 1399373535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 93295825000 beta4^2 nu + 1703814908250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1916250000 beta4^2 nu^2 + 93334150000 beta4^2 nu - 3402032833500 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 150 nu - 3647 = 0 ]]]] \/ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2555000000 beta4^2 nu^2 + 279874700000 beta4^2 nu + 6813393972000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [63875000000 beta4^2 nu^3 + 13992457500000 beta4^2 nu^2 + 681339371650000 beta4^2 nu + 13621190961000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 1460800 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [10000 beta4^2 nu + 985700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 2920400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 2920400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]] \/ [50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] \/ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 985700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 < 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1065800000000 beta4^2 - 399784500000 beta4 nu - 7995690000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [7300000000 beta4^2 nu + 533046000000 beta4^2 - 1825500000 beta4 nu^2 - 266596020000 beta4 nu - 5331190200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1149750000 beta4^2 nu + 323759745000 beta4^2 - 212975000 beta4 nu^2 - 119943869000 beta4 nu - 2398792190 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [62050000 beta4^2 nu + 7195391000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 62050000 beta4 nu + 7195391000 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [407668500000 beta4^2 - 135482525000 beta4 nu - 2709650500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1241000 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [3212000 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 3212000 beta4 - 547650 nu - 10953 = 0 ]]] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [563541750000 beta4^2 - 164355850000 beta4 nu - 3287117000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [1350500 beta4 - 182550 nu - 3651 = 0 /\ [1715500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [62050000 beta4^2 nu + 1241000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [3285000000 beta4^2 nu + 323802450000 beta4^2 - 608500000 beta4 nu^2 - 119959690000 beta4 nu - 2398950400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [5000 beta4^2 nu + 985600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 < 0 /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 109540000 beta4^2 nu + 2190400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 20000 beta4 nu + 2190400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 730800 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 40000 beta4 nu + 730800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [10000 beta4^2 nu + 985700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ] /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 730000 beta4 - 60850 nu - 1217 = 0 ]] /\ [14600000000 beta4^2 nu + 533192000000 beta4^2 - 3651000000 beta4 nu^2 - 266669040000 beta4 nu - 5331920400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [[730000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [5475000000 beta4^2 nu^2 + 266669000000 beta4^2 nu - 9720093810000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 \/ 150 nu - 3647 = 0 ]]] /\ [175000 beta4^2 nu^2 + 62057000 beta4^2 nu + 3598316070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 5475000000 beta4^2 nu^2 - 486271140500000 beta4^2 nu - 9725424270000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu^2 + 73000000 beta4^2 nu - 9725424270000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [12500000 beta4^2 nu^3 + 3650750000 beta4^2 nu^2 + 199983515000 beta4^2 nu + 3998210100 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [7300000000 beta4^2 nu + 533046000000 beta4^2 - 1825500000 beta4 nu^2 - 266596020000 beta4 nu - 5331190200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [1065800000000 beta4^2 - 399784500000 beta4 nu - 7995690000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]] \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [7000 beta4^2 nu + 438140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 511420 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [21000 beta4 nu + 511420 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 350 nu - 18243 < 0 /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 12803000 beta4^2 nu + 255780 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 438140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 5329365000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4^2 nu + 2665595000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2665047500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 766640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 12803000 beta4^2 nu + 255780 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [175000 beta4^2 nu^2 + 31032000 beta4^2 nu + 899889320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 3750 beta4 nu^2 + 228275 beta4 nu + 3335189 beta4 < 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 < 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [91250000000 beta4^2 nu^3 + 13327975000000 beta4^2 nu^2 + 486804259500000 beta4^2 nu + 9730754730000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 399821000000 beta4^2 nu + 9733419960000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [17500000 beta4^2 nu^3 + 2556050000 beta4^2 nu^2 + 93359721000 beta4^2 nu + 1866172140 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 76664000 beta4^2 nu + 3731833140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [35000000 beta4^2 nu^3 + 3834600000 beta4^2 nu^2 + 93410842000 beta4^2 nu + 1866683280 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 < 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 933086070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 5329365000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 5329365000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 2665595000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [91250000000 beta4^2 nu^3 + 26650475000000 beta4^2 nu^2 + 1946150909500000 beta4^2 nu + 38912358730000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [91250000000 beta4^2 nu^3 + 33311725000000 beta4^2 nu^2 + 2918959859500000 beta4^2 nu + 58365873230000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 799496000000 beta4^2 nu + 38917688460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 19461509095000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4 nu^3 + 45632500 beta4 nu^2 + 3998575150 beta4 nu + 79953251 beta4 < 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 350 nu - 18243 <= 0 /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 12803000 beta4^2 nu + 255780 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 <= 0 /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 2664682500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4^2 nu + 1332797500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [2281250000 beta4^2 nu^2 + 33397500000 beta4^2 nu + 667037500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [456250000 beta4^2 nu^2 + 99937000000 beta4^2 nu + 1998557500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu + 666855000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 1332797500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5000 nu^2 - 91050 nu - 1823 > 0 \/ 100 nu - 1823 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2281250000 beta4^2 nu^2 + 33397500000 beta4^2 nu + 667037500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 45625000 beta4 nu + 667037500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 350 nu - 18243 <= 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 766640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 12803000 beta4^2 nu + 255780 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [175000 beta4^2 nu^2 + 31032000 beta4^2 nu + 899889320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 3750 beta4 nu^2 + 228275 beta4 nu + 3335189 beta4 < 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 < 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 <= 0 /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 2664682500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 2664682500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [27375000 beta4^2 nu + 1332797500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2281250000 beta4^2 nu^2 + 33397500000 beta4^2 nu + 667037500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [456250000 beta4^2 nu^2 + 99937000000 beta4^2 nu + 1998557500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2281250000 beta4^2 nu^2 + 33397500000 beta4^2 nu + 667037500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 6663987500000 beta4^2 nu^2 + 243402129750000 beta4^2 nu + 4865377365000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 + 486670979750000 beta4^2 nu + 9729422115000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 199910500000 beta4^2 nu + 4866709980000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [17500000 beta4^2 nu^3 + 2556050000 beta4^2 nu^2 + 93359721000 beta4^2 nu + 1866172140 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 76664000 beta4^2 nu + 3731833140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [35000000 beta4^2 nu^3 + 3834600000 beta4^2 nu^2 + 93410842000 beta4^2 nu + 1866683280 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 < 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 2432688682500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 933086070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 666234500000 beta4^2 nu + 38915023595000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 33311725000000 beta4^2 nu^2 + 2918959859500000 beta4^2 nu + 58365873230000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 799496000000 beta4^2 nu + 38917688460000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 729900 nu - 14599 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 5330095000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 7994230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [91250000000 beta4^2 nu^3 + 26650475000000 beta4^2 nu^2 + 1946150909500000 beta4^2 nu + 38912358730000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [91250000000 beta4^2 nu^3 + 33311725000000 beta4^2 nu^2 + 2918959859500000 beta4^2 nu + 58365873230000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 799496000000 beta4^2 nu + 38917688460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 19461509095000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2131600000000 beta4^2 - 666307500000 beta4 nu - 13326150000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2920000 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 291816040000000000 beta4^2 nu + 5835787900000000 beta4^2 - 666307500000000 beta4 nu^3 - 73000649700000000 beta4 nu^2 - 2919226419000000 beta4 nu - 29189598960000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 999735075 beta4 nu - 9996438 beta4 < 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 9992604850 beta4 nu - 199844799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2920000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 19461509095000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 - 266377000000 beta4^2 nu - 77808728270000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 106587299 > 0 ]]]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 27367500 beta4 nu^2 - 2665594850 beta4 nu - 53300949 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 912600 beta4 nu + 79953251 beta4 < 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 7993864850 beta4 nu - 159873649 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [7000 beta4^2 nu + 438140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [1050000 beta4^2 nu^2 + 25592000 beta4^2 nu + 511420 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [21000 beta4 nu + 511420 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 1022280 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 >= 0 /\ 175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 175000 beta4^2 nu^2 + 62057000 beta4^2 nu + 3598316070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 175000 beta4^2 nu^2 + 62057000 beta4^2 nu + 3598316070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3193750000 beta4^2 nu^2 + 299884000000 beta4^2 nu + 4868708902500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 175000 beta4^2 nu^2 + 71182000 beta4^2 nu + 4264623570 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2497968750000000 beta4^2 nu^2 + 30491871875000000 beta4^2 nu + 608838250000000 beta4^2 - 916172812500000 beta4 nu^3 - 6135026306250000 beta4 nu^2 - 244301644875000 beta4 nu - 2439351757500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [365000000000 beta4^2 nu^3 + 36658775000000 beta4^2 nu^2 + 730872788000000 beta4^2 nu + 14602795170000 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 \/ [146000000 beta4 nu + 3999670000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2281250000 beta4^2 nu + 999233125000 beta4^2 - 456375000 beta4 nu^2 - 366487380000 beta4 nu - 7329565050 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 1095050 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 732847000000 beta4^2 nu + 38916355845000 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 54750000 beta4 nu + 10659095000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [3746953125000000 beta4^2 nu^2 + 121717690625000000 beta4^2 nu + 2432855031250000 beta4^2 - 1166038125000000 beta4 nu^3 - 24390186037500000 beta4 nu^2 - 974208195750000 beta4 nu - 9737417805000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[82125000 beta4 nu + 2666142500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [159687500000 beta4^2 nu^3 + 14997393750000 beta4^2 nu^2 + 243735329125000 beta4^2 nu + 4868708902500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 63875000 beta4 nu + 1333527500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2281250000 beta4^2 nu^2 + 166622500000 beta4^2 nu + 3331537500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000000 beta4^2 nu + 1498963750000 beta4^2 - 1825500000 beta4 nu^2 - 466488270000 beta4 nu - 9329035200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 1642700 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 82135000 beta4^2 nu + 4664517600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 1277600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [45625000 beta4^2 nu + 3331537500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000 beta4^2 nu + 3331537500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 912500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2281250000 beta4^2 nu^2 + 166622500000 beta4^2 nu + 3331537500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [912500 beta4 - 182550 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 19461509095000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4 - 182550 nu - 3651 = 0 \/ 2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 1095050 beta4 - 182550 nu - 3651 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [136875000000 beta4^2 nu^3 + 26653212500000 beta4^2 nu^2 + 973608464250000 beta4^2 nu + 19461509095000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 5000 beta4 nu + 1460100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [730000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 175000 beta4^2 nu^2 + 31032000 beta4^2 nu + 899889320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [[730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 5001412500000 beta4^2 nu^2 + 60983853250000 beta4^2 nu + 1217677230000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 \/ 73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 999917600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [730000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 >= 0 /\ 175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2281250000 beta4^2 nu^2 + 266541250000 beta4^2 nu + 5329912500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4^2 nu + 7994230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 3649300 nu - 72993 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 194561790000000000 beta4^2 nu + 3890702900000000 beta4^2 - 666307500000000 beta4 nu^3 - 48680425950000000 beta4 nu^2 - 1946417469000000 beta4 nu - 19461509460000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2281250000 beta4^2 nu^2 + 266541250000 beta4^2 nu + 5329912500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4^2 nu + 7994230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 3649300 nu - 72993 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 194561790000000000 beta4^2 nu + 3890702900000000 beta4^2 - 666307500000000 beta4 nu^3 - 48680425950000000 beta4 nu^2 - 1946417469000000 beta4 nu - 19461509460000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 175000 beta4^2 nu^2 + 43807000 beta4^2 nu + 2265701070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3193750000 beta4^2 nu^2 + 366496500000 beta4^2 nu + 9732753652500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 175000 beta4^2 nu^2 + 52932000 beta4^2 nu + 2932008570 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [333062500000000 beta4^2 nu^2 + 6091713125000000 beta4^2 nu + 121701037500000 beta4^2 - 194339687500000 beta4 nu^3 - 2038345693750000 beta4 nu^2 - 81300620125000 beta4 nu - 812228842500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [228125000000 beta4^2 nu^3 + 23328062500000 beta4^2 nu^2 + 487204098750000 beta4^2 nu + 9734752575000 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [456250000 beta4^2 nu + 133234125000 beta4^2 - 152125000 beta4 nu^2 - 77741960000 beta4 nu - 1554778350 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [1825000000 beta4^2 nu^2 + 466360500000 beta4^2 nu + 24322888980000 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 36500000 beta4 nu + 6661980000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [912500000 beta4^2 nu + 166549500000 beta4^2 - 304250000 beta4 nu^2 - 88853170000 beta4 nu - 1776941700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [125000 beta4^2 nu^2 + 45630000 beta4^2 nu + 2665412550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [182500 beta4 - 60850 nu - 1217 = 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [416328125000000 beta4^2 nu^2 + 12173434375000000 beta4^2 nu + 243302156250000 beta4^2 - 222102500000000 beta4 nu^3 - 4066696775000000 beta4 nu^2 - 162401348000000 beta4 nu - 1623125070000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [91250000000 beta4^2 nu^3 + 8332037500000 beta4^2 nu^2 + 121900984500000 beta4^2 nu + 2434687605000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [91250000 beta4^2 nu + 2666325000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 5330095000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 364900 nu - 7299 < 0 \/ 50 nu - 3649 /= 0 ] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 666234500000 beta4^2 nu + 38915023595000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [365000 beta4 - 182550 nu - 3651 = 0 \/ 2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [68437500000 beta4^2 nu^3 + 13326606250000 beta4^2 nu^2 + 486804232125000 beta4^2 nu + 9730754547500 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 2500706250000 beta4^2 nu^2 + 30491926625000 beta4^2 nu + 608838615000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 175000 beta4^2 nu^2 + 43807000 beta4^2 nu + 2265701070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ] /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 532900000000 beta4^2 - 155471750000 beta4 nu - 3109435000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 365000 beta4 - 60850 nu - 1217 /= 0 /\ [666125000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 333153750000000 beta4 nu^3 - 4073359850000000 beta4 nu^2 - 162534609500000 beta4 nu - 1624013480000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 48667092500000000 beta4^2 nu + 972942175000000 beta4^2 - 333153750000000 beta4 nu^3 - 8126730475000000 beta4 nu^2 - 324669434500000 beta4 nu - 3245361730000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 175000 beta4^2 nu^2 + 43807000 beta4^2 nu + 2265701070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [45625000000 beta4^2 nu^3 + 2737500000 beta4^2 nu^2 - 243135570250000 beta4^2 nu - 4862712135000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 4862712135000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 1999105050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 - 133188500000 beta4^2 nu - 14590801635000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 7298731807350 beta4 nu + 145947991149 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 10949 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [68437500000 beta4^2 nu^3 + 6665356250000 beta4^2 nu^2 + 121834344625000 beta4^2 nu + 2434021297500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 5329365000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 5329365000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 2665595000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ] /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [4562500000 beta4^2 nu^2 + 133407500000 beta4^2 nu + 2666325000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 3193750000 beta4^2 nu^2 + 133352750000 beta4^2 nu + 2665777500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 54750000 beta4^2 nu + 5330095000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 3649300 nu - 72993 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [54750000 beta4^2 nu + 2665595000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 666125000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 532900000000 beta4^2 - 155471750000 beta4 nu - 3109435000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 365000 beta4 - 60850 nu - 1217 /= 0 /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 333153750000000 beta4 nu^3 - 4073359850000000 beta4 nu^2 - 162534609500000 beta4 nu - 1624013480000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 48667092500000000 beta4^2 nu + 972942175000000 beta4^2 - 333153750000000 beta4 nu^3 - 8126730475000000 beta4 nu^2 - 324669434500000 beta4 nu - 3245361730000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [4080015625000000 beta4^2 nu^2 + 42711935000000000 beta4^2 nu + 852606693750000 beta4^2 - 1166038125000000 beta4 nu^3 - 6150018225000000 beta4 nu^2 - 244601483250000 beta4 nu - 2441350680000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[63875000 beta4 nu + 667402500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [1596875000 beta4^2 nu^2 + 66676375000 beta4^2 nu + 1332888750 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [31937500 beta4 nu + 1332888750 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [1865150000000 beta4^2 - 499730625000 beta4 nu - 9994612500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1460000 beta4 - 182550 nu - 3651 = 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [4015000 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 4015000 beta4 - 547650 nu - 10953 = 0 ]]] /\ [63875000 beta4^2 nu + 1277500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [699431250000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1277500 beta4 - 182550 nu - 3651 = 0 \/ 547500 beta4 - 60850 nu - 1217 = 0 ] /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2564581250000 beta4^2 - 599676750000 beta4 nu - 11993535000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2007500 beta4 - 182550 nu - 3651 = 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [547500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 547500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4 - 182550 nu - 3651 = 0 ]] /\ [63875000 beta4^2 nu + 1277500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4 - 182550 nu - 3651 = 0 ]] /\ [4080015625000000 beta4^2 nu^2 + 85260669375000000 beta4^2 nu + 1703581381250000 beta4^2 - 1166038125000000 beta4 nu^3 - 12230074162500000 beta4 nu^2 - 487803720750000 beta4 nu - 4873373055000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[63875000 beta4 nu + 1333527500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [3193750000 beta4^2 nu^2 + 33434000000 beta4^2 nu + 667402500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 63875000 beta4 nu + 667402500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [4080015625000000 beta4^2 nu^2 + 170358138125000000 beta4^2 nu + 3405530756250000 beta4^2 - 1166038125000000 beta4 nu^3 - 24390186037500000 beta4 nu^2 - 974208195750000 beta4 nu - 9737417805000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[63875000 beta4 nu + 2665777500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [3193750000 beta4^2 nu^2 + 66740250000 beta4^2 nu + 1333527500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 63875000 beta4 nu + 1333527500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 3649300 nu - 72993 > 0 /\ [4562500000 beta4^2 nu^2 + 133407500000 beta4^2 nu + 2666325000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [127750000 beta4^2 nu + 5331555000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [127750000 beta4 nu + 5331555000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [54750000 beta4^2 nu + 5330095000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 10659095000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 10659095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [3193750000 beta4^2 nu^2 + 133352750000 beta4^2 nu + 2665777500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 63875000 beta4 nu + 2665777500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 7299 < 0 \/ [2500 nu^2 - 729900 nu - 14599 < 0 /\ 50 nu - 7299 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [54750000 beta4^2 nu + 2665595000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 5330095000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 1606000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 365000 beta4 - 60850 nu - 1217 /= 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [1825000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [932575000000 beta4^2 - 222102500000 beta4 nu - 4442050000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [2555000 beta4 - 182550 nu - 3651 = 0 /\ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 48667092500000000 beta4^2 nu + 972942175000000 beta4^2 - 333153750000000 beta4 nu^3 - 8126730475000000 beta4 nu^2 - 324669434500000 beta4 nu - 3245361730000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 97294217500000000 beta4^2 nu + 1945484675000000 beta4^2 - 333153750000000 beta4 nu^3 - 16233471725000000 beta4 nu^2 - 648939084500000 beta4 nu - 6488058230000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 /\ 175000 beta4^2 nu^2 + 80307000 beta4^2 nu + 4930931070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[365000 beta4 - 60850 nu - 1217 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[365000 beta4 - 60850 nu - 1217 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 - 133188500000 beta4^2 nu - 14590801635000 beta4^2 - 152125000 beta4 nu^3 + 22201122500 beta4 nu^2 + 2432910602450 beta4 nu + 48649330383 beta4 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 \/ 50 nu - 10949 = 0 ]]] /\ [3193750000 beta4^2 nu^2 + 266577750000 beta4^2 nu + 2436686527500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 63875000 beta4 nu + 667402500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 532936500000 beta4^2 - 304250000 beta4 nu^2 - 155483920000 beta4 nu - 3109556700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[5000 beta4 nu + 1460100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 4664335050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 1277550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3650000000 beta4^2 nu + 666198000000 beta4^2 - 608500000 beta4 nu^2 - 177706340000 beta4 nu - 3553883400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1825200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [250000 beta4^2 nu^2 + 91260000 beta4^2 nu + 5330825100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 1460100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 4862712135000 beta4^2 - 152125000 beta4 nu^3 - 9127500 beta4 nu^2 + 810673942450 beta4 nu + 16213481283 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 /= 0 ] /\ [45625000000 beta4^2 nu^3 + 2737500000 beta4^2 nu^2 - 243135570250000 beta4^2 nu - 4862712135000 beta4^2 - 7606250000 beta4 nu^4 - 608500000 beta4 nu^3 + 40533687995000 beta4 nu^2 + 1621348006600 beta4 nu + 16213481283 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 /= 0 ] /\ [1332250000000000 beta4^2 nu^2 + 24366852500000000 beta4^2 nu + 486804150000000 beta4^2 - 388679375000000 beta4 nu^3 - 4076691387500000 beta4 nu^2 - 162601240250000 beta4 nu - 1624457685000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [159687500000 beta4^2 nu^3 + 13332081250000 beta4^2 nu^2 + 122100904125000 beta4^2 nu + 2436686527500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 63875000 beta4 nu + 667402500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1665312500000000 beta4^2 nu^2 + 48693737500000000 beta4^2 nu + 973208625000000 beta4^2 - 444205000000000 beta4 nu^3 - 8133393550000000 beta4 nu^2 - 324802696000000 beta4 nu - 3246250140000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[91250000 beta4 nu + 2666325000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [182500000000 beta4^2 nu^3 + 16664075000000 beta4^2 nu^2 + 243801969000000 beta4^2 nu + 4869375210000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 175000 beta4^2 nu^2 + 43807000 beta4^2 nu + 2265701070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3500 beta4^2 nu + 620570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1022140 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 3649300 nu - 72993 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [146000000 beta4^2 nu + 5331920000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 5331920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 >= 0 /\ 500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1022140 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 933086070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 175000 beta4^2 nu^2 + 43807000 beta4^2 nu + 2265701070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [91250000 beta4^2 nu + 1825000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 60850 nu - 1217 = 0 ]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 60850 nu - 1217 = 0 ]] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [532900000000 beta4^2 - 155471750000 beta4 nu - 3109435000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1460000 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [666125000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1825000 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [4015000 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 4015000 beta4 - 547650 nu - 10953 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 333153750000000 beta4 nu^3 - 4073359850000000 beta4 nu^2 - 162534609500000 beta4 nu - 1624013480000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 48667092500000000 beta4^2 nu + 972942175000000 beta4^2 - 333153750000000 beta4 nu^3 - 8126730475000000 beta4 nu^2 - 324669434500000 beta4 nu - 3245361730000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1665860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [27375000 beta4 nu + 1665860000 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 175000 beta4^2 nu^2 + 43807000 beta4^2 nu + 2265701070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [45625000000 beta4^2 nu^3 + 2737500000 beta4^2 nu^2 - 243135570250000 beta4^2 nu - 4862712135000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 4862712135000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 1999105050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 - 133188500000 beta4^2 nu - 14590801635000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 7298731807350 beta4 nu + 145947991149 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 10949 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [68437500000 beta4^2 nu^3 + 6665356250000 beta4^2 nu^2 + 121834344625000 beta4^2 nu + 2434021297500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 5329365000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 5329365000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 2665595000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ] /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 933086070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 3649300 nu - 72993 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3500 beta4^2 nu + 620570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1022140 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 933086070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 511000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1022000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 3649300 nu - 72993 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1065800000000 beta4^2 - 399784500000 beta4 nu - 7995690000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 97307540000000000 beta4^2 nu + 1945617900000000 beta4^2 - 666307500000000 beta4 nu^3 - 24360202200000000 beta4 nu^2 - 973608519000000 beta4 nu - 9733419960000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 333153750000000 beta4 nu^3 - 4073359850000000 beta4 nu^2 - 162534609500000 beta4 nu - 1624013480000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 1332797500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [27375000 beta4 nu + 1332797500 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [532900000000 beta4^2 - 155471750000 beta4 nu - 3109435000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1460000 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [3650000 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 3650000 beta4 - 547650 nu - 10953 = 0 ]]] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [666125000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1825000 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 60850 nu - 1217 = 0 ]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 60850 nu - 1217 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 48667092500000000 beta4^2 nu + 972942175000000 beta4^2 - 333153750000000 beta4 nu^3 - 8126730475000000 beta4 nu^2 - 324669434500000 beta4 nu - 3245361730000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 3649300 nu - 72993 > 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [109500000 beta4^2 nu + 5331190000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [109500000 beta4 nu + 5331190000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 10658730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 36500000 beta4 nu + 10658730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ] /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [730000 beta4 - 60850 nu - 1217 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 194561790000000000 beta4^2 nu + 3890702900000000 beta4^2 - 666307500000000 beta4 nu^3 - 48680425950000000 beta4 nu^2 - 1946417469000000 beta4 nu - 19461509460000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 175000 beta4^2 nu^2 + 62057000 beta4^2 nu + 3598316070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 - 266377000000 beta4^2 nu - 29181603270000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 7298731807350 beta4 nu + 145947991149 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 10949 = 0 ]]] /\ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 3998210100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 5475000000 beta4^2 nu^2 - 486271140500000 beta4^2 nu - 9725424270000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu^2 + 73000000 beta4^2 nu - 9725424270000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [136875000000 beta4^2 nu^3 + 13330712500000 beta4^2 nu^2 + 243668689250000 beta4^2 nu + 4868042595000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 933086070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ [1065800000000 beta4^2 - 399784500000 beta4 nu - 7995690000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 97307540000000000 beta4^2 nu + 1945617900000000 beta4^2 - 666307500000000 beta4 nu^3 - 24360202200000000 beta4 nu^2 - 973608519000000 beta4 nu - 9733419960000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [511000 beta4 - 182550 nu - 3651 = 0 /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1022000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [50 beta4 nu + beta4 > 0 /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3832500000 beta4^2 nu^2 + 93410800000 beta4^2 nu + 1866683000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [10000 beta4^2 nu + 547700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 547700 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [30000 beta4^2 nu + 730600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]]] \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 25 nu - 912 < 0 /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 18290000 beta4^2 nu + 365400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 365400 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 547700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 2797980500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4^2 nu + 933341500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1095000000 beta4^2 nu^2 + 93301300000 beta4^2 nu + 1865588000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5000 nu^2 - 127550 nu - 2553 > 0 \/ 100 nu - 2553 = 0 ] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 25 nu - 912 < 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 /\ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 18290000 beta4^2 nu + 365400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 365400 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 999917600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 3750 beta4 nu^2 + 228275 beta4 nu + 3335189 beta4 < 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 < 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 2797980500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 933341500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 9329582500000 beta4^2 nu^2 + 340762981650000 beta4^2 nu + 6811528311000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 13992457500000 beta4^2 nu^2 + 681339371650000 beta4^2 nu + 13621190961000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 279874700000 beta4^2 nu + 6813393972000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [25000000 beta4^2 nu^3 + 3651500000 beta4^2 nu^2 + 133371030000 beta4^2 nu + 2665960200 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 109520000 beta4^2 nu + 5331190200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [50000000 beta4^2 nu^3 + 5478000000 beta4^2 nu^2 + 133444060000 beta4^2 nu + 2666690400 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 < 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 3405764155500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 18655332500000 beta4^2 nu^2 + 1362305636650000 beta4^2 nu + 27238651111000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 23318207500000 beta4^2 nu^2 + 2043271901650000 beta4^2 nu + 40856111261000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 559647200000 beta4^2 nu + 27242381922000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2463750000 beta4^2 nu^2 + 453063550000 beta4^2 nu + 13624655285500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4 nu^3 + 45632500 beta4 nu^2 + 3998575150 beta4 nu + 79953251 beta4 < 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]] \/ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 60232000 beta4^2 nu + 5063754570 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 ] /\ [2281250000 beta4^2 nu^2 + 599603750000 beta4^2 nu + 38913691162500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 45625000 beta4 nu + 5329912500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu + 99927875000 beta4^2 - 456375000 beta4 nu^2 - 133279755000 beta4 nu - 2665412550 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 16655862500000 beta4^2 nu^2 + 1459479929750000 beta4^2 nu + 29182936615000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [166531250000000 beta4^2 nu^2 + 12163442500000000 beta4^2 nu + 243202237500000 beta4^2 - 249865312500000 beta4 nu^3 - 12175103793750000 beta4 nu^2 - 486704313375000 beta4 nu - 4866043672500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [17500 nu^2 - 3649300 nu - 72993 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2281250000 beta4^2 nu^2 + 266541250000 beta4^2 nu + 5329912500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [45625000 beta4 nu + 5329912500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 7994230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1022140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [3500 beta4^2 nu + 693570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 76664000 beta4^2 nu + 1533140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1533140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 1022280 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 50 nu - 3649 <= 0 /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 13325237500000 beta4^2 nu^2 + 973075454750000 beta4^2 nu + 19456179365000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 16655862500000 beta4^2 nu^2 + 1459479929750000 beta4^2 nu + 29182936615000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2281250000 beta4^2 nu^2 + 399766250000 beta4^2 nu + 9733419412500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [525000 beta4^2 nu^2 + 25571000 beta4^2 nu + 511210 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10500 beta4 nu + 511210 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] \/ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 1241070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [3500 beta4^2 nu + 1022070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 1022070 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [525000 beta4^2 nu^2 + 25571000 beta4^2 nu + 511210 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10500 beta4 nu + 511210 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ [2281250000 beta4^2 nu^2 + 399766250000 beta4^2 nu + 9733419412500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 - 266377000000 beta4^2 nu - 77808728270000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 106587299 > 0 ]]]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 27367500 beta4 nu^2 - 2665594850 beta4 nu - 53300949 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 912600 beta4 nu + 79953251 beta4 < 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 7993864850 beta4 nu - 159873649 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1022000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[730000 beta4 - 60850 nu - 1217 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 194561790000000000 beta4^2 nu + 3890702900000000 beta4^2 - 666307500000000 beta4 nu^3 - 48680425950000000 beta4 nu^2 - 1946417469000000 beta4 nu - 19461509460000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 5329729850 beta4 nu - 106587299 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [10000 beta4^2 nu + 547700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 >= 0 /\ 250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 226581050000 beta4^2 nu + 3408429385500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 3998210100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 2463750000 beta4^2 nu^2 + 226581050000 beta4^2 nu + 3408429385500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 3998210100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2920000000 beta4^2 nu^2 + 259905550000 beta4^2 nu + 3409095693000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 82135000 beta4^2 nu + 4664517600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2497968750000000 beta4^2 nu^2 + 30491871875000000 beta4^2 nu + 608838250000000 beta4^2 - 916172812500000 beta4 nu^3 - 6135026306250000 beta4 nu^2 - 244301644875000 beta4 nu - 2439351757500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [365000000000 beta4^2 nu^3 + 36658775000000 beta4^2 nu^2 + 730872788000000 beta4^2 nu + 14602795170000 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 \/ [146000000 beta4 nu + 3999670000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2281250000 beta4^2 nu + 999233125000 beta4^2 - 456375000 beta4 nu^2 - 366487380000 beta4 nu - 7329565050 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 1095050 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 732847000000 beta4^2 nu + 38916355845000 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 54750000 beta4 nu + 10659095000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [3746953125000000 beta4^2 nu^2 + 121717690625000000 beta4^2 nu + 2432855031250000 beta4^2 - 1166038125000000 beta4 nu^3 - 24390186037500000 beta4 nu^2 - 974208195750000 beta4 nu - 9737417805000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[82125000 beta4 nu + 2666142500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [159687500000 beta4^2 nu^3 + 14997393750000 beta4^2 nu^2 + 243735329125000 beta4^2 nu + 4868708902500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 63875000 beta4 nu + 1333527500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2281250000 beta4^2 nu^2 + 166622500000 beta4^2 nu + 3331537500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000000 beta4^2 nu + 1498963750000 beta4^2 - 1825500000 beta4 nu^2 - 466488270000 beta4 nu - 9329035200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [5000 beta4 nu + 1277600 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4 nu + 1642700 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [45625000 beta4^2 nu + 3331537500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000 beta4^2 nu + 3331537500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 912500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2281250000 beta4^2 nu^2 + 166622500000 beta4^2 nu + 3331537500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [912500 beta4 - 182550 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 453063550000 beta4^2 nu + 13624655285500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4 - 182550 nu - 3651 = 0 \/ 2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 1095050 beta4 - 182550 nu - 3651 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [136875000000 beta4^2 nu^3 + 26653212500000 beta4^2 nu^2 + 973608464250000 beta4^2 nu + 19461509095000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [5000 beta4 nu + 1460100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [730000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 999917600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [[730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 5001412500000 beta4^2 nu^2 + 60983853250000 beta4^2 nu + 1217677230000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 \/ 73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [730000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 266541250000 beta4^2 nu + 5329912500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 3649300 nu - 72993 > 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [146000000 beta4^2 nu + 10660920000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [36500000 beta4^2 nu + 7994230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 799496000000 beta4^2 nu + 15988460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 >= 0 /\ 175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 >= 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2281250000 beta4^2 nu^2 + 266541250000 beta4^2 nu + 5329912500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4^2 nu + 7994230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 3649300 nu - 72993 >= 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 >= 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 50 beta4 nu + beta4 > 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 194561790000000000 beta4^2 nu + 3890702900000000 beta4^2 - 666307500000000 beta4 nu^3 - 48680425950000000 beta4 nu^2 - 1946417469000000 beta4 nu - 19461509460000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1022000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 511000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]]] \/ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2281250000 beta4^2 nu^2 + 266541250000 beta4^2 nu + 5329912500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4^2 nu + 7994230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 3649300 nu - 72993 >= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 194561790000000000 beta4^2 nu + 3890702900000000 beta4^2 - 666307500000000 beta4 nu^3 - 48680425950000000 beta4 nu^2 - 1946417469000000 beta4 nu - 19461509460000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [474500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [2081640625000000 beta4^2 nu^2 + 60867171875000000 beta4^2 nu + 1216510781250000 beta4^2 - 832884375000000 beta4 nu^3 - 12210084937500000 beta4 nu^2 - 487403936250000 beta4 nu - 4870707825000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [2281250000 beta4^2 nu^2 + 199928750000 beta4^2 nu + 3997662500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [45625000 beta4 nu + 3997662500 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [1165718750000 beta4^2 - 399784500000 beta4 nu - 7995690000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1277500 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [1003750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1003750 beta4 - 182550 nu - 3651 = 0 ]]] /\ [45625000 beta4^2 nu + 912500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [2164906250000 beta4^2 - 599676750000 beta4 nu - 11993535000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2372500 beta4 - 182550 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [547500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 547500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 912500 beta4 - 182550 nu - 3651 = 0 ]] /\ [45625000 beta4^2 nu + 912500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 912500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2081640625000000 beta4^2 nu^2 + 243218890625000000 beta4^2 nu + 4863545156250000 beta4^2 - 832884375000000 beta4 nu^3 - 48690420562500000 beta4 nu^2 - 1946617361250000 beta4 nu - 19462842075000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[45625000 beta4 nu + 5329912500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [2281250000 beta4^2 nu^2 + 133316250000 beta4^2 nu + 2665412500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 45625000 beta4 nu + 2665412500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 3649300 nu - 72993 > 0 /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [109500000 beta4^2 nu + 10660190000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [109500000 beta4 nu + 10660190000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [36500000 beta4^2 nu + 7994230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 15987730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 36500000 beta4 nu + 15987730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2281250000 beta4^2 nu^2 + 266541250000 beta4^2 nu + 5329912500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 45625000 beta4 nu + 5329912500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 10658730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1496500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ] /\ [2131600000000 beta4^2 - 666307500000 beta4 nu - 13326150000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [2920000 beta4 - 182550 nu - 3651 = 0 /\ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 291816040000000000 beta4^2 nu + 5835787900000000 beta4^2 - 666307500000000 beta4 nu^3 - 73000649700000000 beta4 nu^2 - 2919226419000000 beta4 nu - 29189598960000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 199910500000 beta4^2 nu + 3997480000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 3997480000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [[730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 - 266377000000 beta4^2 nu - 77808728270000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 14599 = 0 ]]] /\ [2281250000 beta4^2 nu^2 + 399766250000 beta4^2 nu + 9733419412500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 5000 beta4 nu + 1460100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 73000000 beta4^2 nu - 38901699270000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [91250000000 beta4^2 nu^3 + 5475000000 beta4^2 nu^2 - 1945084890500000 beta4^2 nu - 38901699270000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 486404420235000 beta4 nu^2 + 19456178269800 beta4 nu + 194561786349 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [136875000000 beta4^2 nu^3 + 26653212500000 beta4^2 nu^2 + 973608464250000 beta4^2 nu + 19461509095000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2920000000 beta4^2 nu^2 + 346501800000 beta4^2 nu + 9732353868000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 58410000 beta4^2 nu + 2932118100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [226482500000000 beta4^2 nu^2 + 4871771800000000 beta4^2 nu + 97344843000000 beta4^2 - 161024312500000 beta4 nu^3 - 2036346771250000 beta4 nu^2 - 81260641675000 beta4 nu - 811962319500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [187062500000 beta4^2 nu^3 + 19328848750000 beta4^2 nu^2 + 414103491975000 beta4^2 nu + 8274339796500 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 \/ [74825000 beta4 nu + 2266321500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [365000000 beta4^2 nu + 90600300000 beta4^2 - 152125000 beta4 nu^2 - 64415810000 beta4 nu - 1288255350 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [1551250000 beta4^2 nu^2 + 386414550000 beta4^2 nu + 19944848920500 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 31025000 beta4 nu + 5462845500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [365000000 beta4^2 nu^2 + 26659600000 beta4^2 nu + 533046000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [7300000 beta4^2 nu + 533046000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [7300000 beta4^2 nu + 533046000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 146000 beta4 - 60850 nu - 1217 = 0 ]] /\ [365000000 beta4^2 nu^2 + 26659600000 beta4^2 nu + 533046000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [146000 beta4 - 60850 nu - 1217 = 0 /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [620500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [511000000 beta4^2 nu + 101261220000 beta4^2 - 212975000 beta4 nu^2 - 68860294000 beta4 nu - 1377120690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [87500 beta4^2 nu^2 + 34678500 beta4^2 nu + 2065681035 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 565785 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [253127500000000 beta4^2 nu^2 + 6817922600000000 beta4^2 nu + 136257201000000 beta4^2 - 172129437500000 beta4 nu^3 - 2847687203750000 beta4 nu^2 - 113700932825000 beta4 nu - 1136320810500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [70718750000 beta4^2 nu^3 + 6332430625000 beta4^2 nu^2 + 85350681112500 beta4^2 nu + 1704481215750 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 28287500 beta4 nu + 466853250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ 50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000 beta4^2 nu + 1866427500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [63875000 beta4 nu + 1866427500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 186591650000 beta4^2 nu + 3731066500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 3731066500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1916250000 beta4^2 nu^2 + 93334150000 beta4^2 nu + 1865916500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 364900 nu - 7299 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 38353000 beta4^2 nu + 766780 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 766780 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1277640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 1277640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3500 beta4^2 nu + 693570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4 - 182550 nu - 3651 = 0 \/ 2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 38328500 beta4^2 nu + 3731066535 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 9328624375000 beta4^2 nu^2 + 340762962487500 beta4^2 nu + 6811528183250 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 12778500 beta4^2 nu + 349971160 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 1750494375000 beta4^2 nu^2 + 21344348637500 beta4^2 nu + 426187030500 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ 50 nu - 3649 <= 0 /\ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1715500 beta4 - 182550 nu - 3651 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 328500 beta4 - 60850 nu - 1217 /= 0 /\ [407668500000 beta4^2 - 135482525000 beta4 nu - 2709650500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ] /\ [563541750000 beta4^2 - 164355850000 beta4 nu - 3287117000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 1715500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [809341875000000 beta4^2 nu^2 + 15349918050000000 beta4^2 nu + 306674624250000 beta4^2 - 299838375000000 beta4 nu^3 - 2855349740000000 beta4 nu^2 - 113854183550000 beta4 nu - 1137342482000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [809341875000000 beta4^2 nu^2 + 43796786175000000 beta4^2 nu + 875611986750000 beta4^2 - 299838375000000 beta4 nu^3 - 8124731552500000 beta4 nu^2 - 324629456050000 beta4 nu - 3245095207000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 170194899175000 beta4^2 nu - 3403898494500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 3403898494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 25553500 beta4^2 nu + 1399373535 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 - 93231950000 beta4^2 nu - 10213561144500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 7298731807350 beta4 nu + 145947991149 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 10949 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 4665749375000 beta4^2 nu^2 + 85284041237500 beta4^2 nu + 1703814908250 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]] \/ [4288750000 beta4^2 nu^2 + 133396550000 beta4^2 nu + 2666215500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2920000000 beta4^2 nu^2 + 133341800000 beta4^2 nu + 2665668000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 49275000 beta4^2 nu + 5329985500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 < 0 /\ [49275000 beta4^2 nu + 2665485500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2463750000 beta4^2 nu^2 + 133323550000 beta4^2 nu + 2665485500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 563541750000 beta4^2 - 164355850000 beta4 nu - 3287117000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 328500 beta4 - 60850 nu - 1217 /= 0 /\ [407668500000 beta4^2 - 135482525000 beta4 nu - 2709650500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [809341875000000 beta4^2 nu^2 + 15349918050000000 beta4^2 nu + 306674624250000 beta4^2 - 299838375000000 beta4 nu^3 - 2855349740000000 beta4 nu^2 - 113854183550000 beta4 nu - 1137342482000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [809341875000000 beta4^2 nu^2 + 43796786175000000 beta4^2 nu + 875611986750000 beta4^2 - 299838375000000 beta4 nu^3 - 8124731552500000 beta4 nu^2 - 324629456050000 beta4 nu - 3245095207000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [3410560000000000 beta4^2 nu^2 + 39038122400000000 beta4^2 nu + 779398224000000 beta4^2 - 1066092000000000 beta4 nu^3 - 6144021457500000 beta4 nu^2 - 244481547900000 beta4 nu - 2440551111000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[58400000 beta4 nu + 667293000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [1460000000 beta4^2 nu^2 + 61674962500 beta4^2 nu + 1232915250 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [29200000 beta4 nu + 1232915250 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [1577384000000 beta4^2 - 459752175000 beta4 nu - 9195043500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1350500 beta4 - 182550 nu - 3651 = 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [3686500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 3686500 beta4 - 547650 nu - 10953 = 0 ]]] /\ [58400000 beta4^2 nu + 1168000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [2216864000000 beta4^2 - 559698300000 beta4 nu - 11193966000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [511000 beta4 - 60850 nu - 1217 = 0 /\ [1898000 beta4 - 182550 nu - 3651 = 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1168000 beta4 - 182550 nu - 3651 = 0 ]] /\ [58400000 beta4^2 nu + 1168000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [67525000 beta4^2 nu + 1350500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1168000 beta4 - 182550 nu - 3651 = 0 ]] /\ [554216000000 beta4^2 - 157692775000 beta4 nu - 3153855500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1168000 beta4 - 182550 nu - 3651 = 0 \/ 474500 beta4 - 60850 nu - 1217 = 0 ] /\ [1295750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1295750 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3410560000000000 beta4^2 nu^2 + 54598802400000000 beta4^2 nu + 1090611824000000 beta4^2 - 1066092000000000 beta4 nu^3 - 8576043832500000 beta4 nu^2 - 341762442900000 beta4 nu - 3413360061000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[58400000 beta4 nu + 933743000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [2920000000 beta4^2 nu^2 + 23431175000 beta4^2 nu + 467455500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 58400000 beta4 nu + 467455500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [3410560000000000 beta4^2 nu^2 + 155743222400000000 beta4^2 nu + 3113500224000000 beta4^2 - 1066092000000000 beta4 nu^3 - 24384189270000000 beta4 nu^2 - 974088260400000 beta4 nu - 9736618236000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[58400000 beta4 nu + 2665668000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [2920000000 beta4^2 nu^2 + 66729300000 beta4^2 nu + 1333418000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 58400000 beta4 nu + 1333418000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 133323550000 beta4^2 nu + 2665485500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 < 0 /\ [4288750000 beta4^2 nu^2 + 133396550000 beta4^2 nu + 2666215500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [122275000 beta4^2 nu + 5331445500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [122275000 beta4 nu + 5331445500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [49275000 beta4^2 nu + 5329985500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 5329985500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2463750000 beta4^2 nu^2 + 532998550000 beta4^2 nu + 10658985500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 10658985500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2920000000 beta4^2 nu^2 + 133341800000 beta4^2 nu + 2665668000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 58400000 beta4 nu + 2665668000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [49275000 beta4^2 nu + 2665485500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2463750000 beta4^2 nu^2 + 266548550000 beta4^2 nu + 5329985500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 328500 beta4 - 60850 nu - 1217 /= 0 /\ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1350500 beta4 - 182550 nu - 3651 = 0 ] /\ [803346750000 beta4^2 - 208776350000 beta4 nu - 4175527000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [2445500 beta4 - 182550 nu - 3651 = 0 /\ 1715500 beta4 - 182550 nu - 3651 = 0 ]] /\ [491600250000 beta4^2 - 151029700000 beta4 nu - 3020594000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [1496500 beta4 - 182550 nu - 3651 = 0 /\ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [809341875000000 beta4^2 nu^2 + 30667462425000000 beta4^2 nu + 613025511750000 beta4^2 - 299838375000000 beta4 nu^3 - 5692709177500000 beta4 nu^2 - 227348561050000 beta4 nu - 2272286257000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [809341875000000 beta4^2 nu^2 + 87561198675000000 beta4^2 nu + 1750900236750000 beta4^2 - 299838375000000 beta4 nu^3 - 16231472802500000 beta4 nu^2 - 648899106050000 beta4 nu - 6487791707000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [49275000 beta4 nu + 5329985500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2463750000 beta4^2 nu^2 + 133323550000 beta4^2 nu + 2665485500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 4931040600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[328500 beta4 - 60850 nu - 1217 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[328500 beta4 - 60850 nu - 1217 = 0 \/ 50 nu - 3649 = 0 ] /\ [821250000 beta4^2 nu^2 - 119869650000 beta4^2 nu - 13131721471500 beta4^2 - 152125000 beta4 nu^3 + 22201122500 beta4 nu^2 + 2432910602450 beta4 nu + 48649330383 beta4 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 \/ 50 nu - 10949 = 0 ]]] /\ [2920000000 beta4^2 nu^2 + 246583050000 beta4^2 nu + 2436286743000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 58400000 beta4 nu + 667293000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [3285000000 beta4^2 nu + 563607450000 beta4^2 - 608500000 beta4 nu^2 - 164380190000 beta4 nu - 3287360400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [5000 beta4 nu + 1350600 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [821250000 beta4^2 nu^2 + 32850000 beta4^2 nu - 4376440921500 beta4^2 - 152125000 beta4 nu^3 - 9127500 beta4 nu^2 + 810673942450 beta4 nu + 16213481283 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 /= 0 ] /\ [41062500000 beta4^2 nu^3 + 2463750000 beta4^2 nu^2 - 218822013225000 beta4^2 nu - 4376440921500 beta4^2 - 7606250000 beta4 nu^4 - 608500000 beta4 nu^3 + 40533687995000 beta4 nu^2 + 1621348006600 beta4 nu + 16213481283 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 /= 0 ] /\ [1149750000 beta4^2 nu + 407691495000 beta4^2 - 212975000 beta4 nu^2 - 135491044000 beta4 nu - 2709735690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [87500 beta4^2 nu^2 + 62053500 beta4^2 nu + 4064603535 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 1113285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1019171250000000 beta4^2 nu^2 + 15358311225000000 beta4^2 nu + 306758556000000 beta4^2 - 338706312500000 beta4 nu^3 - 2857681816250000 beta4 nu^2 - 113900825075000 beta4 nu - 1137653425500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [139156250000 beta4^2 nu^3 + 11332474375000 beta4^2 nu^2 + 85550600737500 beta4^2 nu + 1706480138250 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 55662500 beta4 nu + 467400750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1408854375000000 beta4^2 nu^2 + 43820766675000000 beta4^2 nu + 875851791750000 beta4^2 - 410889625000000 beta4 nu^3 - 8131394627500000 beta4 nu^2 - 324762717550000 beta4 nu - 3245983617000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [168812500000 beta4^2 nu^3 + 15664066250000 beta4^2 nu^2 + 243761985075000 beta4^2 nu + 4868975425500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [5000 beta4^2 nu + 620600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [2463750000 beta4^2 nu^2 + 133323550000 beta4^2 nu + 2665485500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [146000000 beta4^2 nu + 5331920000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 5331920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 3405764155500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 3730811000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 >= 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [85775000 beta4^2 nu + 1715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [407668500000 beta4^2 - 135482525000 beta4 nu - 2709650500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1241000 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1113250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1113250 beta4 - 182550 nu - 3651 = 0 ]]] /\ [563541750000 beta4^2 - 164355850000 beta4 nu - 3287117000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1715500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [3686500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 3686500 beta4 - 547650 nu - 10953 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [809341875000000 beta4^2 nu^2 + 15349918050000000 beta4^2 nu + 306674624250000 beta4^2 - 299838375000000 beta4 nu^3 - 2855349740000000 beta4 nu^2 - 113854183550000 beta4 nu - 1137342482000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2463750000 beta4^2 nu^2 + 23412925000 beta4^2 nu + 467273000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 49275000 beta4 nu + 467273000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [809341875000000 beta4^2 nu^2 + 43796786175000000 beta4^2 nu + 875611986750000 beta4^2 - 299838375000000 beta4 nu^3 - 8124731552500000 beta4 nu^2 - 324629456050000 beta4 nu - 3245095207000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1565886500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [24637500 beta4 nu + 1565886500 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 170194899175000 beta4^2 nu - 3403898494500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 3403898494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 25553500 beta4^2 nu + 1399373535 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 - 93231950000 beta4^2 nu - 10213561144500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 7298731807350 beta4 nu + 145947991149 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 10949 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 4665749375000 beta4^2 nu^2 + 85284041237500 beta4^2 nu + 1703814908250 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1715500 beta4 - 182550 nu - 3651 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2463750000 beta4^2 nu^2 + 133323550000 beta4^2 nu + 2665485500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [5000 beta4^2 nu + 620600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 1460200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2463750000 beta4^2 nu^2 + 133323550000 beta4^2 nu + 2665485500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 < 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1065800000000 beta4^2 - 399784500000 beta4 nu - 7995690000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 97307540000000000 beta4^2 nu + 1945617900000000 beta4^2 - 666307500000000 beta4 nu^3 - 24360202200000000 beta4 nu^2 - 973608519000000 beta4 nu - 9733419960000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [809341875000000 beta4^2 nu^2 + 15349918050000000 beta4^2 nu + 306674624250000 beta4^2 - 299838375000000 beta4 nu^3 - 2855349740000000 beta4 nu^2 - 113854183550000 beta4 nu - 1137342482000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1231875000 beta4^2 nu^2 + 56669900000 beta4^2 nu + 1132905250 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [24637500 beta4 nu + 1132905250 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [407668500000 beta4^2 - 135482525000 beta4 nu - 2709650500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1241000 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [3212000 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 3212000 beta4 - 547650 nu - 10953 = 0 ]]] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [563541750000 beta4^2 - 164355850000 beta4 nu - 3287117000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [1350500 beta4 - 182550 nu - 3651 = 0 /\ [1715500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [62050000 beta4^2 nu + 1241000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [809341875000000 beta4^2 nu^2 + 43796786175000000 beta4^2 nu + 875611986750000 beta4^2 - 299838375000000 beta4 nu^3 - 8124731552500000 beta4 nu^2 - 324629456050000 beta4 nu - 3245095207000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2463750000 beta4^2 nu^2 + 66711050000 beta4^2 nu + 1333235500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 < 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [109500000 beta4^2 nu + 5331190000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [109500000 beta4 nu + 5331190000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 10658730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 36500000 beta4 nu + 10658730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2463750000 beta4^2 nu^2 + 133323550000 beta4^2 nu + 2665485500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ] /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 730000 beta4 - 60850 nu - 1217 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 194561790000000000 beta4^2 nu + 3890702900000000 beta4^2 - 666307500000000 beta4 nu^3 - 48680425950000000 beta4 nu^2 - 1946417469000000 beta4 nu - 19461509460000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 3998210100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[730000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 - 266377000000 beta4^2 nu - 29181603270000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 7298731807350 beta4 nu + 145947991149 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 10949 = 0 ]]] /\ [2463750000 beta4^2 nu^2 + 226581050000 beta4^2 nu + 3408429385500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1065946000000 beta4^2 - 1825500000 beta4 nu^2 - 399857520000 beta4 nu - 7996420200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 5475000000 beta4^2 nu^2 - 486271140500000 beta4^2 nu - 9725424270000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu^2 + 73000000 beta4^2 nu - 9725424270000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 97360830000000000 beta4^2 nu + 1946150800000000 beta4^2 - 999461250000000 beta4 nu^3 - 24380191425000000 beta4 nu^2 - 974008303500000 beta4 nu - 9736085190000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [136875000000 beta4^2 nu^3 + 13330712500000 beta4^2 nu^2 + 243668689250000 beta4^2 nu + 4868042595000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 /= 0 /\ [1065800000000 beta4^2 - 399784500000 beta4 nu - 7995690000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 97307540000000000 beta4^2 nu + 1945617900000000 beta4^2 - 666307500000000 beta4 nu^3 - 24360202200000000 beta4 nu^2 - 973608519000000 beta4 nu - 9733419960000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1496500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [21900000000 beta4^2 nu + 533338000000 beta4^2 - 5476500000 beta4 nu^2 - 266742060000 beta4 nu - 5332650600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [219000000 beta4^2 nu + 5333380000 beta4^2 - 27382500 beta4 nu^2 - 1333710300 beta4 nu - 26663253 beta4 < 0 \/ 219000000 beta4 nu + 5333380000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 ]]] /\ [2131600000000 beta4^2 - 666307500000 beta4 nu - 13326150000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2920000 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2920000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 3672500 beta4 nu^2 - 133078550 beta4 nu - 2663037 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2555000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1131500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000 beta4^2 nu + 912500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [5475000000 beta4^2 nu + 133334500000 beta4^2 - 2738250000 beta4 nu^2 - 133371030000 beta4 nu - 2666325300 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000 beta4^2 nu + 1333162500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [18250000 beta4^2 nu - 2664135000 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [532900000000 beta4^2 - 333153750000 beta4 nu - 6663075000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1460000 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [638750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1387000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [7300000000 beta4^2 nu + 133371000000 beta4^2 - 3651000000 beta4 nu^2 - 133407540000 beta4 nu - 2666690400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ] /\ [666125000000 beta4^2 - 399784500000 beta4 nu - 7995690000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]] \/ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 500000 beta4^2 nu^2 + 45645000 beta4^2 nu + 1000100200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 4166018750000 beta4^2 nu^2 + 91342445375000 beta4^2 nu + 1825182865000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 \/ 36500000 beta4 nu + 1999105000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ]]] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [684375000 beta4^2 nu^2 + 33333625000 beta4^2 nu + 304585930000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 27375000 beta4 nu + 333610000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [228125000 beta4^2 nu^2 + 9125000 beta4^2 nu - 303919440000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 25 nu - 912 = 0 ]]]] \/ [2190000000 beta4^2 nu^2 + 253215100000 beta4^2 nu + 6812860926000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1825000000 beta4^2 nu^2 + 199910500000 beta4^2 nu + 4866709980000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu + 399748000000 beta4^2 - 1825500000 beta4 nu^2 - 266596020000 beta4 nu - 5331190200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 48667092500000000 beta4^2 nu + 972942175000000 beta4^2 - 666307500000000 beta4 nu^3 - 24360202200000000 beta4 nu^2 - 973608519000000 beta4 nu - 9733419960000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2434021297500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2555000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [1131500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1131500 beta4 - 182550 nu - 3651 = 0 ] /\ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu + 133334500000 beta4^2 - 2738250000 beta4 nu^2 - 133371030000 beta4 nu - 2666325300 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 7500 beta4^2 nu + 365150 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 7500 beta4 nu + 365150 beta4 - 182550 nu - 3651 = 0 ] /\ [532900000000 beta4^2 - 333153750000 beta4 nu - 6663075000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ]] \/ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 45645000 beta4^2 nu + 1000100200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [11406250000 beta4^2 nu^3 + 684375000 beta4^2 nu^2 - 15195962875000 beta4^2 nu - 303919440000 beta4^2 - 5704687500 beta4 nu^4 - 456375000 beta4 nu^3 + 7600056230625 beta4 nu^2 + 304002614325 beta4 nu + 3040027056 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [228125000 beta4^2 nu^2 + 9125000 beta4^2 nu - 303919440000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 912875000 beta4^2 nu^2 + 25016195000 beta4^2 nu + 499958800 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 16689625000 beta4^2 nu - 607505635000 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 100 nu - 1823 = 0 ]]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[365000 beta4 - 60850 nu - 1217 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 3750 beta4 nu^2 + 228275 beta4 nu + 3335189 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [750000 beta4 nu^3 + 4607500 beta4 nu^2 - 332879100 beta4 nu - 6659419 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [5475000000 beta4^2 nu + 133334500000 beta4^2 - 2738250000 beta4 nu^2 - 133371030000 beta4 nu - 2666325300 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [45625000 beta4^2 nu + 1333162500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ]]] /\ [18250000 beta4^2 nu - 2664135000 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [532900000000 beta4^2 - 333153750000 beta4 nu - 6663075000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ [638750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 + 1277800 beta4 nu + 26670553 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1496500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 /= 0 ] /\ [21900000000 beta4^2 nu + 533338000000 beta4^2 - 5476500000 beta4 nu^2 - 266742060000 beta4 nu - 5332650600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [219000000 beta4^2 nu + 5333380000 beta4^2 - 27382500 beta4 nu^2 - 1333710300 beta4 nu - 26663253 beta4 < 0 \/ 219000000 beta4 nu + 5333380000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 ]]] /\ [2131600000000 beta4^2 - 666307500000 beta4 nu - 13326150000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2920000 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2920000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 + 1277800 beta4 nu + 26670553 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 3672500 beta4 nu^2 - 133078550 beta4 nu - 2663037 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 + 1277800 beta4 nu + 26670553 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [250000 beta4 nu^3 + 13702500 beta4 nu^2 - 332514700 beta4 nu - 6655773 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 45645000 beta4^2 nu + 1000100200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 4166018750000 beta4^2 nu^2 + 91342445375000 beta4^2 nu + 1825182865000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 \/ 36500000 beta4 nu + 1999105000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [684375000 beta4^2 nu^2 + 33333625000 beta4^2 nu + 304585930000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 27375000 beta4 nu + 333610000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [228125000 beta4^2 nu^2 + 9125000 beta4^2 nu - 303919440000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [20000 beta4^2 nu + 1095400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 1823 <= 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4^2 nu + 1460800 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 2920800 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 40000 beta4 nu + 2920800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ [3000000 beta4^2 nu^2 + 73120000 beta4^2 nu + 1461200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [60000 beta4 nu + 1461200 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu + 666855000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5000 nu^2 - 91050 nu - 1823 > 0 \/ 100 nu - 1823 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 3750 beta4 nu^2 + 228275 beta4 nu + 3335189 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [750000 beta4 nu^3 + 4607500 beta4 nu^2 - 332879100 beta4 nu - 6659419 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [250000 beta4 nu^3 + 13702500 beta4 nu^2 - 332514700 beta4 nu - 6655773 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 25 nu - 912 < 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 54770000 beta4^2 nu + 1095200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 365400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 20000 beta4 nu + 365400 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 3333362500000 beta4^2 nu^2 + 60917186000000 beta4^2 nu + 1217010740000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [5000 nu^2 - 91050 nu - 1823 > 0 /\ 50 nu - 3649 = 0 ]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 999917600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu - 1215011270000 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 45725 nu - 1664399 > 0 ]]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 3750 beta4 nu^2 + 228275 beta4 nu + 3335189 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [750000 beta4 nu^3 + 4607500 beta4 nu^2 - 332879100 beta4 nu - 6659419 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [250000 beta4 nu^3 + 13702500 beta4 nu^2 - 332514700 beta4 nu - 6655773 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [1496500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [21900000000 beta4^2 nu + 533338000000 beta4^2 - 5476500000 beta4 nu^2 - 266742060000 beta4 nu - 5332650600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [219000000 beta4^2 nu + 5333380000 beta4^2 - 27382500 beta4 nu^2 - 1333710300 beta4 nu - 26663253 beta4 < 0 \/ 219000000 beta4 nu + 5333380000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 ]]] /\ [2131600000000 beta4^2 - 666307500000 beta4 nu - 13326150000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2920000 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2920000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 3672500 beta4 nu^2 - 133078550 beta4 nu - 2663037 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 31032000 beta4^2 nu + 899889320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 33368300000 beta4^2 nu + 666745500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [175000 beta4^2 nu^2 + 31032000 beta4^2 nu + 899889320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu - 1215011270000 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 45725 nu - 1664399 < 0 ]]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 3750 beta4 nu^2 + 228275 beta4 nu + 3335189 beta4 < 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [750000 beta4 nu^3 + 4607500 beta4 nu^2 - 332879100 beta4 nu - 6659419 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 < 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [250000 beta4 nu^3 + 13702500 beta4 nu^2 - 332514700 beta4 nu - 6655773 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [14600000000 beta4^2 nu + 533192000000 beta4^2 - 3651000000 beta4 nu^2 - 266669040000 beta4 nu - 5331920400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ]]] /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4 - 60850 nu - 1217 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [125000 beta4 nu^3 + 2288750 beta4 nu^2 - 83174225 beta4 nu - 1664399 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 3333362500000 beta4^2 nu^2 + 60917186000000 beta4^2 nu + 1217010740000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 31032000 beta4^2 nu + 899889320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [68437500000 beta4^2 nu^3 + 10828637500000 beta4^2 nu^2 + 547488219625000 beta4^2 nu + 8885395745985000 beta4^2 - 11409375000 beta4 nu^4 - 2083123687500 beta4 nu^3 - 121726078788750 beta4 nu^2 - 2224086960955725 beta4 nu - 44433065450763 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [68437500000 beta4^2 nu^3 + 14159262500000 beta4^2 nu^2 + 912324882125000 beta4^2 nu + 17767141459485000 beta4^2 - 11409375000 beta4 nu^4 - 3748892437500 beta4 nu^3 - 304227703038750 beta4 nu^2 - 6669825861378225 beta4 nu - 133274856135663 beta4 < 0 \/ 54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [22812500000 beta4^2 nu^3 - 831287500000 beta4^2 nu^2 - 303952810125000 beta4^2 nu - 8880529036005000 beta4^2 - 11409375000 beta4 nu^4 + 415529437500 beta4 nu^3 + 152026357586250 beta4 nu^2 + 4444521389678025 beta4 nu + 88829620576587 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [5703125000000 beta4^2 nu^4 + 791479687500000 beta4^2 nu^3 + 33478623531250000 beta4^2 nu^2 + 445060710973125000 beta4^2 nu + 8887829100975000 beta4^2 - 1711406250000 beta4 nu^5 - 229214343750000 beta4 nu^4 - 9138414208125000 beta4 nu^3 - 111508775734350000 beta4 nu^2 - 4449392265814125 beta4 nu - 44457405667389 beta4 < 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]] \/ [136875000000 beta4^2 nu^3 + 13330712500000 beta4^2 nu^2 + 243668689250000 beta4^2 nu + 4868042595000 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 /\ 10950000000 beta4^2 nu^2 + 466725500000 beta4^2 nu + 4872042630000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 /\ 2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 /\ 1575000 beta4^2 nu^2 + 131463000 beta4^2 nu + 2267453630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [6843750000 beta4^2 nu^2 + 266723750000 beta4^2 nu + 2436687987500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [45625000 beta4 nu + 667037500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [547500000000 beta4^2 nu^3 + 73306600000000 beta4^2 nu^2 + 2920559107000000 beta4^2 nu + 35556183113880000 beta4^2 - 68456250000 beta4 nu^4 - 11665857750000 beta4 nu^3 - 608705380920000 beta4 nu^2 - 8901215887148100 beta4 nu - 177780928906503 beta4 > 0 \/ 54750000 beta4^2 nu + 1333345000 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 < 0 ] /\ [547500000000 beta4^2 nu^3 + 93290350000000 beta4^2 nu^2 + 4866443457000000 beta4^2 nu + 71092894057380000 beta4^2 - 68456250000 beta4 nu^4 - 21660470250000 beta4 nu^3 - 1582114007670000 beta4 nu^2 - 26693903576183100 beta4 nu - 533245399193403 beta4 < 0 \/ 5475000000 beta4^2 nu + 266559500000 beta4^2 - 2738250000 beta4 nu^2 - 200001780000 beta4 nu - 3998940300 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 24366852500000000 beta4^2 nu + 486804150000000 beta4^2 - 832884375000000 beta4 nu^3 - 12210084937500000 beta4 nu^2 - 487403936250000 beta4 nu - 4870707825000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [500000 beta4^2 nu^2 + 164270000 beta4^2 nu + 13325785200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 + 486670979750000 beta4^2 nu + 9729422115000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ [4562500000000 beta4^2 nu^4 + 1499146250000000 beta4^2 nu^3 + 158128094075000000 beta4^2 nu^2 + 5330993512433500000 beta4^2 nu + 106556631003480000 beta4^2 - 1140937500000 beta4 nu^5 - 333267843750000 beta4 nu^4 - 30426936551250000 beta4 nu^3 - 889512983316525000 beta4 nu^2 - 35544017672457750 beta4 nu - 355318522295751 beta4 > 0 \/ [36500000 beta4 nu + 3997480000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [1368750000 beta4^2 nu^2 + 266504750000 beta4^2 nu + 9730754547500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 36642350000000 beta4^2 nu^2 + 4621042459500000 beta4^2 nu + 177581412442980000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 1338212037765000 beta4 nu^2 - 53314806499015200 beta4 nu - 1065760925133051 beta4 < 0 \/ 36500000 beta4 nu + 6661980000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000000000 beta4^2 nu^4 + 2498698750000000 beta4^2 nu^3 + 206815181275000000 beta4^2 nu^2 + 5332939796604500000 beta4^2 nu + 106576089847710000 beta4^2 - 3422812500000 beta4 nu^5 - 833226656250000 beta4 nu^4 - 54787147878750000 beta4 nu^3 - 890973396277575000 beta4 nu^2 - 35573217934163250 beta4 nu - 355513164049953 beta4 < 0 \/ [73000000 beta4 nu + 3998210000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1140625000000 beta4^2 nu^4 + 208255312500000 beta4^2 nu^3 + 3051687893750000 beta4^2 nu^2 - 443600697979125000 beta4^2 nu - 8873232968880000 beta4^2 - 570468750000 beta4 nu^5 - 104167593750000 beta4 nu^4 - 1528345110000000 beta4 nu^3 + 221830590968737500 beta4 nu^2 + 8875054319974875 beta4 nu + 88756639916112 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 25 nu - 912 = 0 ]]]] \/ [45625000000 beta4^2 nu^3 + 13325237500000 beta4^2 nu^2 + 729939829750000 beta4^2 nu + 14593466865000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 < 0 /\ 912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 14593466865000 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 /\ 250000 beta4^2 nu^2 + 127760000 beta4^2 nu + 15989555100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 94907000 beta4^2 nu + 12391823070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [4562500000000 beta4^2 nu^4 + 1998740000000000 beta4^2 nu^3 + 267569100950000000 beta4^2 nu^2 + 10660040740696000000 beta4^2 nu + 213093803162730000 beta4^2 - 1140937500000 beta4 nu^5 - 416556281250000 beta4 nu^4 - 42593711501250000 beta4 nu^3 - 1334086873358775000 beta4 nu^2 - 53312375809437750 beta4 nu - 532953449891901 beta4 > 0 \/ 912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 7296733432500 beta4^2 - 152125000 beta4 nu^3 - 33324502500 beta4 nu^2 - 1332797550 beta4 nu - 13327367 beta4 > 0 \/ [9125000 beta4 nu + 666307500 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 > 0 ] /\ [1825000000 beta4^2 nu + 532936500000 beta4^2 - 912750000 beta4 nu^2 - 333190260000 beta4 nu - 6663440100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000000000 beta4^2 nu^4 + 3331355000000000 beta4^2 nu^3 + 340589734400000000 beta4^2 nu^2 + 10662959967042000000 beta4^2 nu + 213122990096460000 beta4^2 - 3422812500000 beta4 nu^5 - 1083091968750000 beta4 nu^4 - 79127360853750000 beta4 nu^3 - 1336277292816825000 beta4 nu^2 - 53356173535853250 beta4 nu - 533245399193403 beta4 < 0 \/ 666125000000000 beta4^2 nu^2 + 72967332500000000 beta4^2 nu + 1459080200000000 beta4^2 - 499730625000000 beta4 nu^3 - 36510319462500000 beta4 nu^2 - 1459813101750000 beta4 nu - 14596132095000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [136875000000 beta4^2 nu^3 + 3338837500000 beta4^2 nu^2 - 729273485750000 beta4^2 nu - 17763487429155000 beta4^2 - 68456250000 beta4 nu^4 - 1671245250000 beta4 nu^3 + 364703245830000 beta4 nu^2 + 8891471801886900 beta4 nu + 177683541380397 beta4 < 0 /\ 2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 /\ 1575000 beta4^2 nu^2 + 131463000 beta4^2 nu + 2267453630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [10950000000 beta4^2 nu^2 + 466725500000 beta4^2 nu + 4872042630000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [6843750000000 beta4^2 nu^4 + 167078750000000 beta4^2 nu^3 - 36460335450000000 beta4^2 nu^2 - 888903644943500000 beta4^2 nu - 17763487429155000 beta4^2 - 3422812500000 beta4 nu^5 - 83630718750000 beta4 nu^4 + 18233491046250000 beta4 nu^3 + 444938293340175000 beta4 nu^2 + 17775648870906750 beta4 nu + 177683541380397 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [6843750000 beta4^2 nu^2 + 266723750000 beta4^2 nu + 2436687987500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [45625000 beta4 nu + 667037500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [18750000 beta4^2 nu^3 + 3194875000 beta4^2 nu^2 + 166659022500 beta4^2 nu + 2434688152650 beta4^2 - 456375000 beta4 nu^3 - 44447882500 beta4 nu^2 - 812451492650 beta4 nu - 16231254351 beta4 < 0 \/ 5475000000 beta4^2 nu + 266559500000 beta4^2 - 2738250000 beta4 nu^2 - 200001780000 beta4 nu - 3998940300 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 2500 beta4 nu + 182550 beta4 - 60850 nu - 1217 = 0 ] /\ [17109375000000 beta4^2 nu^4 + 1916478125000000 beta4^2 nu^3 + 54820463250000000 beta4^2 nu^2 + 445913034928750000 beta4^2 nu + 8896347842362500 beta4^2 - 3422812500000 beta4 nu^5 - 333496031250000 beta4 nu^4 - 6106721928750000 beta4 nu^3 - 365603199075000 beta4 nu^2 - 7306730783250 beta4 nu - 48693763053 beta4 < 0 \/ 1332250000000000 beta4^2 nu^2 + 24366852500000000 beta4^2 nu + 486804150000000 beta4^2 - 832884375000000 beta4 nu^3 - 12210084937500000 beta4 nu^2 - 487403936250000 beta4 nu - 4870707825000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 45625000 beta4 nu + 667037500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 - 242735895250000 beta4^2 nu - 53251560590385000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 + 121301225610000 beta4 nu^2 + 26635503053502300 beta4 nu + 532661500590399 beta4 > 0 /\ 175000 beta4^2 nu^2 + 94907000 beta4^2 nu + 12391823070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 127760000 beta4^2 nu + 15989555100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1460100 beta4 - 182550 nu - 3651 = 0 ] /\ [2281250000000 beta4^2 nu^4 + 499776250000000 beta4^2 nu^3 - 12126800150000000 beta4^2 nu^2 - 2662820765414500000 beta4^2 nu - 53251560590385000 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 + 6060062148750000 beta4 nu^3 + 1331896453900725000 beta4 nu^2 + 53268578083022250 beta4 nu + 532661500590399 beta4 > 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 7296733432500 beta4^2 - 152125000 beta4 nu^3 - 33324502500 beta4 nu^2 - 1332797550 beta4 nu - 13327367 beta4 > 0 \/ [9125000 beta4 nu + 666307500 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 > 0 ] /\ [6250000 beta4^2 nu^3 + 4106625000 beta4^2 nu^2 + 766208007500 beta4^2 nu + 36485666267550 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 1825000000 beta4^2 nu + 532936500000 beta4^2 - 912750000 beta4 nu^2 - 333190260000 beta4 nu - 6663440100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 2500 beta4 nu + 912550 beta4 - 182550 nu - 3651 = 0 ] /\ [1140625000000 beta4^2 nu^4 + 416419375000000 beta4^2 nu^3 + 42573716800000000 beta4^2 nu^2 + 1332869995880250000 beta4^2 nu + 26640373762057500 beta4^2 - 380312500000 beta4 nu^5 - 111089281250000 beta4 nu^4 - 6088941558750000 beta4 nu^3 - 365069909675000 beta4 nu^2 - 7299621069250 beta4 nu - 48658216917 beta4 < 0 \/ 666125000000000 beta4^2 nu^2 + 72967332500000000 beta4^2 nu + 1459080200000000 beta4^2 - 499730625000000 beta4 nu^3 - 36510319462500000 beta4 nu^2 - 1459813101750000 beta4 nu - 14596132095000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [6843750000000 beta4^2 nu^4 + 1832391250000000 beta4^2 nu^3 + 60893833300000000 beta4^2 nu^2 - 2659901539068500000 beta4^2 nu - 53222373656655000 beta4^2 - 3422812500000 beta4 nu^5 - 916515093750000 beta4 nu^4 - 30473587203750000 beta4 nu^3 + 1329706034442675000 beta4 nu^2 + 53224780356606750 beta4 nu + 532369551288897 beta4 < 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [175000 beta4^2 nu^2 + 80307000 beta4^2 nu + 4930931070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [4562500000 beta4^2 nu^2 + 333245000000 beta4^2 nu + 6663075000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [1825000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3193750000 beta4^2 nu^2 + 266577750000 beta4^2 nu + 2436686527500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [63875000 beta4 nu + 667402500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [91250000 beta4^2 nu + 6663075000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 365000 beta4 - 60850 nu - 1217 = 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [1825000000 beta4^2 nu + 532936500000 beta4^2 - 304250000 beta4 nu^2 - 155483920000 beta4 nu - 3109556700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[5000 beta4 nu + 1460100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 beta4^2 nu + 1277550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 1277550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3650000000 beta4^2 nu + 666198000000 beta4^2 - 608500000 beta4 nu^2 - 177706340000 beta4 nu - 3553883400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1825200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [91250000 beta4^2 nu + 14656575000 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 \/ 91250000 beta4 nu + 14656575000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [1332250000000000 beta4^2 nu^2 + 24366852500000000 beta4^2 nu + 486804150000000 beta4^2 - 388679375000000 beta4 nu^3 - 4076691387500000 beta4 nu^2 - 162601240250000 beta4 nu - 1624457685000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [3193750000 beta4^2 nu^2 + 33434000000 beta4^2 nu + 667402500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 63875000 beta4 nu + 667402500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1665312500000000 beta4^2 nu^2 + 48693737500000000 beta4^2 nu + 973208625000000 beta4^2 - 444205000000000 beta4 nu^3 - 8133393550000000 beta4 nu^2 - 324802696000000 beta4 nu - 3246250140000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[91250000 beta4 nu + 2666325000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [10037500000 beta4^2 nu^2 + 333464000000 beta4^2 nu + 6665265000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 \/ [200750000 beta4 nu + 6665265000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 91250000 beta4 nu + 2666325000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 1369125000 beta4^2 nu^2 + 91646945000 beta4^2 nu + 1825349578800 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2281250000000 beta4^2 nu^4 + 291612187500000 beta4^2 nu^3 + 10654674850000000 beta4^2 nu^2 + 111356466038625000 beta4^2 nu + 2222869783365000 beta4^2 - 570468750000 beta4 nu^5 - 62523375000000 beta4 nu^4 - 1525013572500000 beta4 nu^3 - 91350803887500 beta4 nu^2 - 1826016160125 beta4 nu - 12170108313 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 164270000 beta4^2 nu + 13325785200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1825200 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [1368750000 beta4^2 nu^2 + 266504750000 beta4^2 nu + 9730754547500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 + 486670979750000 beta4^2 nu + 9729422115000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 3194125000 beta4^2 nu^2 + 466415257500 beta4^2 nu + 19460177027550 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3421875000000 beta4^2 nu^4 + 916195625000000 beta4^2 nu^3 + 72995651025000000 beta4^2 nu^2 + 1777808789215750000 beta4^2 nu + 35526984852922500 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 - 12180105663750000 beta4 nu^3 - 730206480525000 beta4 nu^2 - 14600130852750 beta4 nu - 97320877101 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 <= 0 ]] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [68437500000 beta4^2 nu^3 + 14159262500000 beta4^2 nu^2 + 912324882125000 beta4^2 nu + 17767141459485000 beta4^2 - 11409375000 beta4 nu^4 - 3748892437500 beta4 nu^3 - 304227703038750 beta4 nu^2 - 6669825861378225 beta4 nu - 133274856135663 beta4 < 0 \/ 54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [22812500000 beta4^2 nu^3 - 831287500000 beta4^2 nu^2 - 303952810125000 beta4^2 nu - 8880529036005000 beta4^2 - 11409375000 beta4 nu^4 + 415529437500 beta4 nu^3 + 152026357586250 beta4 nu^2 + 4444521389678025 beta4 nu + 88829620576587 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [5703125000000 beta4^2 nu^4 + 791479687500000 beta4^2 nu^3 + 33478623531250000 beta4^2 nu^2 + 445060710973125000 beta4^2 nu + 8887829100975000 beta4^2 - 1711406250000 beta4 nu^5 - 229214343750000 beta4 nu^4 - 9138414208125000 beta4 nu^3 - 111508775734350000 beta4 nu^2 - 4449392265814125 beta4 nu - 44457405667389 beta4 < 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 < 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [22812500000 beta4^2 nu^3 - 831287500000 beta4^2 nu^2 - 303952810125000 beta4^2 nu - 8880529036005000 beta4^2 - 11409375000 beta4 nu^4 + 415529437500 beta4 nu^3 + 152026357586250 beta4 nu^2 + 4444521389678025 beta4 nu + 88829620576587 beta4 > 0 \/ 50 nu - 3649 /= 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 125000 nu^3 - 9117500 nu^2 - 1332614850 nu - 26648649 < 0 ]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 375000 beta4 nu^3 + 36522500 beta4 nu^2 + 667585450 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [18750000 beta4 nu^4 - 911000000 beta4 nu^3 - 233198455000 beta4 nu^2 - 4872039344400 beta4 nu - 97347514797 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 375000 beta4 nu^3 + 36522500 beta4 nu^2 + 667585450 beta4 nu + 13337103 beta4 > 0 /\ 187500 beta4 nu^3 + 25105000 beta4 nu^2 + 1000191475 beta4 nu + 12176775039 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18750000 beta4 nu^4 - 911000000 beta4 nu^3 - 233198455000 beta4 nu^2 - 4872039344400 beta4 nu - 97347514797 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 1250 nu^2 + 136925 nu + 3333363 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 3333362500000 beta4^2 nu^2 + 60917186000000 beta4^2 nu + 1217010740000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 + 182600 nu + 3651 > 0 \/ 50 nu - 3649 /= 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 31032000 beta4^2 nu + 899889320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 99955250000 beta4^2 nu + 2433354990000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 50 nu - 3649 /= 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 136925 nu + 3333363 > 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 187500 beta4 nu^3 + 25105000 beta4 nu^2 + 1000191475 beta4 nu + 12176775039 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [375000 beta4 nu^3 + 36522500 beta4 nu^2 + 667585450 beta4 nu + 13337103 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [50 beta4 nu + beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 <= 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 6250000 beta4 nu^4 + 2738000000 beta4 nu^3 + 366533015000 beta4 nu^2 + 14602795535200 beta4 nu + 291909319401 beta4 > 0 /\ 125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 15972500 beta4 nu^2 + 333701325 beta4 nu - 36463676112 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 266504750000 beta4^2 nu + 9730754547500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ [91250000000 beta4^2 nu^3 + 36642350000000 beta4^2 nu^2 + 4621042459500000 beta4^2 nu + 177581412442980000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 1338212037765000 beta4 nu^2 - 53314806499015200 beta4 nu - 1065760925133051 beta4 < 0 \/ 36500000 beta4 nu + 6661980000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [9125000000000 beta4^2 nu^4 + 2498698750000000 beta4^2 nu^3 + 206815181275000000 beta4^2 nu^2 + 5332939796604500000 beta4^2 nu + 106576089847710000 beta4^2 - 3422812500000 beta4 nu^5 - 833226656250000 beta4 nu^4 - 54787147878750000 beta4 nu^3 - 890973396277575000 beta4 nu^2 - 35573217934163250 beta4 nu - 355513164049953 beta4 < 0 \/ [73000000 beta4 nu + 3998210000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1140625000000 beta4^2 nu^4 + 208255312500000 beta4^2 nu^3 + 3051687893750000 beta4^2 nu^2 - 443600697979125000 beta4^2 nu - 8873232968880000 beta4^2 - 570468750000 beta4 nu^5 - 104167593750000 beta4 nu^4 - 1528345110000000 beta4 nu^3 + 221830590968737500 beta4 nu^2 + 8875054319974875 beta4 nu + 88756639916112 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 1332797500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 + 45675 nu - 3329712 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 1022140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1533140 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1533140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 15972500 beta4 nu^2 + 333701325 beta4 nu - 36463676112 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 + 166987575 beta4 nu - 24310227312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 6250000 beta4 nu^4 + 2738000000 beta4 nu^3 + 366533015000 beta4 nu^2 + 14602795535200 beta4 nu + 291909319401 beta4 > 0 /\ 125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 15972500 beta4 nu^2 + 333701325 beta4 nu - 36463676112 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 > 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 <= 0 /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 13325237500000 beta4^2 nu^2 + 973075454750000 beta4^2 nu + 19456179365000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 16655862500000 beta4^2 nu^2 + 1459479929750000 beta4^2 nu + 29182936615000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2281250000 beta4^2 nu^2 + 399766250000 beta4^2 nu + 9733419412500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 547600 nu + 26655951 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 6250000 beta4 nu^4 + 2738000000 beta4 nu^3 + 366533015000 beta4 nu^2 + 14602795535200 beta4 nu + 291909319401 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 999917600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 <= 0 /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 13325237500000 beta4^2 nu^2 + 973075454750000 beta4^2 nu + 19456179365000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 16655862500000 beta4^2 nu^2 + 1459479929750000 beta4^2 nu + 29182936615000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2281250000 beta4^2 nu^2 + 399766250000 beta4^2 nu + 9733419412500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 25 nu - 912 <= 0 /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 18290000 beta4^2 nu + 365400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 365400 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 620700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 985600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 2664682500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4^2 nu + 1332797500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [2281250000 beta4^2 nu^2 + 33397500000 beta4^2 nu + 667037500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [456250000 beta4^2 nu^2 + 99937000000 beta4^2 nu + 1998557500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 33368300000 beta4^2 nu + 666745500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1095000000 beta4^2 nu^2 + 66656300000 beta4^2 nu + 1332688000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5000 nu^2 - 91050 nu - 1823 > 0 \/ 100 nu - 1823 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2281250000 beta4^2 nu^2 + 33397500000 beta4^2 nu + 667037500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 45625000 beta4 nu + 667037500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 25 nu - 912 <= 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 /\ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 18290000 beta4^2 nu + 365400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 365400 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 999917600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 3750 beta4 nu^2 + 228275 beta4 nu + 3335189 beta4 < 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 < 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 2664682500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 2664682500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [27375000 beta4^2 nu + 1332797500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 <= 0 /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 13325237500000 beta4^2 nu^2 + 973075454750000 beta4^2 nu + 19456179365000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 16655862500000 beta4^2 nu^2 + 1459479929750000 beta4^2 nu + 29182936615000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2281250000 beta4^2 nu^2 + 399766250000 beta4^2 nu + 9733419412500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4 nu^3 + 45632500 beta4 nu^2 + 3998575150 beta4 nu + 79953251 beta4 < 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2281250000 beta4^2 nu^2 + 33397500000 beta4^2 nu + 667037500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [456250000 beta4^2 nu^2 + 99937000000 beta4^2 nu + 1998557500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2281250000 beta4^2 nu^2 + 33397500000 beta4^2 nu + 667037500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 6663987500000 beta4^2 nu^2 + 243402129750000 beta4^2 nu + 4865377365000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 + 486670979750000 beta4^2 nu + 9729422115000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 199910500000 beta4^2 nu + 4866709980000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [25000000 beta4^2 nu^3 + 3651500000 beta4^2 nu^2 + 133371030000 beta4^2 nu + 2665960200 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 109520000 beta4^2 nu + 5331190200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [50000000 beta4^2 nu^3 + 5478000000 beta4^2 nu^2 + 133444060000 beta4^2 nu + 2666690400 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 < 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 2432688682500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [2682750000 beta4^2 nu + 65333905000 beta4^2 - 1916775000 beta4 nu^2 - 93359721000 beta4 nu - 1866427710 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 <= 0 /\ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 >= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 <= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [2445500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1022000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2682750000 beta4^2 nu + 65333905000 beta4^2 - 1916775000 beta4 nu^2 - 93359721000 beta4 nu - 1866427710 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1022000 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [3577000000 beta4^2 nu + 65351790000 beta4^2 - 2555700000 beta4 nu^2 - 93385278000 beta4 nu - 1866683280 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 63875000 beta4^2 nu + 1866427500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 63875000 beta4 nu + 1866427500 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ] /\ [326401250000 beta4^2 - 279849150000 beta4 nu - 5596983000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1788500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 1788500 beta4 - 547650 nu - 10953 = 0 ]] \/ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 3042500 nu^2 - 444326700 nu - 8885317 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [1596875000 beta4^2 nu^2 + 81664187500 beta4^2 nu + 852607332500 beta4^2 - 684562500 beta4 nu^3 - 25027605000 beta4 nu^2 - 1000282725 beta4 nu - 10000089 beta4 < 0 \/ 63875000 beta4 nu + 933852500 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 25 nu - 912 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [95812500000 beta4^2 nu^3 + 16325811250000 beta4^2 nu^2 + 681432667475000 beta4^2 nu + 13622123791500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ 1788500000 beta4^2 nu + 195876520000 beta4^2 - 1277850000 beta4 nu^2 - 186617214000 beta4 nu - 3731833140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 38325000 beta4 nu + 3731066500 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ] /\ [489601875000000 beta4^2 nu^2 + 23846875325000000 beta4^2 nu + 476741665750000 beta4^2 - 466415250000000 beta4 nu^3 - 17052141540000000 beta4 nu^2 - 681525963300000 beta4 nu - 6813393972000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 3193750000 beta4^2 nu^2 + 326529000000 beta4^2 nu + 6814326802500 beta4^2 - 1369125000 beta4 nu^3 - 100028272500 beta4 nu^2 - 3999487950 beta4 nu - 39989403 beta4 < 0 \/ 63875000 beta4 nu + 1866427500 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2445500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1350500 beta4 - 182550 nu - 3651 = 0 ] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2682750000 beta4^2 nu + 65333905000 beta4^2 - 1916775000 beta4 nu^2 - 93359721000 beta4 nu - 1866427710 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5250 beta4^2 nu + 255605 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5250 beta4 nu + 255605 beta4 - 182550 nu - 3651 = 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 638750 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7984375000 beta4^2 nu^3 + 479062500 beta4^2 nu^2 - 10637174012500 beta4^2 nu - 212743608000 beta4^2 - 5704687500 beta4 nu^4 - 456375000 beta4 nu^3 + 7600056230625 beta4 nu^2 + 304002614325 beta4 nu + 3040027056 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 639012500 beta4^2 nu^2 + 17511336500 beta4^2 nu + 349971160 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 34997112500 beta4^2 nu + 426187030500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 11682737500 beta4^2 nu - 425253944500 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 100 nu - 1823 = 0 ]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]]] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[255500 beta4 - 60850 nu - 1217 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [6022500000 beta4^2 nu^2 + 246707150000 beta4^2 nu + 2436287984000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 /\ 1916250000 beta4^2 nu^2 - 93180850000 beta4^2 nu - 3405763133500 beta4^2 - 1369125000 beta4 nu^3 + 66548602500 beta4 nu^2 + 2434685962050 beta4 nu + 48667088847 beta4 < 0 /\ 1500000 beta4^2 nu^2 + 85835000 beta4^2 nu + 1200741100 beta4^2 - 9127500 beta4 nu^2 - 222467600 beta4 nu - 4445701 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [95812500000 beta4^2 nu^3 + 9331498750000 beta4^2 nu^2 + 170568082475000 beta4^2 nu + 3407629816500 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [95812500000 beta4^2 nu^3 - 4657126250000 beta4^2 nu^2 - 170381337525000 beta4^2 nu - 3405763133500 beta4^2 - 68456250000 beta4 nu^4 + 3326061000000 beta4 nu^3 + 121800846705000 beta4 nu^2 + 4868040404400 beta4 nu + 48667088847 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [239531250000 beta4^2 nu^3 + 9340121875000 beta4^2 nu^2 + 85470786187500 beta4^2 nu + 1705681591250 beta4^2 - 68456250000 beta4 nu^4 - 1671245250000 beta4 nu^3 - 100110420000 beta4 nu^2 - 2001113100 beta4 nu - 13337103 beta4 < 0 \/ 652802500000000 beta4^2 nu^2 + 11939757725000000 beta4^2 nu + 238534033500000 beta4^2 - 583019062500000 beta4 nu^3 - 8547059456250000 beta4 nu^2 - 341182755375000 beta4 nu - 3409495477500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 31937500 beta4 nu + 466926250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [262500 beta4^2 nu^2 + 25560500 beta4^2 nu + 466798605 beta4^2 - 9127500 beta4 nu^2 - 222467600 beta4 nu - 4445701 beta4 < 0 \/ 2682750000 beta4^2 nu + 130614155000 beta4^2 - 1916775000 beta4 nu^2 - 140001246000 beta4 nu - 2799258210 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 127785 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 3042500 nu^2 - 444326700 nu - 8885317 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 25 nu - 912 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [1596875000 beta4^2 nu^2 + 81664187500 beta4^2 nu + 852607332500 beta4^2 - 684562500 beta4 nu^3 - 25027605000 beta4 nu^2 - 1000282725 beta4 nu - 10000089 beta4 < 0 \/ 63875000 beta4 nu + 933852500 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]]]] \/ [10128750000 beta4^2 nu^2 + 446708900000 beta4^2 nu + 4871642626500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 6022500000 beta4^2 nu^2 + 246707150000 beta4^2 nu + 2436287984000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 /\ 2250000 beta4^2 nu^2 + 147915000 beta4^2 nu + 2267782400 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 38325000 beta4^2 nu + 933341500 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [383250000000 beta4^2 nu^3 + 30331682500000 beta4^2 nu^2 + 511797619900000 beta4^2 nu + 10223822791000 beta4^2 - 68456250000 beta4 nu^4 - 11665857750000 beta4 nu^3 - 243902024670000 beta4 nu^2 - 9742084148100 beta4 nu - 97374189003 beta4 < 0 \/ 2682750000 beta4^2 nu + 130614155000 beta4^2 - 1916775000 beta4 nu^2 - 140001246000 beta4 nu - 2799258210 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 51100000 beta4 nu + 2798747000 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ] /\ [652802500000000 beta4^2 nu^2 + 11939757725000000 beta4^2 nu + 238534033500000 beta4^2 - 583019062500000 beta4 nu^3 - 8547059456250000 beta4 nu^2 - 341182755375000 beta4 nu - 3409495477500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 11497500000 beta4^2 nu^2 + 420118650000 beta4^2 nu + 3412296524000 beta4^2 - 4107375000 beta4 nu^3 - 100192567500 beta4 nu^2 - 4002773850 beta4 nu - 40011309 beta4 < 0 \/ 76650000 beta4 nu + 934108000 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]] \/ [1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 279823600000 beta4^2 nu + 13621190961000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2555000000 beta4^2 nu^2 + 466389700000 beta4^2 nu + 13624921772000 beta4^2 - 1369125000 beta4 nu^3 - 199974397500 beta4 nu^2 - 7997332950 beta4 nu - 79967853 beta4 < 0 \/ 51100000 beta4 nu + 1866172000 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 25 nu - 912 = 0 ]]]] \/ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 2797980500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 /\ 365000000 beta4^2 nu^2 + 113255850000 beta4^2 nu + 7296333721000 beta4^2 - 152125000 beta4 nu^3 - 33324502500 beta4 nu^2 - 1332797550 beta4 nu - 13327367 beta4 > 0 /\ 250000 beta4^2 nu^2 + 122285000 beta4^2 nu + 14790420600 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [63875000000 beta4^2 nu^3 + 25649645000000 beta4^2 nu^2 + 2553949971650000 beta4^2 nu + 51068740086000 beta4^2 - 22818750000 beta4 nu^4 - 8330669250000 beta4 nu^3 - 730106497890000 beta4 nu^2 - 29194263842700 beta4 nu - 291909319401 beta4 < 0 \/ 894250000 beta4^2 nu + 261138885000 beta4^2 - 638925000 beta4 nu^2 - 233233182000 beta4 nu - 4664408070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 25550000 beta4 nu + 4663386000 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 35753992925000000 beta4^2 nu + 714949298000000 beta4^2 - 349811437500000 beta4 nu^3 - 25557223623750000 beta4 nu^2 - 1021869171225000 beta4 nu - 10217292466500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 2555000000 beta4^2 nu^2 + 699533450000 beta4^2 nu + 30649078397000 beta4^2 - 1369125000 beta4 nu^3 - 299920522500 beta4 nu^2 - 11995177950 beta4 nu - 119946303 beta4 < 0 \/ 51100000 beta4 nu + 2798747000 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]] \/ [95812500000 beta4^2 nu^3 + 2337186250000 beta4^2 nu^2 - 510491440025000 beta4^2 nu - 12434441200408500 beta4^2 - 68456250000 beta4 nu^4 - 1671245250000 beta4 nu^3 + 364703245830000 beta4 nu^2 + 8891471801886900 beta4 nu + 177683541380397 beta4 < 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 /\ 2250000 beta4^2 nu^2 + 147915000 beta4^2 nu + 2267782400 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [6022500000 beta4^2 nu^2 + 246707150000 beta4^2 nu + 2436287984000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [40150000 beta4 nu + 666928000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [10128750000 beta4^2 nu^2 + 446708900000 beta4^2 nu + 4871642626500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4790625000000 beta4^2 nu^4 + 116955125000000 beta4^2 nu^3 - 25522234815000000 beta4^2 nu^2 - 622232551460450000 beta4^2 nu - 12434441200408500 beta4^2 - 3422812500000 beta4 nu^5 - 83630718750000 beta4 nu^4 + 18233491046250000 beta4 nu^3 + 444938293340175000 beta4 nu^2 + 17775648870906750 beta4 nu + 177683541380397 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [13125000 beta4^2 nu^3 + 2236412500 beta4^2 nu^2 + 116661315750 beta4^2 nu + 1704281706855 beta4^2 - 456375000 beta4 nu^3 - 44447882500 beta4 nu^2 - 812451492650 beta4 nu - 16231254351 beta4 < 0 \/ 2682750000 beta4^2 nu + 130614155000 beta4^2 - 1916775000 beta4 nu^2 - 140001246000 beta4 nu - 2799258210 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 127785 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [958125000 beta4^2 nu^2 - 11618862500 beta4^2 nu - 851207448000 beta4^2 - 684562500 beta4 nu^3 + 8287770000 beta4 nu^2 + 608337926025 beta4 nu + 12163437936 beta4 < 0 \/ 1250 nu^2 + 45675 nu - 3329712 > 0 ]]] /\ [11976562500000 beta4^2 nu^4 + 1341534687500000 beta4^2 nu^3 + 38374324275000000 beta4^2 nu^2 + 312139124450125000 beta4^2 nu + 6227443489653750 beta4^2 - 3422812500000 beta4 nu^5 - 333496031250000 beta4 nu^4 - 6106721928750000 beta4 nu^3 - 365603199075000 beta4 nu^2 - 7306730783250 beta4 nu - 48693763053 beta4 < 0 \/ 652802500000000 beta4^2 nu^2 + 11939757725000000 beta4^2 nu + 238534033500000 beta4^2 - 583019062500000 beta4 nu^3 - 8547059456250000 beta4 nu^2 - 341182755375000 beta4 nu - 3409495477500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 31937500 beta4 nu + 466926250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [31937500000 beta4^2 nu^3 + 6996228750000 beta4^2 nu^2 - 169915126675000 beta4^2 nu - 37276092413269500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 + 121301225610000 beta4 nu^2 + 26635503053502300 beta4 nu + 532661500590399 beta4 > 0 /\ 250000 beta4^2 nu^2 + 122285000 beta4^2 nu + 14790420600 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [365000000 beta4^2 nu^2 + 113255850000 beta4^2 nu + 7296333721000 beta4^2 - 152125000 beta4 nu^3 - 33324502500 beta4 nu^2 - 1332797550 beta4 nu - 13327367 beta4 > 0 \/ [7300000 beta4 nu + 666271000 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1596875000000 beta4^2 nu^4 + 349843375000000 beta4^2 nu^3 - 8488760105000000 beta4^2 nu^2 - 1863974535790150000 beta4^2 nu - 37276092413269500 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 + 6060062148750000 beta4 nu^3 + 1331896453900725000 beta4 nu^2 + 53268578083022250 beta4 nu + 532661500590399 beta4 > 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 2797980500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 > 0 ] /\ [4375000 beta4^2 nu^3 + 2874637500 beta4^2 nu^2 + 536345605250 beta4^2 nu + 25539966387285 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 894250000 beta4^2 nu + 261138885000 beta4^2 - 638925000 beta4 nu^2 - 233233182000 beta4 nu - 4664408070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 638785 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 + 58298712500 beta4^2 nu - 2551758216000 beta4^2 - 228187500 beta4 nu^3 - 41657910000 beta4 nu^2 + 1822350738675 beta4 nu + 36463676112 beta4 < 0 \/ 1250 nu^2 + 45675 nu - 3329712 > 0 ]]] /\ [798437500000 beta4^2 nu^4 + 291493562500000 beta4^2 nu^3 + 29801601760000000 beta4^2 nu^2 + 933008997116175000 beta4^2 nu + 18648261633440250 beta4^2 - 380312500000 beta4 nu^5 - 111089281250000 beta4 nu^4 - 6088941558750000 beta4 nu^3 - 365069909675000 beta4 nu^2 - 7299621069250 beta4 nu - 48658216917 beta4 < 0 \/ 326401250000000 beta4^2 nu^2 + 35753992925000000 beta4^2 nu + 714949298000000 beta4^2 - 349811437500000 beta4 nu^3 - 25557223623750000 beta4 nu^2 - 1021869171225000 beta4 nu - 10217292466500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 6387500 beta4 nu + 466415250 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [4790625000000 beta4^2 nu^4 + 1282673875000000 beta4^2 nu^3 + 42625683310000000 beta4^2 nu^2 - 1861931077347950000 beta4^2 nu - 37255661559658500 beta4^2 - 3422812500000 beta4 nu^5 - 916515093750000 beta4 nu^4 - 30473587203750000 beta4 nu^3 + 1329706034442675000 beta4 nu^2 + 53224780356606750 beta4 nu + 532369551288897 beta4 < 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 4931040600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2920000000 beta4^2 nu^2 + 246583050000 beta4^2 nu + 2436286743000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [58400000 beta4 nu + 667293000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [85775000 beta4^2 nu + 6263290500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ [4288750000 beta4^2 nu^2 + 313250300000 beta4^2 nu + 6263290500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [1715500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [1149750000 beta4^2 nu + 407691495000 beta4^2 - 212975000 beta4 nu^2 - 135491044000 beta4 nu - 2709735690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1750 beta4^2 nu + 1113285 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1750 beta4 nu + 1113285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3285000000 beta4^2 nu + 563607450000 beta4^2 - 608500000 beta4 nu^2 - 164380190000 beta4 nu - 3287360400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [85775000 beta4^2 nu + 13457440500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 \/ 85775000 beta4 nu + 13457440500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [410625000 beta4^2 nu^2 + 15004237500 beta4^2 nu - 1093810392000 beta4^2 - 76062500 beta4 nu^3 - 2780845000 beta4 nu^2 + 202557388725 beta4 nu + 4052259504 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 1250 nu^2 + 45675 nu - 3329712 > 0 ]]]] /\ [1019171250000000 beta4^2 nu^2 + 15358311225000000 beta4^2 nu + 306758556000000 beta4^2 - 338706312500000 beta4 nu^3 - 2857681816250000 beta4 nu^2 - 113900825075000 beta4 nu - 1137653425500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2783125000 beta4^2 nu^2 + 23425700000 beta4^2 nu + 467400750 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 55662500 beta4 nu + 467400750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1408854375000000 beta4^2 nu^2 + 43820766675000000 beta4^2 nu + 875851791750000 beta4^2 - 410889625000000 beta4 nu^3 - 8131394627500000 beta4 nu^2 - 324762717550000 beta4 nu - 3245983617000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [9216250000 beta4^2 nu^2 + 313447400000 beta4^2 nu + 6265261500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 \/ [184325000 beta4 nu + 6265261500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu + 851674246500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 958387500 beta4^2 nu^2 + 64152861500 beta4^2 nu + 1277744705160 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu + 851674246500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu - 3329712 > 0 ]]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [1596875000000 beta4^2 nu^4 + 204128531250000 beta4^2 nu^3 + 7458272395000000 beta4^2 nu^2 + 77949526227037500 beta4^2 nu + 1556008848355500 beta4^2 - 570468750000 beta4 nu^5 - 62523375000000 beta4 nu^4 - 1525013572500000 beta4 nu^3 - 91350803887500 beta4 nu^2 - 1826016160125 beta4 nu - 12170108313 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [21900000 beta4 nu + 1332688000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 6996228750000 beta4^2 nu^2 + 340669685825000 beta4^2 nu + 6810595480500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 6810595480500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 2235887500 beta4^2 nu^2 + 326490680250 beta4^2 nu + 13622123919285 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu - 3329712 > 0 ]]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2395312500000 beta4^2 nu^4 + 641336937500000 beta4^2 nu^3 + 51096955717500000 beta4^2 nu^2 + 1244466152451025000 beta4^2 nu + 24868889397045750 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 - 12180105663750000 beta4 nu^3 - 730206480525000 beta4 nu^2 - 14600130852750 beta4 nu - 97320877101 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 6810595480500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [350 nu - 18243 < 0 \/ [2500 nu^2 + 182600 nu + 3651 < 0 /\ 350 nu - 18243 = 0 ]] /\ [3500 beta4^2 nu + 1241070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [17500000 beta4^2 nu^3 + 3194800000 beta4^2 nu^2 + 140014021000 beta4^2 nu + 2799002640 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 89439000 beta4^2 nu + 4664663640 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 1277640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 nu^3 + 2285000 nu^2 - 166439925 nu - 3329712 > 0 /\ 50 nu - 3649 = 0 ]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [35000000 beta4^2 nu^3 + 4473350000 beta4^2 nu^2 + 140065142000 beta4^2 nu + 2799513780 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [14000 beta4 nu + 766780 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [95812500000 beta4^2 nu^3 + 9331498750000 beta4^2 nu^2 + 170568082475000 beta4^2 nu + 3407629816500 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 > 0 /\ 95812500000 beta4^2 nu^3 + 2337186250000 beta4^2 nu^2 - 510491440025000 beta4^2 nu - 12434441200408500 beta4^2 - 68456250000 beta4 nu^4 - 1671245250000 beta4 nu^3 + 364703245830000 beta4 nu^2 + 8891471801886900 beta4 nu + 177683541380397 beta4 < 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 /\ 2250000 beta4^2 nu^2 + 147915000 beta4^2 nu + 2267782400 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [4790625000000 beta4^2 nu^4 + 116955125000000 beta4^2 nu^3 - 25522234815000000 beta4^2 nu^2 - 622232551460450000 beta4^2 nu - 12434441200408500 beta4^2 - 3422812500000 beta4 nu^5 - 83630718750000 beta4 nu^4 + 18233491046250000 beta4 nu^3 + 444938293340175000 beta4 nu^2 + 17775648870906750 beta4 nu + 177683541380397 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [10128750000 beta4^2 nu^2 + 446708900000 beta4^2 nu + 4871642626500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [6022500000 beta4^2 nu^2 + 246707150000 beta4^2 nu + 2436287984000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [40150000 beta4 nu + 666928000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [13125000 beta4^2 nu^3 + 2236412500 beta4^2 nu^2 + 116661315750 beta4^2 nu + 1704281706855 beta4^2 - 456375000 beta4 nu^3 - 44447882500 beta4 nu^2 - 812451492650 beta4 nu - 16231254351 beta4 < 0 \/ 2682750000 beta4^2 nu + 130614155000 beta4^2 - 1916775000 beta4 nu^2 - 140001246000 beta4 nu - 2799258210 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 127785 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [5748750000 beta4^2 nu^2 + 229950000 beta4^2 nu - 3403896450500 beta4^2 - 4107375000 beta4 nu^3 - 246442500 beta4 nu^2 + 2432017446150 beta4 nu + 48640414641 beta4 > 0 \/ 7500 nu^2 + 365300 nu - 13315197 < 0 ]]] /\ [11976562500000 beta4^2 nu^4 + 1341534687500000 beta4^2 nu^3 + 38374324275000000 beta4^2 nu^2 + 312139124450125000 beta4^2 nu + 6227443489653750 beta4^2 - 3422812500000 beta4 nu^5 - 333496031250000 beta4 nu^4 - 6106721928750000 beta4 nu^3 - 365603199075000 beta4 nu^2 - 7306730783250 beta4 nu - 48693763053 beta4 < 0 \/ 652802500000000 beta4^2 nu^2 + 11939757725000000 beta4^2 nu + 238534033500000 beta4^2 - 583019062500000 beta4 nu^3 - 8547059456250000 beta4 nu^2 - 341182755375000 beta4 nu - 3409495477500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 31937500 beta4 nu + 466926250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [31937500000 beta4^2 nu^3 + 9327666250000 beta4^2 nu^2 + 510957880825000 beta4^2 nu + 10215426805500 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 /\ 31937500000 beta4^2 nu^3 + 6996228750000 beta4^2 nu^2 - 169915126675000 beta4^2 nu - 37276092413269500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 + 121301225610000 beta4 nu^2 + 26635503053502300 beta4 nu + 532661500590399 beta4 > 0 /\ 250000 beta4^2 nu^2 + 122285000 beta4^2 nu + 14790420600 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [1596875000000 beta4^2 nu^4 + 349843375000000 beta4^2 nu^3 - 8488760105000000 beta4^2 nu^2 - 1863974535790150000 beta4^2 nu - 37276092413269500 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 + 6060062148750000 beta4 nu^3 + 1331896453900725000 beta4 nu^2 + 53268578083022250 beta4 nu + 532661500590399 beta4 > 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 2797980500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 > 0 ] /\ [365000000 beta4^2 nu^2 + 113255850000 beta4^2 nu + 7296333721000 beta4^2 - 152125000 beta4 nu^3 - 33324502500 beta4 nu^2 - 1332797550 beta4 nu - 13327367 beta4 > 0 \/ [7300000 beta4 nu + 666271000 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [4375000 beta4^2 nu^3 + 2874637500 beta4^2 nu^2 + 536345605250 beta4^2 nu + 25539966387285 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 894250000 beta4^2 nu + 261138885000 beta4^2 - 638925000 beta4 nu^2 - 233233182000 beta4 nu - 4664408070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 638785 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1916250000 beta4^2 nu^2 + 373106650000 beta4^2 nu - 10204234883500 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 + 7285404562050 beta4 nu + 145814722347 beta4 > 0 \/ 7500 nu^2 + 365300 nu - 13315197 < 0 ]]] /\ [798437500000 beta4^2 nu^4 + 291493562500000 beta4^2 nu^3 + 29801601760000000 beta4^2 nu^2 + 933008997116175000 beta4^2 nu + 18648261633440250 beta4^2 - 380312500000 beta4 nu^5 - 111089281250000 beta4 nu^4 - 6088941558750000 beta4 nu^3 - 365069909675000 beta4 nu^2 - 7299621069250 beta4 nu - 48658216917 beta4 < 0 \/ 326401250000000 beta4^2 nu^2 + 35753992925000000 beta4^2 nu + 714949298000000 beta4^2 - 349811437500000 beta4 nu^3 - 25557223623750000 beta4 nu^2 - 1021869171225000 beta4 nu - 10217292466500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 6387500 beta4 nu + 466415250 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [4790625000000 beta4^2 nu^4 + 1282673875000000 beta4^2 nu^3 + 42625683310000000 beta4^2 nu^2 - 1861931077347950000 beta4^2 nu - 37255661559658500 beta4^2 - 3422812500000 beta4 nu^5 - 916515093750000 beta4 nu^4 - 30473587203750000 beta4 nu^3 + 1329706034442675000 beta4 nu^2 + 53224780356606750 beta4 nu + 532369551288897 beta4 < 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 4931040600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ [4288750000 beta4^2 nu^2 + 313250300000 beta4^2 nu + 6263290500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [1715500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2920000000 beta4^2 nu^2 + 246583050000 beta4^2 nu + 2436286743000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [58400000 beta4 nu + 667293000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [85775000 beta4^2 nu + 6263290500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [1149750000 beta4^2 nu + 407691495000 beta4^2 - 212975000 beta4 nu^2 - 135491044000 beta4 nu - 2709735690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1750 beta4^2 nu + 1113285 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1750 beta4 nu + 1113285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3285000000 beta4^2 nu + 563607450000 beta4^2 - 608500000 beta4 nu^2 - 164380190000 beta4 nu - 3287360400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [85775000 beta4^2 nu + 13457440500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 \/ 85775000 beta4 nu + 13457440500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [2463750000 beta4^2 nu^2 + 120001050000 beta4^2 nu - 4374042214500 beta4^2 - 456375000 beta4 nu^3 - 22237632500 beta4 nu^2 + 809785167350 beta4 nu + 16204594749 beta4 > 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 7500 nu^2 + 365300 nu - 13315197 < 0 ]]]] /\ [1019171250000000 beta4^2 nu^2 + 15358311225000000 beta4^2 nu + 306758556000000 beta4^2 - 338706312500000 beta4 nu^3 - 2857681816250000 beta4 nu^2 - 113900825075000 beta4 nu - 1137653425500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2783125000 beta4^2 nu^2 + 23425700000 beta4^2 nu + 467400750 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 55662500 beta4 nu + 467400750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1408854375000000 beta4^2 nu^2 + 43820766675000000 beta4^2 nu + 875851791750000 beta4^2 - 410889625000000 beta4 nu^3 - 8131394627500000 beta4 nu^2 - 324762717550000 beta4 nu - 3245983617000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [9216250000 beta4^2 nu^2 + 313447400000 beta4^2 nu + 6265261500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 \/ [184325000 beta4 nu + 6265261500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu + 851674246500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 958387500 beta4^2 nu^2 + 64152861500 beta4^2 nu + 1277744705160 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu + 851674246500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [958125000 beta4^2 nu^2 + 11695512500 beta4^2 nu - 850741160500 beta4^2 - 684562500 beta4 nu^3 - 8369917500 beta4 nu^2 + 607671618525 beta4 nu + 12156774861 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 365300 nu - 13315197 < 0 ]]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [1596875000000 beta4^2 nu^4 + 204128531250000 beta4^2 nu^3 + 7458272395000000 beta4^2 nu^2 + 77949526227037500 beta4^2 nu + 1556008848355500 beta4^2 - 570468750000 beta4 nu^5 - 62523375000000 beta4 nu^4 - 1525013572500000 beta4 nu^3 - 91350803887500 beta4 nu^2 - 1826016160125 beta4 nu - 12170108313 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [31937500000 beta4^2 nu^3 + 6996228750000 beta4^2 nu^2 + 340669685825000 beta4^2 nu + 6810595480500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 6810595480500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 ] /\ [1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [21900000 beta4 nu + 1332688000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 2235887500 beta4^2 nu^2 + 326490680250 beta4^2 nu + 13622123919285 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1916250000 beta4^2 nu^2 + 233220400000 beta4^2 nu - 6803133858500 beta4^2 - 1369125000 beta4 nu^3 - 166659022500 beta4 nu^2 + 4857380032050 beta4 nu + 97214253297 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 365300 nu - 13315197 < 0 ]]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2395312500000 beta4^2 nu^4 + 641336937500000 beta4^2 nu^3 + 51096955717500000 beta4^2 nu^2 + 1244466152451025000 beta4^2 nu + 24868889397045750 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 - 12180105663750000 beta4 nu^3 - 730206480525000 beta4 nu^2 - 14600130852750 beta4 nu - 97320877101 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 6810595480500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [17500000 beta4^2 nu^3 + 3194800000 beta4^2 nu^2 + 140014021000 beta4^2 nu + 2799002640 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3500 beta4^2 nu + 1241070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 89439000 beta4^2 nu + 4664663640 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 1277640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [35000000 beta4^2 nu^3 + 4473350000 beta4^2 nu^2 + 140065142000 beta4^2 nu + 2799513780 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [14000 beta4 nu + 766780 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [85775000 beta4^2 nu + 1715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [1149750000 beta4^2 nu + 323759745000 beta4^2 - 212975000 beta4 nu^2 - 119943869000 beta4 nu - 2398792190 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1750 beta4^2 nu + 985535 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1750 beta4 nu + 985535 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3285000000 beta4^2 nu + 323802450000 beta4^2 - 608500000 beta4 nu^2 - 119959690000 beta4 nu - 2398950400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [85775000 beta4^2 nu + 7195865500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 85775000 beta4 nu + 7195865500 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [407668500000 beta4^2 - 135482525000 beta4 nu - 2709650500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1241000 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1113250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1113250 beta4 - 182550 nu - 3651 = 0 ]]] /\ [563541750000 beta4^2 - 164355850000 beta4 nu - 3287117000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1715500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [3686500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 3686500 beta4 - 547650 nu - 10953 = 0 ]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1715500 beta4 - 182550 nu - 3651 = 0 ] /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]]] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1095000000 beta4^2 nu^2 + 113285050000 beta4^2 nu + 2433621513000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 3403898494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 985700 beta4 - 182550 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 170194899175000 beta4^2 nu - 3403898494500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1277762500 beta4^2 nu^2 + 69994230250 beta4^2 nu + 1399373535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 93295825000 beta4^2 nu + 1703814908250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1916250000 beta4^2 nu^2 + 93334150000 beta4^2 nu - 3402032833500 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 150 nu - 3647 = 0 ]]]] \/ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 <= 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 >= 0 /\ 50 nu - 3649 = 0 ]]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1022000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 <= 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 <= 0 \/ 50 nu - 3649 /= 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1125000 beta4 nu^3 + 67500 beta4 nu^2 - 666123650 beta4 nu - 13322491 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 >= 0 \/ 50 nu - 3649 /= 0 ] /\ [2682750000 beta4^2 nu + 65333905000 beta4^2 - 1916775000 beta4 nu^2 - 93359721000 beta4 nu - 1866427710 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 <= 0 \/ 50 nu - 3649 /= 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1125000 beta4 nu^3 + 67500 beta4 nu^2 - 666123650 beta4 nu - 13322491 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]] \/ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 >= 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 182400 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 >= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 3042500 nu^2 - 444326700 nu - 8885317 = 0 ]]] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 <= 0 /\ 50 nu - 3649 = 0 ]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1596875000 beta4^2 nu^2 + 81664187500 beta4^2 nu + 852607332500 beta4^2 - 684562500 beta4 nu^3 - 25027605000 beta4 nu^2 - 1000282725 beta4 nu - 10000089 beta4 < 0 \/ 63875000 beta4 nu + 933852500 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]]]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 620700 beta4 - 182550 nu - 3651 = 0 ] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 45575 nu - 912 <= 0 ]]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 58324262500 beta4^2 nu + 852140789500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1551250000 beta4^2 nu^2 + 33368300000 beta4^2 nu + 666745500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [10000 beta4^2 nu + 620700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 620700 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [30000 beta4^2 nu + 730600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 beta4 nu^2 - 136825 beta4 nu - 6663987 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [31250 beta4 nu^3 + 1875 beta4 nu^2 - 41632775 beta4 nu - 832656 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 >= 0 \/ 50 nu - 3649 /= 0 ] /\ [2682750000 beta4^2 nu + 65333905000 beta4^2 - 1916775000 beta4 nu^2 - 93359721000 beta4 nu - 1866427710 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 <= 0 /\ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 >= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]] \/ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 <= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 <= 0 /\ 50 nu - 3649 = 0 ]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 638750 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [2682750000 beta4^2 nu + 65333905000 beta4^2 - 1916775000 beta4 nu^2 - 93359721000 beta4 nu - 1866427710 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5250 beta4^2 nu + 255605 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5250 beta4 nu + 255605 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [7984375000 beta4^2 nu^3 + 479062500 beta4^2 nu^2 - 10637174012500 beta4^2 nu - 212743608000 beta4^2 - 5704687500 beta4 nu^4 - 456375000 beta4 nu^3 + 7600056230625 beta4 nu^2 + 304002614325 beta4 nu + 3040027056 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 34997112500 beta4^2 nu + 426187030500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 639012500 beta4^2 nu^2 + 17511336500 beta4^2 nu + 349971160 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 11682737500 beta4^2 nu - 425253944500 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 100 nu - 1823 = 0 ]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[255500 beta4 - 60850 nu - 1217 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 - 2496600000000 beta4^2 nu^2 - 121667703875000 beta4^2 nu - 2432355255000 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 511420 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [21000 beta4 nu + 511420 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu + 666855000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [6205000000 beta4^2 nu + 385144350000 beta4^2 - 1825500000 beta4 nu^2 - 226617570000 beta4 nu - 4531621200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 620700 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [49275000 beta4^2 nu + 2265810500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 49275000 beta4 nu + 2265810500 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ]]] /\ [837985250000 beta4^2 - 359806050000 beta4 nu - 7196121000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1350500 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [702095750000 beta4^2 - 319827600000 beta4 nu - 6396552000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1131500 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [4343500000 beta4^2 nu + 385107120000 beta4^2 - 1277850000 beta4 nu^2 - 226595664000 beta4 nu - 4531402140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 620570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 ]]] /\ [31025000 beta4^2 nu - 4529029500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 /= 0 ]] \/ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 38353000 beta4^2 nu + 766780 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 766780 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 255920 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 21000 beta4 nu + 255920 beta4 - 182550 nu - 3651 = 0 ]]] /\ [7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1350500 beta4 - 182550 nu - 3651 = 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [638750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2682750000 beta4^2 nu + 65333905000 beta4^2 - 1916775000 beta4 nu^2 - 93359721000 beta4 nu - 1866427710 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [5250 beta4^2 nu + 255605 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5250 beta4 nu + 255605 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 11682737500 beta4^2 nu - 425253944500 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 100 nu - 1823 = 0 ]]] /\ [250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 620700 beta4 - 182550 nu - 3651 = 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 34997112500 beta4^2 nu + 426187030500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [7984375000 beta4^2 nu^3 + 479062500 beta4^2 nu^2 - 10637174012500 beta4^2 nu - 212743608000 beta4^2 - 5704687500 beta4 nu^4 - 456375000 beta4 nu^3 + 7600056230625 beta4 nu^2 + 304002614325 beta4 nu + 3040027056 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 639012500 beta4^2 nu^2 + 17511336500 beta4^2 nu + 349971160 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 /= 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1022000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1496500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu - 5328270000 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 /= 0 ] /\ [21900000000 beta4^2 nu + 533338000000 beta4^2 - 5476500000 beta4 nu^2 - 266742060000 beta4 nu - 5332650600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [219000000 beta4^2 nu + 5333380000 beta4^2 - 27382500 beta4 nu^2 - 1333710300 beta4 nu - 26663253 beta4 < 0 \/ 219000000 beta4 nu + 5333380000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 ]]] /\ [2131600000000 beta4^2 - 666307500000 beta4 nu - 13326150000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2920000 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2920000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 3672500 beta4 nu^2 - 133078550 beta4 nu - 2663037 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 3333362500000 beta4^2 nu^2 + 60917186000000 beta4^2 nu + 1217010740000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 999917600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [456250000 beta4^2 nu^2 + 18250000 beta4^2 nu - 607838880000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 625 nu^2 + 25 nu - 832656 > 0 ]]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ]] \/ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu + 666855000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 999917600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu - 1215011270000 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 45725 nu - 1664399 < 0 ]]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 3750 beta4 nu^2 + 228275 beta4 nu + 3335189 beta4 < 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [750000 beta4 nu^3 + 4607500 beta4 nu^2 - 332879100 beta4 nu - 6659419 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 < 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [250000 beta4 nu^3 + 13702500 beta4 nu^2 - 332514700 beta4 nu - 6655773 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [182500 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [14600000000 beta4^2 nu + 533192000000 beta4^2 - 3651000000 beta4 nu^2 - 266669040000 beta4 nu - 5331920400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ]]] /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4 - 60850 nu - 1217 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [125000 beta4 nu^3 + 2288750 beta4 nu^2 - 83174225 beta4 nu - 1664399 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1022000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 <= 0 \/ 50 nu - 3649 /= 0 ]] \/ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 <= 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1125000 beta4 nu^3 + 67500 beta4 nu^2 - 666123650 beta4 nu - 13322491 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2682750000 beta4^2 nu + 65333905000 beta4^2 - 1916775000 beta4 nu^2 - 93359721000 beta4 nu - 1866427710 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 >= 0 \/ 50 nu - 3649 /= 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 <= 0 \/ 50 nu - 3649 /= 0 ]] \/ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 >= 0 /\ 50 nu - 3649 = 0 ]]] \/ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 >= 0 /\ 50 nu - 3649 = 0 ]]] \/ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 3042500 nu^2 - 444326700 nu - 8885317 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1596875000 beta4^2 nu^2 + 81664187500 beta4^2 nu + 852607332500 beta4^2 - 684562500 beta4 nu^3 - 25027605000 beta4 nu^2 - 1000282725 beta4 nu - 10000089 beta4 < 0 \/ 63875000 beta4 nu + 933852500 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 <= 0 /\ 50 nu - 3649 = 0 ]]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 985900 beta4 - 182550 nu - 3651 = 0 ] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 58324262500 beta4^2 nu + 852140789500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 45575 nu - 912 <= 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [5000 nu^2 - 91050 nu - 1823 > 0 \/ 100 nu - 1823 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1551250000 beta4^2 nu^2 + 33368300000 beta4^2 nu + 666745500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 1823 <= 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 1460800 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [20000 beta4^2 nu + 985900 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 985900 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 146080000 beta4^2 nu + 2920800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 40000 beta4 nu + 2920800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ [60000 beta4^2 nu + 1461200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [60000 beta4 nu + 1461200 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 beta4 nu^2 - 136825 beta4 nu - 6663987 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [31250 beta4 nu^3 + 1875 beta4 nu^2 - 41632775 beta4 nu - 832656 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 <= 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1125000 beta4 nu^3 + 67500 beta4 nu^2 - 666123650 beta4 nu - 13322491 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 182400 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 >= 0 /\ 50 nu - 3649 = 0 ]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]] \/ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 /\ 912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 31032000 beta4^2 nu + 899889320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 985640 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 - 4993200000000 beta4^2 nu^2 - 243335407750000 beta4^2 nu - 4864710510000 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu - 2430689030000 beta4^2 - 684562500 beta4 nu^3 - 8369917500 beta4 nu^2 + 607671618525 beta4 nu + 12156774861 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 - 182200 nu - 3647 < 0 ]]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 166640750000 beta4^2 nu + 2434687970000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 985640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 511420 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [21000 beta4 nu + 511420 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 nu^2 - 182200 nu - 3647 > 0 /\ 50 nu - 3649 = 0 ]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1125000 beta4 nu^3 + 67500 beta4 nu^2 - 666123650 beta4 nu - 13322491 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 2445500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2682750000 beta4^2 nu + 65333905000 beta4^2 - 1916775000 beta4 nu^2 - 93359721000 beta4 nu - 1866427710 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 <= 0 /\ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 >= 0 \/ 50 nu - 3649 /= 0 ]] \/ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 <= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 <= 0 /\ 50 nu - 3649 = 0 ]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 >= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2445500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 638750 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2682750000 beta4^2 nu + 65333905000 beta4^2 - 1916775000 beta4 nu^2 - 93359721000 beta4 nu - 1866427710 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5250 beta4^2 nu + 255605 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5250 beta4 nu + 255605 beta4 - 182550 nu - 3651 = 0 ]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [7984375000 beta4^2 nu^3 + 479062500 beta4^2 nu^2 - 10637174012500 beta4^2 nu - 212743608000 beta4^2 - 5704687500 beta4 nu^4 - 456375000 beta4 nu^3 + 7600056230625 beta4 nu^2 + 304002614325 beta4 nu + 3040027056 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 34997112500 beta4^2 nu + 426187030500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 639012500 beta4^2 nu^2 + 17511336500 beta4^2 nu + 349971160 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 11682737500 beta4^2 nu - 425253944500 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 100 nu - 1823 = 0 ]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[255500 beta4 - 60850 nu - 1217 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 166640750000 beta4^2 nu + 2434687970000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 31032000 beta4^2 nu + 899889320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 985640 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 - 4993200000000 beta4^2 nu^2 - 243335407750000 beta4^2 nu - 4864710510000 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 511420 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [21000 beta4 nu + 511420 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 985640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [1250 beta4 nu^2 - 136825 beta4 nu - 6663987 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [6570000000 beta4^2 nu + 323868150000 beta4^2 - 1217000000 beta4 nu^2 - 119984030000 beta4 nu - 2399193800 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[20000 beta4 nu + 985900 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [85775000 beta4^2 nu + 3598790500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 85775000 beta4 nu + 3598790500 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ]]] /\ [803346750000 beta4^2 - 208776350000 beta4 nu - 4175527000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [1350500 beta4 - 182550 nu - 3651 = 0 /\ [2445500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [491600250000 beta4^2 - 151029700000 beta4 nu - 3020594000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1496500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [85775000 beta4^2 nu + 1715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [16425000 beta4^2 nu - 2397721500 beta4^2 - 3042500 beta4 nu^2 + 444083300 beta4 nu + 8882883 beta4 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 \/ 50 nu - 3649 /= 0 ] /\ [2299500000 beta4^2 nu + 323782740000 beta4^2 - 425950000 beta4 nu^2 - 119952388000 beta4 nu - 2398877380 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[7000 beta4 nu + 985640 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 38353000 beta4^2 nu + 766780 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 766780 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 255920 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 21000 beta4 nu + 255920 beta4 - 182550 nu - 3651 = 0 ]]] /\ [7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 985640 beta4 - 182550 nu - 3651 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2445500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2445500 beta4 - 182550 nu - 3651 = 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [638750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2682750000 beta4^2 nu + 65333905000 beta4^2 - 1916775000 beta4 nu^2 - 93359721000 beta4 nu - 1866427710 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [5250 beta4^2 nu + 255605 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5250 beta4 nu + 255605 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 11682737500 beta4^2 nu - 425253944500 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 100 nu - 1823 = 0 ]]] /\ [500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 985900 beta4 - 182550 nu - 3651 = 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 34997112500 beta4^2 nu + 426187030500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [7984375000 beta4^2 nu^3 + 479062500 beta4^2 nu^2 - 10637174012500 beta4^2 nu - 212743608000 beta4^2 - 5704687500 beta4 nu^4 - 456375000 beta4 nu^3 + 7600056230625 beta4 nu^2 + 304002614325 beta4 nu + 3040027056 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 639012500 beta4^2 nu^2 + 17511336500 beta4^2 nu + 349971160 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [1250 beta4 nu^2 - 136825 beta4 nu - 6663987 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu - 1864894500 beta4^2 - 9127500 beta4 nu^2 + 1332249900 beta4 nu + 26648649 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [182500 beta4 - 60850 nu - 1217 = 0 /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]]]] \/ [50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 >= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu + 666855000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5000 nu^2 - 91050 nu - 1823 > 0 \/ 100 nu - 1823 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 182400 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 3042500 nu^2 - 444326700 nu - 8885317 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1596875000 beta4^2 nu^2 + 81664187500 beta4^2 nu + 852607332500 beta4^2 - 684562500 beta4 nu^3 - 25027605000 beta4 nu^2 - 1000282725 beta4 nu - 10000089 beta4 < 0 \/ 63875000 beta4 nu + 933852500 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [20000 beta4^2 nu + 985900 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 1823 <= 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4^2 nu + 1460800 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 2920800 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 40000 beta4 nu + 2920800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ [3000000 beta4^2 nu^2 + 73120000 beta4^2 nu + 1461200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [60000 beta4 nu + 1461200 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1551250000 beta4^2 nu^2 + 33368300000 beta4^2 nu + 666745500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5000 nu^2 - 91050 nu - 1823 > 0 \/ 100 nu - 1823 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 182400 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [1250 beta4 nu^2 - 136825 beta4 nu - 6663987 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [31250 beta4 nu^3 + 1875 beta4 nu^2 - 41632775 beta4 nu - 832656 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 >= 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 >= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 73022500 beta4 nu^2 - 1995454550 beta4 nu - 39938297 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 >= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 >= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 73022500 beta4 nu^2 - 1995454550 beta4 nu - 39938297 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 <= 0 /\ 50 nu - 3649 = 0 ]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 466389700000 beta4^2 nu + 13624921772000 beta4^2 - 1369125000 beta4 nu^3 - 199974397500 beta4 nu^2 - 7997332950 beta4 nu - 79967853 beta4 < 0 \/ 51100000 beta4 nu + 1866172000 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 3042500 nu^2 - 444326700 nu - 8885317 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 1022070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 1022070 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4^2 nu + 511210 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]]] \/ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 <= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu - 10209830844500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 + 7293401347350 beta4 nu + 145894686549 beta4 > 0 /\ 365000000 beta4^2 nu^2 + 113255850000 beta4^2 nu + 7296333721000 beta4^2 - 152125000 beta4 nu^3 - 33324502500 beta4 nu^2 - 1332797550 beta4 nu - 13327367 beta4 > 0 /\ 500000 beta4^2 nu^2 + 231795000 beta4^2 nu + 26782860700 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [31937500000 beta4^2 nu^3 + 4664791250000 beta4^2 nu^2 - 510398259175000 beta4^2 nu - 10209830844500 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 + 364603409235000 beta4 nu^2 + 14588135674800 beta4 nu + 145894686549 beta4 > 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [125000 beta4^2 nu^2 + 67530000 beta4^2 nu + 8794200550 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 803050 beta4 - 182550 nu - 3651 = 0 ] /\ [15968750000 beta4^2 nu^3 + 4663833125000 beta4^2 nu^2 + 255478940412500 beta4^2 nu + 5107713402750 beta4^2 - 7606250000 beta4 nu^4 - 1666377250000 beta4 nu^3 - 99964380000 beta4 nu^2 - 1999165900 beta4 nu - 13327367 beta4 < 0 \/ 326401250000000 beta4^2 nu^2 + 35753992925000000 beta4^2 nu + 714949298000000 beta4^2 - 349811437500000 beta4 nu^3 - 25557223623750000 beta4 nu^2 - 1021869171225000 beta4 nu - 10217292466500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 6387500 beta4 nu + 466415250 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [87500 beta4^2 nu^2 + 51103500 beta4^2 nu + 6995334535 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 \/ 894250000 beta4^2 nu + 261138885000 beta4^2 - 638925000 beta4 nu^2 - 233233182000 beta4 nu - 4664408070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 638785 beta4 - 182550 nu - 3651 = 0 ] /\ [95812500000 beta4^2 nu^3 + 18657248750000 beta4^2 nu^2 - 509838637525000 beta4^2 nu - 10204234883500 beta4^2 - 68456250000 beta4 nu^4 - 13331626500000 beta4 nu^3 + 364003622955000 beta4 nu^2 + 14576140679400 beta4 nu + 145814722347 beta4 < 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2007500000 beta4^2 nu^2 + 179934050000 beta4^2 nu + 2434954128000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 104045000 beta4^2 nu + 4931405700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1551250000 beta4^2 nu^2 + 113303300000 beta4^2 nu + 2265445500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [620500 beta4 - 182550 nu - 3651 = 0 /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [31025000 beta4^2 nu + 2265445500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [1358895000000000 beta4^2 nu^2 + 28987495175000000 beta4^2 nu + 579206345500000 beta4^2 - 682965187500000 beta4 nu^3 - 8553056223750000 beta4 nu^2 - 341302690725000 beta4 nu - 3410295046500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [93531250000 beta4^2 nu^3 + 7999111875000 beta4^2 nu^2 + 85417320987500 beta4^2 nu + 1705147523250 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 37412500 beta4 nu + 467035750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1551250000 beta4^2 nu^2 + 113303300000 beta4^2 nu + 2265445500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [31025000 beta4^2 nu + 2265445500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [3102500000 beta4^2 nu + 611564800000 beta4^2 - 912750000 beta4 nu^2 - 293211810000 beta4 nu - 5863871100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [2463750000 beta4^2 nu^2 + 586288550000 beta4^2 nu + 29674271035500 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 49275000 beta4 nu + 8127710500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [2171750000 beta4^2 nu + 543601435000 beta4^2 - 638925000 beta4 nu^2 - 273211632000 beta4 nu - 5463977070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 43803500 beta4^2 nu + 2731988535 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 748285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1528756875000000 beta4^2 nu^2 + 41394206525000000 beta4^2 nu + 827272627750000 beta4^2 - 732938250000000 beta4 nu^3 - 12204088170000000 beta4 nu^2 - 487284000900000 beta4 nu - 4869908256000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [278312500000 beta4^2 nu^3 + 29326198750000 beta4^2 nu^2 + 657638901475000 beta4^2 nu + 13141049776500 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 \/ [111325000 beta4 nu + 3599301500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [775625000 beta4^2 nu^2 + 28341337500 beta4^2 nu - 2066086296000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 + 607672166175 beta4 nu + 12156778512 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 1750494375000 beta4^2 nu^2 + 21344348637500 beta4^2 nu + 426187030500 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 12778500 beta4^2 nu + 349971160 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1277640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 1277640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 38353000 beta4^2 nu + 766780 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 766780 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 9328624375000 beta4^2 nu^2 + 340762962487500 beta4^2 nu + 6811528183250 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 38328500 beta4^2 nu + 3731066535 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [255500 beta4 - 182550 nu - 3651 = 0 \/ 2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [31250 beta4 nu^3 + 1875 beta4 nu^2 - 41632775 beta4 nu - 832656 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [20000 beta4^2 nu + 1095400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 1823 <= 0 /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ [3000000 beta4^2 nu^2 + 73120000 beta4^2 nu + 1461200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [60000 beta4 nu + 1461200 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 2920800 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 40000 beta4 nu + 2920800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4^2 nu + 1460800 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu + 666855000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [5000 nu^2 - 91050 nu - 1823 > 0 \/ 100 nu - 1823 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [31250 beta4 nu^3 + 1875 beta4 nu^2 - 41632775 beta4 nu - 832656 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 >= 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 - 332788675 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 1332797500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 - 332788675 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] \/ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 1095000000 beta4^2 nu^2 + 113285050000 beta4^2 nu + 2433621513000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu - 850741416000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 + 607672166175 beta4 nu + 12156778512 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [2007500000 beta4^2 nu^2 + 179934050000 beta4^2 nu + 2434954128000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 104045000 beta4^2 nu + 4931405700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1528756875000000 beta4^2 nu^2 + 41394206525000000 beta4^2 nu + 827272627750000 beta4^2 - 732938250000000 beta4 nu^3 - 12204088170000000 beta4 nu^2 - 487284000900000 beta4 nu - 4869908256000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [278312500000 beta4^2 nu^3 + 29326198750000 beta4^2 nu^2 + 657638901475000 beta4^2 nu + 13141049776500 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 \/ [111325000 beta4 nu + 3599301500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [3102500000 beta4^2 nu + 611564800000 beta4^2 - 912750000 beta4 nu^2 - 293211810000 beta4 nu - 5863871100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [2463750000 beta4^2 nu^2 + 586288550000 beta4^2 nu + 29674271035500 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 49275000 beta4 nu + 8127710500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [1358895000000000 beta4^2 nu^2 + 28987495175000000 beta4^2 nu + 579206345500000 beta4^2 - 682965187500000 beta4 nu^3 - 8553056223750000 beta4 nu^2 - 341302690725000 beta4 nu - 3410295046500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [93531250000 beta4^2 nu^3 + 7999111875000 beta4^2 nu^2 + 85417320987500 beta4^2 nu + 1705147523250 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 37412500 beta4 nu + 467035750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1551250000 beta4^2 nu^2 + 113303300000 beta4^2 nu + 2265445500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [31025000 beta4^2 nu + 2265445500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 113303300000 beta4^2 nu + 2265445500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [620500 beta4 - 182550 nu - 3651 = 0 /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [31025000 beta4^2 nu + 2265445500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2171750000 beta4^2 nu + 543601435000 beta4^2 - 638925000 beta4 nu^2 - 273211632000 beta4 nu - 5463977070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 43803500 beta4^2 nu + 2731988535 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 748285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [775625000 beta4^2 nu^2 + 28341337500 beta4^2 nu - 2066086296000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 + 607672166175 beta4 nu + 12156778512 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 38353000 beta4^2 nu + 766780 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 766780 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1277640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 1277640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]]] \/ [1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4 - 182550 nu - 3651 = 0 \/ 2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 9328624375000 beta4^2 nu^2 + 340762962487500 beta4^2 nu + 6811528183250 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 38328500 beta4^2 nu + 3731066535 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 1750494375000 beta4^2 nu^2 + 21344348637500 beta4^2 nu + 426187030500 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 12778500 beta4^2 nu + 349971160 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [31250 beta4 nu^3 + 1875 beta4 nu^2 - 41632775 beta4 nu - 832656 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 - 332788675 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1095000000 beta4^2 nu^2 + 113285050000 beta4^2 nu + 2433621513000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu - 850741416000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 + 607672166175 beta4 nu + 12156778512 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [10000 beta4^2 nu + 985700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 1823 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 2920400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 2920400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1095000000 beta4^2 nu^2 + 33350050000 beta4^2 nu + 666563000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5000 nu^2 - 91050 nu - 1823 > 0 \/ 100 nu - 1823 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 2432688682500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1125000 beta4 nu^3 + 67500 beta4 nu^2 - 666123650 beta4 nu - 13322491 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [22812500000 beta4^2 nu^3 - 2496600000000 beta4^2 nu^2 - 121667703875000 beta4^2 nu - 2432355255000 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1368750000 beta4^2 nu^2 + 16707875000 beta4^2 nu - 1215344515000 beta4^2 - 684562500 beta4 nu^3 - 8369917500 beta4 nu^2 + 607671618525 beta4 nu + 12156774861 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 - 182200 nu - 3647 < 0 ]]]]] \/ [2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 511420 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [21000 beta4 nu + 511420 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu + 666855000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 nu^2 - 182200 nu - 3647 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1125000 beta4 nu^3 + 67500 beta4 nu^2 - 666123650 beta4 nu - 13322491 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [1250 beta4 nu^2 - 136825 beta4 nu - 6663987 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 + 2292500 beta4 nu^2 - 166439775 beta4 nu - 3329711 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1125000 beta4 nu^3 + 67500 beta4 nu^2 - 666123650 beta4 nu - 13322491 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 182400 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 3333362500000 beta4^2 nu^2 + 60917186000000 beta4^2 nu + 1217010740000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 nu^2 - 182200 nu - 3647 > 0 /\ 50 nu - 3649 = 0 ]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 31032000 beta4^2 nu + 899889320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [45625000000 beta4^2 nu^3 - 4993200000000 beta4^2 nu^2 - 243335407750000 beta4^2 nu - 4864710510000 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 62500 nu^3 - 6840000 nu^2 - 333336175 nu - 6663987 < 0 ]] /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 62500 nu^3 + 6847500 nu^2 + 166805075 nu + 3333363 > 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu - 2430689030000 beta4^2 - 684562500 beta4 nu^3 - 8369917500 beta4 nu^2 + 607671618525 beta4 nu + 12156774861 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 3750 nu^2 + 45775 nu - 3329711 > 0 ]]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1125000 beta4 nu^3 + 67500 beta4 nu^2 - 666123650 beta4 nu - 13322491 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 182400 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 >= 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4 nu^2 - 182400 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 >= 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 73022500 beta4 nu^2 - 1995454550 beta4 nu - 39938297 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 1332797500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 nu^2 - 182200 nu - 3647 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 73022500 beta4 nu^2 - 1995454550 beta4 nu - 39938297 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 45647500 beta4 nu^2 - 1330424550 beta4 nu - 26626747 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 - 332788675 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 1022140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1533140 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1533140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 182400 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 73022500 beta4 nu^2 - 1995454550 beta4 nu - 39938297 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 1241070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 1022070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 1022070 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [10500 beta4^2 nu + 511210 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 10500 beta4 nu + 511210 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 <= 0 /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 13325237500000 beta4^2 nu^2 + 973075454750000 beta4^2 nu + 19456179365000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 16655862500000 beta4^2 nu^2 + 1459479929750000 beta4^2 nu + 29182936615000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 nu^2 - 182200 nu - 3647 > 0 /\ 50 nu - 3649 = 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2281250000 beta4^2 nu^2 + 399766250000 beta4^2 nu + 9733419412500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 > 0 ]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [912500000 beta4^2 nu^2 + 99955250000 beta4^2 nu - 4860713760000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 136925 nu - 6658512 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [5475000000 beta4^2 nu^2 + 666344000000 beta4^2 nu - 19437525310000 beta4^2 - 1369125000 beta4 nu^3 - 166659022500 beta4 nu^2 + 4857380032050 beta4 nu + 97214253297 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 912800 nu - 26626747 > 0 ]]]] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 73022500 beta4 nu^2 - 1995454550 beta4 nu - 39938297 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4^2 nu + 985640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ]]] \/ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 1022070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 1022070 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [10500 beta4^2 nu + 511210 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 10500 beta4 nu + 511210 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 1241070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 1022070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4^2 nu + 511210 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]]] \/ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [3500 beta4^2 nu + 985570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 985570 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 136925 nu + 3333363 > 0 /\ 50 nu - 3649 < 0 /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [45625000000 beta4^2 nu^3 + 8329300000000 beta4^2 nu^2 + 365036554750000 beta4^2 nu + 7297399740000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [1825000000 beta4^2 nu^2 + 166604250000 beta4^2 nu + 2434687605000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 > 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [22812500000 beta4^2 nu^3 + 8327931250000 beta4^2 nu^2 + 486604339875000 beta4^2 nu + 9728755807500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [1368750000 beta4^2 nu^2 + 166586000000 beta4^2 nu + 4866043672500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 nu^2 - 182200 nu - 3647 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 nu^2 - 182200 nu - 3647 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 nu^2 - 182200 nu - 3647 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [68437500000 beta4^2 nu^3 + 10828637500000 beta4^2 nu^2 + 547488219625000 beta4^2 nu + 8885395745985000 beta4^2 - 11409375000 beta4 nu^4 - 2083123687500 beta4 nu^3 - 121726078788750 beta4 nu^2 - 2224086960955725 beta4 nu - 44433065450763 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [68437500000 beta4^2 nu^3 + 14159262500000 beta4^2 nu^2 + 912324882125000 beta4^2 nu + 17767141459485000 beta4^2 - 11409375000 beta4 nu^4 - 3748892437500 beta4 nu^3 - 304227703038750 beta4 nu^2 - 6669825861378225 beta4 nu - 133274856135663 beta4 < 0 \/ 54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [22812500000 beta4^2 nu^3 - 831287500000 beta4^2 nu^2 - 303952810125000 beta4^2 nu - 8880529036005000 beta4^2 - 11409375000 beta4 nu^4 + 415529437500 beta4 nu^3 + 152026357586250 beta4 nu^2 + 4444521389678025 beta4 nu + 88829620576587 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [5703125000000 beta4^2 nu^4 + 791479687500000 beta4^2 nu^3 + 33478623531250000 beta4^2 nu^2 + 445060710973125000 beta4^2 nu + 8887829100975000 beta4^2 - 1711406250000 beta4 nu^5 - 229214343750000 beta4 nu^4 - 9138414208125000 beta4 nu^3 - 111508775734350000 beta4 nu^2 - 4449392265814125 beta4 nu - 44457405667389 beta4 < 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1368750000 beta4^2 nu^2 + 16707875000 beta4^2 nu - 1215344515000 beta4^2 - 684562500 beta4 nu^3 - 8369917500 beta4 nu^2 + 607671618525 beta4 nu + 12156774861 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 365300 nu - 13315197 > 0 ]]]] /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]] \/ [136875000000 beta4^2 nu^3 + 13330712500000 beta4^2 nu^2 + 243668689250000 beta4^2 nu + 4868042595000 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 /\ 10950000000 beta4^2 nu^2 + 466725500000 beta4^2 nu + 4872042630000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 /\ 2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 /\ 1575000 beta4^2 nu^2 + 131463000 beta4^2 nu + 2267453630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [6843750000 beta4^2 nu^2 + 266723750000 beta4^2 nu + 2436687987500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [45625000 beta4 nu + 667037500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [547500000000 beta4^2 nu^3 + 73306600000000 beta4^2 nu^2 + 2920559107000000 beta4^2 nu + 35556183113880000 beta4^2 - 68456250000 beta4 nu^4 - 11665857750000 beta4 nu^3 - 608705380920000 beta4 nu^2 - 8901215887148100 beta4 nu - 177780928906503 beta4 > 0 \/ 54750000 beta4^2 nu + 1333345000 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 < 0 ] /\ [547500000000 beta4^2 nu^3 + 93290350000000 beta4^2 nu^2 + 4866443457000000 beta4^2 nu + 71092894057380000 beta4^2 - 68456250000 beta4 nu^4 - 21660470250000 beta4 nu^3 - 1582114007670000 beta4 nu^2 - 26693903576183100 beta4 nu - 533245399193403 beta4 < 0 \/ 5475000000 beta4^2 nu + 266559500000 beta4^2 - 2738250000 beta4 nu^2 - 200001780000 beta4 nu - 3998940300 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 24366852500000000 beta4^2 nu + 486804150000000 beta4^2 - 832884375000000 beta4 nu^3 - 12210084937500000 beta4 nu^2 - 487403936250000 beta4 nu - 4870707825000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [8212500000 beta4^2 nu^2 + 328500000 beta4^2 nu - 4862709215000 beta4^2 - 4107375000 beta4 nu^3 - 246442500 beta4 nu^2 + 2432017446150 beta4 nu + 48640414641 beta4 < 0 \/ 7500 nu^2 + 365300 nu - 13315197 > 0 ]]]] \/ [500000 beta4^2 nu^2 + 164270000 beta4^2 nu + 13325785200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 266504750000 beta4^2 nu + 9730754547500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 + 486670979750000 beta4^2 nu + 9729422115000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ [4562500000000 beta4^2 nu^4 + 1499146250000000 beta4^2 nu^3 + 158128094075000000 beta4^2 nu^2 + 5330993512433500000 beta4^2 nu + 106556631003480000 beta4^2 - 1140937500000 beta4 nu^5 - 333267843750000 beta4 nu^4 - 30426936551250000 beta4 nu^3 - 889512983316525000 beta4 nu^2 - 35544017672457750 beta4 nu - 355318522295751 beta4 > 0 \/ [36500000 beta4 nu + 3997480000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 36642350000000 beta4^2 nu^2 + 4621042459500000 beta4^2 nu + 177581412442980000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 1338212037765000 beta4 nu^2 - 53314806499015200 beta4 nu - 1065760925133051 beta4 < 0 \/ 36500000 beta4 nu + 6661980000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 + 486670979750000 beta4^2 nu + 9729422115000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000000000 beta4^2 nu^4 + 2498698750000000 beta4^2 nu^3 + 206815181275000000 beta4^2 nu^2 + 5332939796604500000 beta4^2 nu + 106576089847710000 beta4^2 - 3422812500000 beta4 nu^5 - 833226656250000 beta4 nu^4 - 54787147878750000 beta4 nu^3 - 890973396277575000 beta4 nu^2 - 35573217934163250 beta4 nu - 355513164049953 beta4 < 0 \/ [73000000 beta4 nu + 3998210000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu - 9718762655000 beta4^2 - 1369125000 beta4 nu^3 - 166659022500 beta4 nu^2 + 4857380032050 beta4 nu + 97214253297 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 365300 nu - 13315197 > 0 ]]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1140625000000 beta4^2 nu^4 + 208255312500000 beta4^2 nu^3 + 3051687893750000 beta4^2 nu^2 - 443600697979125000 beta4^2 nu - 8873232968880000 beta4^2 - 570468750000 beta4 nu^5 - 104167593750000 beta4 nu^4 - 1528345110000000 beta4 nu^3 + 221830590968737500 beta4 nu^2 + 8875054319974875 beta4 nu + 88756639916112 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 25 nu - 912 = 0 ]]]] \/ [45625000000 beta4^2 nu^3 + 13325237500000 beta4^2 nu^2 + 729939829750000 beta4^2 nu + 14593466865000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 < 0 /\ 912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 14593466865000 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 /\ 250000 beta4^2 nu^2 + 127760000 beta4^2 nu + 15989555100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 94907000 beta4^2 nu + 12391823070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 7296733432500 beta4^2 - 152125000 beta4 nu^3 - 33324502500 beta4 nu^2 - 1332797550 beta4 nu - 13327367 beta4 > 0 \/ [9125000 beta4 nu + 666307500 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [4562500000000 beta4^2 nu^4 + 1998740000000000 beta4^2 nu^3 + 267569100950000000 beta4^2 nu^2 + 10660040740696000000 beta4^2 nu + 213093803162730000 beta4^2 - 1140937500000 beta4 nu^5 - 416556281250000 beta4 nu^4 - 42593711501250000 beta4 nu^3 - 1334086873358775000 beta4 nu^2 - 53312375809437750 beta4 nu - 532953449891901 beta4 > 0 \/ 912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 > 0 ] /\ [1825000000 beta4^2 nu + 532936500000 beta4^2 - 912750000 beta4 nu^2 - 333190260000 beta4 nu - 6663440100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000000000 beta4^2 nu^4 + 3331355000000000 beta4^2 nu^3 + 340589734400000000 beta4^2 nu^2 + 10662959967042000000 beta4^2 nu + 213122990096460000 beta4^2 - 3422812500000 beta4 nu^5 - 1083091968750000 beta4 nu^4 - 79127360853750000 beta4 nu^3 - 1336277292816825000 beta4 nu^2 - 53356173535853250 beta4 nu - 533245399193403 beta4 < 0 \/ 666125000000000 beta4^2 nu^2 + 72967332500000000 beta4^2 nu + 1459080200000000 beta4^2 - 499730625000000 beta4 nu^3 - 36510319462500000 beta4 nu^2 - 1459813101750000 beta4 nu - 14596132095000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu - 14577478405000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 + 7285404562050 beta4 nu + 145814722347 beta4 < 0 \/ 7500 nu^2 + 365300 nu - 13315197 > 0 ]]]] \/ [136875000000 beta4^2 nu^3 + 13330712500000 beta4^2 nu^2 + 243668689250000 beta4^2 nu + 4868042595000 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 /\ 136875000000 beta4^2 nu^3 + 3338837500000 beta4^2 nu^2 - 729273485750000 beta4^2 nu - 17763487429155000 beta4^2 - 68456250000 beta4 nu^4 - 1671245250000 beta4 nu^3 + 364703245830000 beta4 nu^2 + 8891471801886900 beta4 nu + 177683541380397 beta4 > 0 /\ 10950000000 beta4^2 nu^2 + 466725500000 beta4^2 nu + 4872042630000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 54750000 beta4^2 nu + 1333345000 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [1575000 beta4^2 nu^2 + 131463000 beta4^2 nu + 2267453630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 620710 beta4 - 182550 nu - 3651 = 0 ] /\ [6843750000 beta4^2 nu^2 + 266723750000 beta4^2 nu + 2436687987500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [45625000 beta4 nu + 667037500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [6843750000000 beta4^2 nu^4 + 167078750000000 beta4^2 nu^3 - 36460335450000000 beta4^2 nu^2 - 888903644943500000 beta4^2 nu - 17763487429155000 beta4^2 - 3422812500000 beta4 nu^5 - 83630718750000 beta4 nu^4 + 18233491046250000 beta4 nu^3 + 444938293340175000 beta4 nu^2 + 17775648870906750 beta4 nu + 177683541380397 beta4 > 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [18750000 beta4^2 nu^3 + 3194875000 beta4^2 nu^2 + 166659022500 beta4^2 nu + 2434688152650 beta4^2 - 456375000 beta4 nu^3 - 44447882500 beta4 nu^2 - 812451492650 beta4 nu - 16231254351 beta4 > 0 \/ 5475000000 beta4^2 nu + 266559500000 beta4^2 - 2738250000 beta4 nu^2 - 200001780000 beta4 nu - 3998940300 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 2500 beta4 nu + 182550 beta4 - 60850 nu - 1217 = 0 ] /\ [17109375000000 beta4^2 nu^4 + 1916478125000000 beta4^2 nu^3 + 54820463250000000 beta4^2 nu^2 + 445913034928750000 beta4^2 nu + 8896347842362500 beta4^2 - 3422812500000 beta4 nu^5 - 333496031250000 beta4 nu^4 - 6106721928750000 beta4 nu^3 - 365603199075000 beta4 nu^2 - 7306730783250 beta4 nu - 48693763053 beta4 > 0 \/ 1332250000000000 beta4^2 nu^2 + 24366852500000000 beta4^2 nu + 486804150000000 beta4^2 - 832884375000000 beta4 nu^3 - 12210084937500000 beta4 nu^2 - 487403936250000 beta4 nu - 4870707825000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 45625000 beta4 nu + 667037500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [8212500000 beta4^2 nu^2 + 328500000 beta4^2 nu - 4862709215000 beta4^2 - 4107375000 beta4 nu^3 - 246442500 beta4 nu^2 + 2432017446150 beta4 nu + 48640414641 beta4 < 0 \/ 7500 nu^2 + 365300 nu - 13315197 < 0 ]]]] \/ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 /\ 2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 1369125000 beta4^2 nu^2 + 91646945000 beta4^2 nu + 1825349578800 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2281250000000 beta4^2 nu^4 + 291612187500000 beta4^2 nu^3 + 10654674850000000 beta4^2 nu^2 + 111356466038625000 beta4^2 nu + 2222869783365000 beta4^2 - 570468750000 beta4 nu^5 - 62523375000000 beta4 nu^4 - 1525013572500000 beta4 nu^3 - 91350803887500 beta4 nu^2 - 1826016160125 beta4 nu - 12170108313 beta4 > 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1368750000 beta4^2 nu^2 + 16707875000 beta4^2 nu - 1215344515000 beta4^2 - 684562500 beta4 nu^3 - 8369917500 beta4 nu^2 + 607671618525 beta4 nu + 12156774861 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 365300 nu - 13315197 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 + 486670979750000 beta4^2 nu + 9729422115000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 /\ 500000 beta4^2 nu^2 + 164270000 beta4^2 nu + 13325785200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 266504750000 beta4^2 nu + 9730754547500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 3194125000 beta4^2 nu^2 + 466415257500 beta4^2 nu + 19460177027550 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3421875000000 beta4^2 nu^4 + 916195625000000 beta4^2 nu^3 + 72995651025000000 beta4^2 nu^2 + 1777808789215750000 beta4^2 nu + 35526984852922500 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 - 12180105663750000 beta4 nu^3 - 730206480525000 beta4 nu^2 - 14600130852750 beta4 nu - 97320877101 beta4 > 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu - 9718762655000 beta4^2 - 1369125000 beta4 nu^3 - 166659022500 beta4 nu^2 + 4857380032050 beta4 nu + 97214253297 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 365300 nu - 13315197 < 0 ]]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 43807000 beta4^2 nu + 2265701070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2434021297500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu - 4860046905000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 365300 nu - 13315197 < 0 ]]]] /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 <= 0 ]] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 /\ 2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [68437500000 beta4^2 nu^3 + 14159262500000 beta4^2 nu^2 + 912324882125000 beta4^2 nu + 17767141459485000 beta4^2 - 11409375000 beta4 nu^4 - 3748892437500 beta4 nu^3 - 304227703038750 beta4 nu^2 - 6669825861378225 beta4 nu - 133274856135663 beta4 < 0 \/ 54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [22812500000 beta4^2 nu^3 - 831287500000 beta4^2 nu^2 - 303952810125000 beta4^2 nu - 8880529036005000 beta4^2 - 11409375000 beta4 nu^4 + 415529437500 beta4 nu^3 + 152026357586250 beta4 nu^2 + 4444521389678025 beta4 nu + 88829620576587 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [5703125000000 beta4^2 nu^4 + 791479687500000 beta4^2 nu^3 + 33478623531250000 beta4^2 nu^2 + 445060710973125000 beta4^2 nu + 8887829100975000 beta4^2 - 1711406250000 beta4 nu^5 - 229214343750000 beta4 nu^4 - 9138414208125000 beta4 nu^3 - 111508775734350000 beta4 nu^2 - 4449392265814125 beta4 nu - 44457405667389 beta4 < 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1368750000 beta4^2 nu^2 + 16707875000 beta4^2 nu - 1215344515000 beta4^2 - 684562500 beta4 nu^3 - 8369917500 beta4 nu^2 + 607671618525 beta4 nu + 12156774861 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 ] /\ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 91250000 beta4 nu + 2666325000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [22812500000 beta4^2 nu^3 - 831287500000 beta4^2 nu^2 - 303952810125000 beta4^2 nu - 8880529036005000 beta4^2 - 11409375000 beta4 nu^4 + 415529437500 beta4 nu^3 + 152026357586250 beta4 nu^2 + 4444521389678025 beta4 nu + 88829620576587 beta4 > 0 \/ 50 nu - 3649 /= 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 125000 nu^3 - 9117500 nu^2 - 1332614850 nu - 26648649 > 0 ]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1368750000 beta4^2 nu^2 + 16707875000 beta4^2 nu - 1215344515000 beta4^2 - 684562500 beta4 nu^3 - 8369917500 beta4 nu^2 + 607671618525 beta4 nu + 12156774861 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 - 182200 nu - 3647 < 0 ]]]]] \/ [2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu + 666855000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [125000 nu^3 - 9117500 nu^2 - 1332614850 nu - 26648649 < 0 \/ 50 nu - 3649 /= 0 ] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 nu^2 - 182200 nu - 3647 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 511420 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [21000 beta4 nu + 511420 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [375000 beta4 nu^3 + 36522500 beta4 nu^2 + 667585450 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [18750000 beta4 nu^4 - 911000000 beta4 nu^3 - 233198455000 beta4 nu^2 - 4872039344400 beta4 nu - 97347514797 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1125000 beta4 nu^3 + 67500 beta4 nu^2 - 666123650 beta4 nu - 13322491 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [3125000 beta4 nu^4 - 113812500 beta4 nu^3 - 41639648750 beta4 nu^2 - 1217343574275 beta4 nu - 24330216537 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 + 2292500 beta4 nu^2 - 166439775 beta4 nu - 3329711 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 375000 beta4 nu^3 + 36522500 beta4 nu^2 + 667585450 beta4 nu + 13337103 beta4 > 0 /\ 187500 beta4 nu^3 + 25105000 beta4 nu^2 + 1000191475 beta4 nu + 12176775039 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18750000 beta4 nu^4 - 911000000 beta4 nu^3 - 233198455000 beta4 nu^2 - 4872039344400 beta4 nu - 97347514797 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1125000 beta4 nu^3 + 67500 beta4 nu^2 - 666123650 beta4 nu - 13322491 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 + 136925 nu + 3333363 > 0 /\ 50 nu - 3649 < 0 /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 8329300000000 beta4^2 nu^2 + 365036554750000 beta4^2 nu + 7297399740000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1998740000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 166604250000 beta4^2 nu + 2434687605000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 1250 nu^2 + 136925 nu + 3333363 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 3333362500000 beta4^2 nu^2 + 60917186000000 beta4^2 nu + 1217010740000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 + 182600 nu + 3651 > 0 \/ 50 nu - 3649 /= 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 nu^2 - 182200 nu - 3647 > 0 /\ 50 nu - 3649 = 0 ]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 31032000 beta4^2 nu + 899889320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 609171860000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [54750000 beta4 nu + 667220000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 99955250000 beta4^2 nu + 2433354990000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 50 nu - 3649 /= 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 136925 nu + 3333363 > 0 ]] /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 62500 nu^3 + 6847500 nu^2 + 166805075 nu + 3333363 > 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu - 2430689030000 beta4^2 - 684562500 beta4 nu^3 - 8369917500 beta4 nu^2 + 607671618525 beta4 nu + 12156774861 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 3750 nu^2 + 45775 nu - 3329711 > 0 ]]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 187500 beta4 nu^3 + 25105000 beta4 nu^2 + 1000191475 beta4 nu + 12176775039 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [375000 beta4 nu^3 + 36522500 beta4 nu^2 + 667585450 beta4 nu + 13337103 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1125000 beta4 nu^3 + 67500 beta4 nu^2 - 666123650 beta4 nu - 13322491 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [50 beta4 nu + beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 <= 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 6250000 beta4 nu^4 + 2738000000 beta4 nu^3 + 366533015000 beta4 nu^2 + 14602795535200 beta4 nu + 291909319401 beta4 > 0 /\ 125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 73022500 beta4 nu^2 - 1995454550 beta4 nu - 39938297 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 15972500 beta4 nu^2 + 333701325 beta4 nu - 36463676112 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 + 486670979750000 beta4^2 nu + 9729422115000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 /\ 912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 266504750000 beta4^2 nu + 9730754547500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ [91250000000 beta4^2 nu^3 + 36642350000000 beta4^2 nu^2 + 4621042459500000 beta4^2 nu + 177581412442980000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 1338212037765000 beta4 nu^2 - 53314806499015200 beta4 nu - 1065760925133051 beta4 < 0 \/ 36500000 beta4 nu + 6661980000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [9125000000000 beta4^2 nu^4 + 2498698750000000 beta4^2 nu^3 + 206815181275000000 beta4^2 nu^2 + 5332939796604500000 beta4^2 nu + 106576089847710000 beta4^2 - 3422812500000 beta4 nu^5 - 833226656250000 beta4 nu^4 - 54787147878750000 beta4 nu^3 - 890973396277575000 beta4 nu^2 - 35573217934163250 beta4 nu - 355513164049953 beta4 < 0 \/ [73000000 beta4 nu + 3998210000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu - 9718762655000 beta4^2 - 1369125000 beta4 nu^3 - 166659022500 beta4 nu^2 + 4857380032050 beta4 nu + 97214253297 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1140625000000 beta4^2 nu^4 + 208255312500000 beta4^2 nu^3 + 3051687893750000 beta4^2 nu^2 - 443600697979125000 beta4^2 nu - 8873232968880000 beta4^2 - 570468750000 beta4 nu^5 - 104167593750000 beta4 nu^4 - 1528345110000000 beta4 nu^3 + 221830590968737500 beta4 nu^2 + 8875054319974875 beta4 nu + 88756639916112 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 1332797500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 nu^2 - 182200 nu - 3647 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 + 45675 nu - 3329712 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 1022140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1533140 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1533140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 73022500 beta4 nu^2 - 1995454550 beta4 nu - 39938297 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 15972500 beta4 nu^2 + 333701325 beta4 nu - 36463676112 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 45647500 beta4 nu^2 - 1330424550 beta4 nu - 26626747 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 + 166987575 beta4 nu - 24310227312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 6250000 beta4 nu^4 + 2738000000 beta4 nu^3 + 366533015000 beta4 nu^2 + 14602795535200 beta4 nu + 291909319401 beta4 > 0 /\ 125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 73022500 beta4 nu^2 - 1995454550 beta4 nu - 39938297 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 15972500 beta4 nu^2 + 333701325 beta4 nu - 36463676112 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 > 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [22812500000 beta4^2 nu^3 + 8327931250000 beta4^2 nu^2 + 486604339875000 beta4^2 nu + 9728755807500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 \/ 9125000 beta4 nu + 2664682500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1368750000 beta4^2 nu^2 + 166586000000 beta4^2 nu + 4866043672500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 > 0 /\ 17500 nu^2 - 911800 nu - 18243 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 <= 0 /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000000 beta4^2 nu^3 + 13325237500000 beta4^2 nu^2 + 973075454750000 beta4^2 nu + 19456179365000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [45625000000 beta4^2 nu^3 + 16655862500000 beta4^2 nu^2 + 1459479929750000 beta4^2 nu + 29182936615000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 nu^2 - 182200 nu - 3647 > 0 /\ 50 nu - 3649 = 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2281250000 beta4^2 nu^2 + 399766250000 beta4^2 nu + 9733419412500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 > 0 ]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 547600 nu + 26655951 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [5475000000 beta4^2 nu^2 + 666344000000 beta4^2 nu - 19437525310000 beta4^2 - 1369125000 beta4 nu^3 - 166659022500 beta4 nu^2 + 4857380032050 beta4 nu + 97214253297 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 912800 nu - 26626747 > 0 ]]]] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 6250000 beta4 nu^4 + 2738000000 beta4 nu^3 + 366533015000 beta4 nu^2 + 14602795535200 beta4 nu + 291909319401 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 73022500 beta4 nu^2 - 1995454550 beta4 nu - 39938297 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 182400 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 3042500 nu^2 - 444326700 nu - 8885317 = 0 ]]] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1596875000 beta4^2 nu^2 + 81664187500 beta4^2 nu + 852607332500 beta4^2 - 684562500 beta4 nu^3 - 25027605000 beta4 nu^2 - 1000282725 beta4 nu - 10000089 beta4 < 0 \/ 63875000 beta4 nu + 933852500 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]]]] \/ [10000 beta4^2 nu + 620700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1551250000 beta4^2 nu^2 + 33368300000 beta4^2 nu + 666745500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 182400 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [1250 beta4 nu^2 - 136825 beta4 nu - 6663987 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [31250 beta4 nu^3 + 1875 beta4 nu^2 - 41632775 beta4 nu - 832656 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [7500 beta4 nu^2 - 912200 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [187500 beta4 nu^3 - 2270000 beta4 nu^2 - 166622275 beta4 nu - 3331536 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 >= 0 /\ 50 nu - 3649 = 0 ]]] \/ [10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 >= 0 /\ 50 nu - 3649 = 0 ]]] \/ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 73022500 beta4 nu^2 - 1995454550 beta4 nu - 39938297 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 >= 0 /\ 50 nu - 3649 = 0 ]]] \/ [1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 466389700000 beta4^2 nu + 13624921772000 beta4^2 - 1369125000 beta4 nu^3 - 199974397500 beta4 nu^2 - 7997332950 beta4 nu - 79967853 beta4 < 0 \/ 51100000 beta4 nu + 1866172000 beta4 - 27382500 nu^2 - 1095300 nu - 10953 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 <= 0 /\ 50 nu - 3649 = 0 ]]] \/ [5000 beta4^2 nu + 985600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 1460200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 2190200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [1095000000 beta4^2 nu^2 + 66656300000 beta4^2 nu + 1332688000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 - 332788675 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 >= 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4 nu^2 - 182400 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 18272500 beta4 nu^2 - 665394550 beta4 nu - 13315197 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 >= 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 73022500 beta4 nu^2 - 1995454550 beta4 nu - 39938297 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 >= 0 /\ 50 nu - 3649 = 0 ]]] \/ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 nu^2 - 182200 nu - 3647 > 0 /\ 50 nu - 3649 = 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 73022500 beta4 nu^2 - 1995454550 beta4 nu - 39938297 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 - 332788675 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 45647500 beta4 nu^2 - 1330424550 beta4 nu - 26626747 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 3042500 nu^2 - 444326700 nu - 8885317 = 0 ]]] /\ [15968750000 beta4^2 nu^3 - 1747620000000 beta4^2 nu^2 - 85167392712500 beta4^2 nu - 1702648678500 beta4^2 - 11409375000 beta4 nu^4 + 1248413812500 beta4 nu^3 + 60875491586250 beta4 nu^2 + 2433521201775 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 <= 0 /\ 50 nu - 3649 = 0 ]]] \/ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 1241070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 1022070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 1022070 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4^2 nu + 511210 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu - 10209830844500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 + 7293401347350 beta4 nu + 145894686549 beta4 > 0 /\ 365000000 beta4^2 nu^2 + 113255850000 beta4^2 nu + 7296333721000 beta4^2 - 152125000 beta4 nu^3 - 33324502500 beta4 nu^2 - 1332797550 beta4 nu - 13327367 beta4 > 0 /\ 250000 beta4^2 nu^2 + 122285000 beta4^2 nu + 14790420600 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [31937500000 beta4^2 nu^3 + 4664791250000 beta4^2 nu^2 - 510398259175000 beta4^2 nu - 10209830844500 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 + 364603409235000 beta4 nu^2 + 14588135674800 beta4 nu + 145894686549 beta4 > 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [15968750000 beta4^2 nu^3 + 4663833125000 beta4^2 nu^2 + 255478940412500 beta4^2 nu + 5107713402750 beta4^2 - 7606250000 beta4 nu^4 - 1666377250000 beta4 nu^3 - 99964380000 beta4 nu^2 - 1999165900 beta4 nu - 13327367 beta4 < 0 \/ 326401250000000 beta4^2 nu^2 + 35753992925000000 beta4^2 nu + 714949298000000 beta4^2 - 349811437500000 beta4 nu^3 - 25557223623750000 beta4 nu^2 - 1021869171225000 beta4 nu - 10217292466500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 6387500 beta4 nu + 466415250 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [87500 beta4^2 nu^2 + 51103500 beta4^2 nu + 6995334535 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 \/ 894250000 beta4^2 nu + 261138885000 beta4^2 - 638925000 beta4 nu^2 - 233233182000 beta4 nu - 4664408070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 638785 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [95812500000 beta4^2 nu^3 + 18657248750000 beta4^2 nu^2 - 509838637525000 beta4^2 nu - 10204234883500 beta4^2 - 68456250000 beta4 nu^4 - 13331626500000 beta4 nu^3 + 364003622955000 beta4 nu^2 + 14576140679400 beta4 nu + 145814722347 beta4 < 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [2920000000 beta4^2 nu^2 + 246583050000 beta4^2 nu + 2436286743000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 4931040600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ [85775000 beta4^2 nu + 1715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [1715500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [1019171250000000 beta4^2 nu^2 + 15358311225000000 beta4^2 nu + 306758556000000 beta4^2 - 338706312500000 beta4 nu^3 - 2857681816250000 beta4 nu^2 - 113900825075000 beta4 nu - 1137653425500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [139156250000 beta4^2 nu^3 + 11332474375000 beta4^2 nu^2 + 85550600737500 beta4^2 nu + 1706480138250 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 55662500 beta4 nu + 467400750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1149750000 beta4^2 nu + 407691495000 beta4^2 - 212975000 beta4 nu^2 - 135491044000 beta4 nu - 2709735690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [87500 beta4^2 nu^2 + 62053500 beta4^2 nu + 4064603535 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 1113285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3285000000 beta4^2 nu + 563607450000 beta4^2 - 608500000 beta4 nu^2 - 164380190000 beta4 nu - 3287360400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [4288750000 beta4^2 nu^2 + 986036550000 beta4^2 nu + 49133115265500 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 85775000 beta4 nu + 13457440500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [410625000 beta4^2 nu^2 + 15004237500 beta4^2 nu - 1093810392000 beta4^2 - 76062500 beta4 nu^3 - 2780845000 beta4 nu^2 + 202557388725 beta4 nu + 4052259504 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [1408854375000000 beta4^2 nu^2 + 43820766675000000 beta4^2 nu + 875851791750000 beta4^2 - 410889625000000 beta4 nu^3 - 8131394627500000 beta4 nu^2 - 324762717550000 beta4 nu - 3245983617000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [460812500000 beta4^2 nu^3 + 49320898750000 beta4^2 nu^2 + 1144709720475000 beta4^2 nu + 22874469736500 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 \/ [184325000 beta4 nu + 6265261500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 1750494375000 beta4^2 nu^2 + 21344348637500 beta4^2 nu + 426187030500 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 12778500 beta4^2 nu + 349971160 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 9328624375000 beta4^2 nu^2 + 340762962487500 beta4^2 nu + 6811528183250 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 38328500 beta4^2 nu + 3731066535 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [255500 beta4 - 182550 nu - 3651 = 0 \/ 2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3500 beta4^2 nu + 1241070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1277640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 1277640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 38353000 beta4^2 nu + 766780 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 766780 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [31250 beta4 nu^3 + 1875 beta4 nu^2 - 41632775 beta4 nu - 832656 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 33415750000 beta4^2 nu + 667220000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [31250 beta4 nu^3 + 1875 beta4 nu^2 - 41632775 beta4 nu - 832656 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] \/ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 >= 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 - 332788675 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 - 332788675 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 - 499137425 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 1241070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] \/ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 1095000000 beta4^2 nu^2 + 113285050000 beta4^2 nu + 2433621513000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu - 850741416000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 + 607672166175 beta4 nu + 12156778512 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [2920000000 beta4^2 nu^2 + 246583050000 beta4^2 nu + 2436286743000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 4931040600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1408854375000000 beta4^2 nu^2 + 43820766675000000 beta4^2 nu + 875851791750000 beta4^2 - 410889625000000 beta4 nu^3 - 8131394627500000 beta4 nu^2 - 324762717550000 beta4 nu - 3245983617000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [460812500000 beta4^2 nu^3 + 49320898750000 beta4^2 nu^2 + 1144709720475000 beta4^2 nu + 22874469736500 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 \/ [184325000 beta4 nu + 6265261500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [3285000000 beta4^2 nu + 563607450000 beta4^2 - 608500000 beta4 nu^2 - 164380190000 beta4 nu - 3287360400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [4288750000 beta4^2 nu^2 + 986036550000 beta4^2 nu + 49133115265500 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 85775000 beta4 nu + 13457440500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [1019171250000000 beta4^2 nu^2 + 15358311225000000 beta4^2 nu + 306758556000000 beta4^2 - 338706312500000 beta4 nu^3 - 2857681816250000 beta4 nu^2 - 113900825075000 beta4 nu - 1137653425500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [139156250000 beta4^2 nu^3 + 11332474375000 beta4^2 nu^2 + 85550600737500 beta4^2 nu + 1706480138250 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 55662500 beta4 nu + 467400750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ [85775000 beta4^2 nu + 1715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [1715500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [1149750000 beta4^2 nu + 407691495000 beta4^2 - 212975000 beta4 nu^2 - 135491044000 beta4 nu - 2709735690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [87500 beta4^2 nu^2 + 62053500 beta4^2 nu + 4064603535 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 1113285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [410625000 beta4^2 nu^2 + 15004237500 beta4^2 nu - 1093810392000 beta4^2 - 76062500 beta4 nu^3 - 2780845000 beta4 nu^2 + 202557388725 beta4 nu + 4052259504 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]]]] \/ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 < 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 38353000 beta4^2 nu + 766780 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 766780 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1277640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 1277640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3500 beta4^2 nu + 1241070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]]] \/ [1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4 - 182550 nu - 3651 = 0 \/ 2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 9328624375000 beta4^2 nu^2 + 340762962487500 beta4^2 nu + 6811528183250 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 38328500 beta4^2 nu + 3731066535 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu - 1701249816000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 + 1215011452425 beta4 nu + 24310227312 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 1750494375000 beta4^2 nu^2 + 21344348637500 beta4^2 nu + 426187030500 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 12778500 beta4^2 nu + 349971160 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [31250 beta4 nu^3 + 1875 beta4 nu^2 - 41632775 beta4 nu - 832656 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 - 332788675 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1095000000 beta4^2 nu^2 + 113285050000 beta4^2 nu + 2433621513000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu - 850741416000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 + 607672166175 beta4 nu + 12156778512 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [5000 beta4^2 nu + 620600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1095000000 beta4^2 nu^2 + 33350050000 beta4^2 nu + 666563000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 2432688682500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 2285000 beta4 nu^2 - 166439925 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 18655332500000 beta4^2 nu^2 + 1362305636650000 beta4^2 nu + 27238651111000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 23318207500000 beta4^2 nu^2 + 2043271901650000 beta4^2 nu + 40856111261000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 559647200000 beta4^2 nu + 27242381922000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2463750000 beta4^2 nu^2 + 453063550000 beta4^2 nu + 13624655285500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 + 136925 nu + 3333363 > 0 /\ 50 nu - 3649 < 0 /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [63875000000 beta4^2 nu^3 + 11661020000000 beta4^2 nu^2 + 511051176650000 beta4^2 nu + 10216359636000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [2555000000 beta4^2 nu^2 + 233245950000 beta4^2 nu + 3408562647000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [31937500000 beta4^2 nu^3 + 11659103750000 beta4^2 nu^2 + 681246075825000 beta4^2 nu + 13620258130500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [1916250000 beta4^2 nu^2 + 233220400000 beta4^2 nu + 6812461141500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1551250000 beta4^2 nu^2 + 46690800000 beta4^2 nu + 933195500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [68437500000 beta4^2 nu^3 + 10828637500000 beta4^2 nu^2 + 547488219625000 beta4^2 nu + 8885395745985000 beta4^2 - 11409375000 beta4 nu^4 - 2083123687500 beta4 nu^3 - 121726078788750 beta4 nu^2 - 2224086960955725 beta4 nu - 44433065450763 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [68437500000 beta4^2 nu^3 + 14159262500000 beta4^2 nu^2 + 912324882125000 beta4^2 nu + 17767141459485000 beta4^2 - 11409375000 beta4 nu^4 - 3748892437500 beta4 nu^3 - 304227703038750 beta4 nu^2 - 6669825861378225 beta4 nu - 133274856135663 beta4 < 0 \/ 54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [22812500000 beta4^2 nu^3 - 831287500000 beta4^2 nu^2 - 303952810125000 beta4^2 nu - 8880529036005000 beta4^2 - 11409375000 beta4 nu^4 + 415529437500 beta4 nu^3 + 152026357586250 beta4 nu^2 + 4444521389678025 beta4 nu + 88829620576587 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [5703125000000 beta4^2 nu^4 + 791479687500000 beta4^2 nu^3 + 33478623531250000 beta4^2 nu^2 + 445060710973125000 beta4^2 nu + 8887829100975000 beta4^2 - 1711406250000 beta4 nu^5 - 229214343750000 beta4 nu^4 - 9138414208125000 beta4 nu^3 - 111508775734350000 beta4 nu^2 - 4449392265814125 beta4 nu - 44457405667389 beta4 < 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]] \/ [136875000000 beta4^2 nu^3 + 13330712500000 beta4^2 nu^2 + 243668689250000 beta4^2 nu + 4868042595000 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 /\ 10950000000 beta4^2 nu^2 + 466725500000 beta4^2 nu + 4872042630000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 /\ 2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 /\ 375000 beta4^2 nu^2 + 36515000 beta4^2 nu + 666855150 beta4^2 - 9127500 beta4 nu^2 - 222467600 beta4 nu - 4445701 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [8486250000 beta4^2 nu^2 + 346724450000 beta4^2 nu + 3410829844500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [56575000 beta4 nu + 933706500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [547500000000 beta4^2 nu^3 + 73306600000000 beta4^2 nu^2 + 2920559107000000 beta4^2 nu + 35556183113880000 beta4^2 - 68456250000 beta4 nu^4 - 11665857750000 beta4 nu^3 - 608705380920000 beta4 nu^2 - 8901215887148100 beta4 nu - 177780928906503 beta4 > 0 \/ 54750000 beta4^2 nu + 1333345000 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 < 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [547500000000 beta4^2 nu^3 + 93290350000000 beta4^2 nu^2 + 4866443457000000 beta4^2 nu + 71092894057380000 beta4^2 - 68456250000 beta4 nu^4 - 21660470250000 beta4 nu^3 - 1582114007670000 beta4 nu^2 - 26693903576183100 beta4 nu - 533245399193403 beta4 < 0 \/ 5475000000 beta4^2 nu + 266559500000 beta4^2 - 2738250000 beta4 nu^2 - 200001780000 beta4 nu - 3998940300 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 24366852500000000 beta4^2 nu + 486804150000000 beta4^2 - 832884375000000 beta4 nu^3 - 12210084937500000 beta4 nu^2 - 487403936250000 beta4 nu - 4870707825000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [500000 beta4^2 nu^2 + 164270000 beta4^2 nu + 13325785200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 + 486670979750000 beta4^2 nu + 9729422115000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ [4562500000000 beta4^2 nu^4 + 1499146250000000 beta4^2 nu^3 + 158128094075000000 beta4^2 nu^2 + 5330993512433500000 beta4^2 nu + 106556631003480000 beta4^2 - 1140937500000 beta4 nu^5 - 333267843750000 beta4 nu^4 - 30426936551250000 beta4 nu^3 - 889512983316525000 beta4 nu^2 - 35544017672457750 beta4 nu - 355318522295751 beta4 > 0 \/ [36500000 beta4 nu + 3997480000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [1551250000 beta4^2 nu^2 + 319802050000 beta4^2 nu + 13621990420500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [31025000 beta4 nu + 1865770500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 36642350000000 beta4^2 nu^2 + 4621042459500000 beta4^2 nu + 177581412442980000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 1338212037765000 beta4 nu^2 - 53314806499015200 beta4 nu - 1065760925133051 beta4 < 0 \/ 36500000 beta4 nu + 6661980000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000000000 beta4^2 nu^4 + 2498698750000000 beta4^2 nu^3 + 206815181275000000 beta4^2 nu^2 + 5332939796604500000 beta4^2 nu + 106576089847710000 beta4^2 - 3422812500000 beta4 nu^5 - 833226656250000 beta4 nu^4 - 54787147878750000 beta4 nu^3 - 890973396277575000 beta4 nu^2 - 35573217934163250 beta4 nu - 355513164049953 beta4 < 0 \/ [73000000 beta4 nu + 3998210000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1140625000000 beta4^2 nu^4 + 208255312500000 beta4^2 nu^3 + 3051687893750000 beta4^2 nu^2 - 443600697979125000 beta4^2 nu - 8873232968880000 beta4^2 - 570468750000 beta4 nu^5 - 104167593750000 beta4 nu^4 - 1528345110000000 beta4 nu^3 + 221830590968737500 beta4 nu^2 + 8875054319974875 beta4 nu + 88756639916112 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 25 nu - 912 = 0 ]]]] \/ [45625000000 beta4^2 nu^3 + 13325237500000 beta4^2 nu^2 + 729939829750000 beta4^2 nu + 14593466865000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 < 0 /\ 912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 14593466865000 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 /\ 250000 beta4^2 nu^2 + 127760000 beta4^2 nu + 15989555100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 9993335050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [4562500000000 beta4^2 nu^4 + 1998740000000000 beta4^2 nu^3 + 267569100950000000 beta4^2 nu^2 + 10660040740696000000 beta4^2 nu + 213093803162730000 beta4^2 - 1140937500000 beta4 nu^5 - 416556281250000 beta4 nu^4 - 42593711501250000 beta4 nu^3 - 1334086873358775000 beta4 nu^2 - 53312375809437750 beta4 nu - 532953449891901 beta4 > 0 \/ 912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1551250000 beta4^2 nu^2 + 479672050000 beta4^2 nu + 30644681570500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [31025000 beta4 nu + 2798345500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 > 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu + 532936500000 beta4^2 - 912750000 beta4 nu^2 - 333190260000 beta4 nu - 6663440100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000000000 beta4^2 nu^4 + 3331355000000000 beta4^2 nu^3 + 340589734400000000 beta4^2 nu^2 + 10662959967042000000 beta4^2 nu + 213122990096460000 beta4^2 - 3422812500000 beta4 nu^5 - 1083091968750000 beta4 nu^4 - 79127360853750000 beta4 nu^3 - 1336277292816825000 beta4 nu^2 - 53356173535853250 beta4 nu - 533245399193403 beta4 < 0 \/ 666125000000000 beta4^2 nu^2 + 72967332500000000 beta4^2 nu + 1459080200000000 beta4^2 - 499730625000000 beta4 nu^3 - 36510319462500000 beta4 nu^2 - 1459813101750000 beta4 nu - 14596132095000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [136875000000 beta4^2 nu^3 + 3338837500000 beta4^2 nu^2 - 729273485750000 beta4^2 nu - 17763487429155000 beta4^2 - 68456250000 beta4 nu^4 - 1671245250000 beta4 nu^3 + 364703245830000 beta4 nu^2 + 8891471801886900 beta4 nu + 177683541380397 beta4 < 0 /\ 2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 /\ 375000 beta4^2 nu^2 + 36515000 beta4^2 nu + 666855150 beta4^2 - 9127500 beta4 nu^2 - 222467600 beta4 nu - 4445701 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [10950000000 beta4^2 nu^2 + 466725500000 beta4^2 nu + 4872042630000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [6843750000000 beta4^2 nu^4 + 167078750000000 beta4^2 nu^3 - 36460335450000000 beta4^2 nu^2 - 888903644943500000 beta4^2 nu - 17763487429155000 beta4^2 - 3422812500000 beta4 nu^5 - 83630718750000 beta4 nu^4 + 18233491046250000 beta4 nu^3 + 444938293340175000 beta4 nu^2 + 17775648870906750 beta4 nu + 177683541380397 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [8486250000 beta4^2 nu^2 + 346724450000 beta4^2 nu + 3410829844500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [56575000 beta4 nu + 933706500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [18750000 beta4^2 nu^3 + 3194875000 beta4^2 nu^2 + 166659022500 beta4^2 nu + 2434688152650 beta4^2 - 456375000 beta4 nu^3 - 44447882500 beta4 nu^2 - 812451492650 beta4 nu - 16231254351 beta4 < 0 \/ 5475000000 beta4^2 nu + 266559500000 beta4^2 - 2738250000 beta4 nu^2 - 200001780000 beta4 nu - 3998940300 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 2500 beta4 nu + 182550 beta4 - 60850 nu - 1217 = 0 ] /\ [17109375000000 beta4^2 nu^4 + 1916478125000000 beta4^2 nu^3 + 54820463250000000 beta4^2 nu^2 + 445913034928750000 beta4^2 nu + 8896347842362500 beta4^2 - 3422812500000 beta4 nu^5 - 333496031250000 beta4 nu^4 - 6106721928750000 beta4 nu^3 - 365603199075000 beta4 nu^2 - 7306730783250 beta4 nu - 48693763053 beta4 < 0 \/ 1332250000000000 beta4^2 nu^2 + 24366852500000000 beta4^2 nu + 486804150000000 beta4^2 - 832884375000000 beta4 nu^3 - 12210084937500000 beta4 nu^2 - 487403936250000 beta4 nu - 4870707825000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 45625000 beta4 nu + 667037500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 - 242735895250000 beta4^2 nu - 53251560590385000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 + 121301225610000 beta4 nu^2 + 26635503053502300 beta4 nu + 532661500590399 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 9993335050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 127760000 beta4^2 nu + 15989555100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1460100 beta4 - 182550 nu - 3651 = 0 ] /\ [2281250000000 beta4^2 nu^4 + 499776250000000 beta4^2 nu^3 - 12126800150000000 beta4^2 nu^2 - 2662820765414500000 beta4^2 nu - 53251560590385000 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 + 6060062148750000 beta4 nu^3 + 1331896453900725000 beta4 nu^2 + 53268578083022250 beta4 nu + 532661500590399 beta4 > 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [1551250000 beta4^2 nu^2 + 479672050000 beta4^2 nu + 30644681570500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [31025000 beta4 nu + 2798345500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 > 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [6250000 beta4^2 nu^3 + 4106625000 beta4^2 nu^2 + 766208007500 beta4^2 nu + 36485666267550 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 1825000000 beta4^2 nu + 532936500000 beta4^2 - 912750000 beta4 nu^2 - 333190260000 beta4 nu - 6663440100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 2500 beta4 nu + 912550 beta4 - 182550 nu - 3651 = 0 ] /\ [1140625000000 beta4^2 nu^4 + 416419375000000 beta4^2 nu^3 + 42573716800000000 beta4^2 nu^2 + 1332869995880250000 beta4^2 nu + 26640373762057500 beta4^2 - 380312500000 beta4 nu^5 - 111089281250000 beta4 nu^4 - 6088941558750000 beta4 nu^3 - 365069909675000 beta4 nu^2 - 7299621069250 beta4 nu - 48658216917 beta4 < 0 \/ 666125000000000 beta4^2 nu^2 + 72967332500000000 beta4^2 nu + 1459080200000000 beta4^2 - 499730625000000 beta4 nu^3 - 36510319462500000 beta4 nu^2 - 1459813101750000 beta4 nu - 14596132095000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [6843750000000 beta4^2 nu^4 + 1832391250000000 beta4^2 nu^3 + 60893833300000000 beta4^2 nu^2 - 2659901539068500000 beta4^2 nu - 53222373656655000 beta4^2 - 3422812500000 beta4 nu^5 - 916515093750000 beta4 nu^4 - 30473587203750000 beta4 nu^3 + 1329706034442675000 beta4 nu^2 + 53224780356606750 beta4 nu + 532369551288897 beta4 < 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 4664335050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [4562500000 beta4^2 nu^2 + 333245000000 beta4^2 nu + 6663075000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [1825000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3376250000 beta4^2 nu^2 + 293230050000 beta4^2 nu + 3409762000500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [67525000 beta4 nu + 933925500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [91250000 beta4^2 nu + 6663075000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 365000 beta4 - 60850 nu - 1217 = 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu + 532936500000 beta4^2 - 304250000 beta4 nu^2 - 155483920000 beta4 nu - 3109556700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[5000 beta4 nu + 1460100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 beta4^2 nu + 1277550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 1277550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3650000000 beta4^2 nu + 666198000000 beta4^2 - 608500000 beta4 nu^2 - 177706340000 beta4 nu - 3553883400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1825200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [91250000 beta4^2 nu + 14656575000 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 \/ 91250000 beta4 nu + 14656575000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [1332250000000000 beta4^2 nu^2 + 24366852500000000 beta4^2 nu + 486804150000000 beta4^2 - 388679375000000 beta4 nu^3 - 4076691387500000 beta4 nu^2 - 162601240250000 beta4 nu - 1624457685000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [3193750000 beta4^2 nu^2 + 33434000000 beta4^2 nu + 667402500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 63875000 beta4 nu + 667402500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1665312500000000 beta4^2 nu^2 + 48693737500000000 beta4^2 nu + 973208625000000 beta4^2 - 444205000000000 beta4 nu^3 - 8133393550000000 beta4 nu^2 - 324802696000000 beta4 nu - 3246250140000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[91250000 beta4 nu + 2666325000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [10037500000 beta4^2 nu^2 + 333464000000 beta4^2 nu + 6665265000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 \/ [200750000 beta4 nu + 6665265000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 91250000 beta4 nu + 2666325000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 1369125000 beta4^2 nu^2 + 91646945000 beta4^2 nu + 1825349578800 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2281250000000 beta4^2 nu^4 + 291612187500000 beta4^2 nu^3 + 10654674850000000 beta4^2 nu^2 + 111356466038625000 beta4^2 nu + 2222869783365000 beta4^2 - 570468750000 beta4 nu^5 - 62523375000000 beta4 nu^4 - 1525013572500000 beta4 nu^3 - 91350803887500 beta4 nu^2 - 1826016160125 beta4 nu - 12170108313 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 164270000 beta4^2 nu + 13325785200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1825200 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [1551250000 beta4^2 nu^2 + 319802050000 beta4^2 nu + 13621990420500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [31025000 beta4 nu + 1865770500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 + 486670979750000 beta4^2 nu + 9729422115000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 3194125000 beta4^2 nu^2 + 466415257500 beta4^2 nu + 19460177027550 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3421875000000 beta4^2 nu^4 + 916195625000000 beta4^2 nu^3 + 72995651025000000 beta4^2 nu^2 + 1777808789215750000 beta4^2 nu + 35526984852922500 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 - 12180105663750000 beta4 nu^3 - 730206480525000 beta4 nu^2 - 14600130852750 beta4 nu - 97320877101 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 <= 0 ]] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [68437500000 beta4^2 nu^3 + 14159262500000 beta4^2 nu^2 + 912324882125000 beta4^2 nu + 17767141459485000 beta4^2 - 11409375000 beta4 nu^4 - 3748892437500 beta4 nu^3 - 304227703038750 beta4 nu^2 - 6669825861378225 beta4 nu - 133274856135663 beta4 < 0 \/ 54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [22812500000 beta4^2 nu^3 - 831287500000 beta4^2 nu^2 - 303952810125000 beta4^2 nu - 8880529036005000 beta4^2 - 11409375000 beta4 nu^4 + 415529437500 beta4 nu^3 + 152026357586250 beta4 nu^2 + 4444521389678025 beta4 nu + 88829620576587 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [5703125000000 beta4^2 nu^4 + 791479687500000 beta4^2 nu^3 + 33478623531250000 beta4^2 nu^2 + 445060710973125000 beta4^2 nu + 8887829100975000 beta4^2 - 1711406250000 beta4 nu^5 - 229214343750000 beta4 nu^4 - 9138414208125000 beta4 nu^3 - 111508775734350000 beta4 nu^2 - 4449392265814125 beta4 nu - 44457405667389 beta4 < 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 < 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [22812500000 beta4^2 nu^3 - 831287500000 beta4^2 nu^2 - 303952810125000 beta4^2 nu - 8880529036005000 beta4^2 - 11409375000 beta4 nu^4 + 415529437500 beta4 nu^3 + 152026357586250 beta4 nu^2 + 4444521389678025 beta4 nu + 88829620576587 beta4 > 0 \/ 50 nu - 3649 /= 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 125000 nu^3 - 9117500 nu^2 - 1332614850 nu - 26648649 < 0 ]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 375000 beta4 nu^3 + 36522500 beta4 nu^2 + 667585450 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [18750000 beta4 nu^4 - 911000000 beta4 nu^3 - 233198455000 beta4 nu^2 - 4872039344400 beta4 nu - 97347514797 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 375000 beta4 nu^3 + 36522500 beta4 nu^2 + 667585450 beta4 nu + 13337103 beta4 > 0 /\ 187500 beta4 nu^3 + 25105000 beta4 nu^2 + 1000191475 beta4 nu + 12176775039 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [18750000 beta4 nu^4 - 911000000 beta4 nu^3 - 233198455000 beta4 nu^2 - 4872039344400 beta4 nu - 97347514797 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 + 136925 nu + 3333363 > 0 /\ 50 nu - 3649 < 0 /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 11661020000000 beta4^2 nu^2 + 511051176650000 beta4^2 nu + 10216359636000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 \/ 25550000 beta4 nu + 2798236000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 233245950000 beta4^2 nu + 3408562647000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 51100000 beta4 nu + 933597000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 + 136925 nu + 3333363 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 4666707500000 beta4^2 nu^2 + 85284060400000 beta4^2 nu + 1703815036000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 + 182600 nu + 3651 > 0 \/ 50 nu - 3649 /= 0 ] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 6998145000000 beta4^2 nu^2 + 170474786650000 beta4^2 nu + 3406696986000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 > 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 116648525000 beta4^2 nu + 1704281579000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 833203800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 99955250000 beta4^2 nu + 2433354990000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 50 nu - 3649 /= 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 136925 nu + 3333363 > 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 187500 beta4 nu^3 + 25105000 beta4 nu^2 + 1000191475 beta4 nu + 12176775039 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [375000 beta4 nu^3 + 36522500 beta4 nu^2 + 667585450 beta4 nu + 13337103 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 beta4 nu + beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 <= 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 6250000 beta4 nu^4 + 2738000000 beta4 nu^3 + 366533015000 beta4 nu^2 + 14602795535200 beta4 nu + 291909319401 beta4 > 0 /\ 125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 15972500 beta4 nu^2 + 333701325 beta4 nu - 36463676112 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1551250000 beta4^2 nu^2 + 319802050000 beta4^2 nu + 13621990420500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [31025000 beta4 nu + 1865770500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ [91250000000 beta4^2 nu^3 + 36642350000000 beta4^2 nu^2 + 4621042459500000 beta4^2 nu + 177581412442980000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 1338212037765000 beta4 nu^2 - 53314806499015200 beta4 nu - 1065760925133051 beta4 < 0 \/ 36500000 beta4 nu + 6661980000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [9125000000000 beta4^2 nu^4 + 2498698750000000 beta4^2 nu^3 + 206815181275000000 beta4^2 nu^2 + 5332939796604500000 beta4^2 nu + 106576089847710000 beta4^2 - 3422812500000 beta4 nu^5 - 833226656250000 beta4 nu^4 - 54787147878750000 beta4 nu^3 - 890973396277575000 beta4 nu^2 - 35573217934163250 beta4 nu - 355513164049953 beta4 < 0 \/ [73000000 beta4 nu + 3998210000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1140625000000 beta4^2 nu^4 + 208255312500000 beta4^2 nu^3 + 3051687893750000 beta4^2 nu^2 - 443600697979125000 beta4^2 nu - 8873232968880000 beta4^2 - 570468750000 beta4 nu^5 - 104167593750000 beta4 nu^4 - 1528345110000000 beta4 nu^3 + 221830590968737500 beta4 nu^2 + 8875054319974875 beta4 nu + 88756639916112 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 3730811000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 3730811000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 279823600000 beta4^2 nu + 5595961000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 + 45675 nu - 3329712 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2500 beta4^2 nu + 730050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 nu^3 + 2285000 nu^2 - 166439925 nu - 3329712 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 15972500 beta4 nu^2 + 333701325 beta4 nu - 36463676112 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 + 166987575 beta4 nu - 24310227312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 6250000 beta4 nu^4 + 2738000000 beta4 nu^3 + 366533015000 beta4 nu^2 + 14602795535200 beta4 nu + 291909319401 beta4 > 0 /\ 125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 15972500 beta4 nu^2 + 333701325 beta4 nu - 36463676112 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [31937500000 beta4^2 nu^3 + 11659103750000 beta4^2 nu^2 + 681246075825000 beta4^2 nu + 13620258130500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 233220400000 beta4^2 nu + 6812461141500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ 50 nu - 3649 <= 0 /\ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 18655332500000 beta4^2 nu^2 + 1362305636650000 beta4^2 nu + 27238651111000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 23318207500000 beta4^2 nu^2 + 2043271901650000 beta4^2 nu + 40856111261000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 559647200000 beta4^2 nu + 27242381922000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2463750000 beta4^2 nu^2 + 453063550000 beta4^2 nu + 13624655285500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 547600 nu + 26655951 > 0 ]]]] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 6250000 beta4 nu^4 + 2738000000 beta4 nu^3 + 366533015000 beta4 nu^2 + 14602795535200 beta4 nu + 291909319401 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 4666707500000 beta4^2 nu^2 + 85284060400000 beta4^2 nu + 1703815036000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 6998145000000 beta4^2 nu^2 + 170474786650000 beta4^2 nu + 3406696986000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 > 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 116648525000 beta4^2 nu + 1704281579000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 833203800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [3376250000 beta4^2 nu^2 + 66747550000 beta4^2 nu + 1333600500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 31025000 beta4^2 nu + 1332870500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [31025000 beta4^2 nu + 2665120500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [31025000 beta4 nu + 2665120500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [31025000 beta4^2 nu + 3997370500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 31025000 beta4 nu + 3997370500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2463750000 beta4^2 nu^2 + 66711050000 beta4^2 nu + 1333235500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [95812500000 beta4^2 nu^3 + 2337186250000 beta4^2 nu^2 - 510491440025000 beta4^2 nu - 12434441200408500 beta4^2 - 68456250000 beta4 nu^4 - 1671245250000 beta4 nu^3 + 364703245830000 beta4 nu^2 + 8891471801886900 beta4 nu + 177683541380397 beta4 > 0 /\ 10128750000 beta4^2 nu^2 + 446708900000 beta4^2 nu + 4871642626500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 38325000 beta4^2 nu + 933341500 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [375000 beta4^2 nu^2 + 31040000 beta4^2 nu + 533520650 beta4^2 - 9127500 beta4 nu^2 - 222467600 beta4 nu - 4445701 beta4 > 0 \/ 2500 beta4 nu + 146050 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [13125000 beta4^2 nu^3 + 2236412500 beta4^2 nu^2 + 116661315750 beta4^2 nu + 1704281706855 beta4^2 - 456375000 beta4 nu^3 - 44447882500 beta4 nu^2 - 812451492650 beta4 nu - 16231254351 beta4 > 0 \/ 2682750000 beta4^2 nu + 130614155000 beta4^2 - 1916775000 beta4 nu^2 - 140001246000 beta4 nu - 2799258210 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 127785 beta4 - 60850 nu - 1217 = 0 ] /\ [11976562500000 beta4^2 nu^4 + 1341534687500000 beta4^2 nu^3 + 38374324275000000 beta4^2 nu^2 + 312139124450125000 beta4^2 nu + 6227443489653750 beta4^2 - 3422812500000 beta4 nu^5 - 333496031250000 beta4 nu^4 - 6106721928750000 beta4 nu^3 - 365603199075000 beta4 nu^2 - 7306730783250 beta4 nu - 48693763053 beta4 > 0 \/ 652802500000000 beta4^2 nu^2 + 11939757725000000 beta4^2 nu + 238534033500000 beta4^2 - 583019062500000 beta4 nu^3 - 8547059456250000 beta4 nu^2 - 341182755375000 beta4 nu - 3409495477500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 31937500 beta4 nu + 466926250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [31937500000 beta4^2 nu^3 + 6996228750000 beta4^2 nu^2 - 169915126675000 beta4^2 nu - 37276092413269500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 + 121301225610000 beta4 nu^2 + 26635503053502300 beta4 nu + 532661500590399 beta4 < 0 /\ 1551250000 beta4^2 nu^2 + 539623300000 beta4^2 nu + 43775204345500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 122285000 beta4^2 nu + 14790420600 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 67530000 beta4^2 nu + 8794200550 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 803050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [4375000 beta4^2 nu^3 + 2874637500 beta4^2 nu^2 + 536345605250 beta4^2 nu + 25539966387285 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 > 0 \/ 894250000 beta4^2 nu + 261138885000 beta4^2 - 638925000 beta4 nu^2 - 233233182000 beta4 nu - 4664408070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 638785 beta4 - 182550 nu - 3651 = 0 ] /\ [798437500000 beta4^2 nu^4 + 291493562500000 beta4^2 nu^3 + 29801601760000000 beta4^2 nu^2 + 933008997116175000 beta4^2 nu + 18648261633440250 beta4^2 - 380312500000 beta4 nu^5 - 111089281250000 beta4 nu^4 - 6088941558750000 beta4 nu^3 - 365069909675000 beta4 nu^2 - 7299621069250 beta4 nu - 48658216917 beta4 > 0 \/ 326401250000000 beta4^2 nu^2 + 35753992925000000 beta4^2 nu + 714949298000000 beta4^2 - 349811437500000 beta4 nu^3 - 25557223623750000 beta4 nu^2 - 1021869171225000 beta4 nu - 10217292466500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 6387500 beta4 nu + 466415250 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [4790625000000 beta4^2 nu^4 + 1282673875000000 beta4^2 nu^3 + 42625683310000000 beta4^2 nu^2 - 1861931077347950000 beta4^2 nu - 37255661559658500 beta4^2 - 3422812500000 beta4 nu^5 - 916515093750000 beta4 nu^4 - 30473587203750000 beta4 nu^3 + 1329706034442675000 beta4 nu^2 + 53224780356606750 beta4 nu + 532369551288897 beta4 > 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 438100 beta4 - 182550 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu + 851674246500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 958387500 beta4^2 nu^2 + 64152861500 beta4^2 nu + 1277744705160 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu + 851674246500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [1596875000000 beta4^2 nu^4 + 204128531250000 beta4^2 nu^3 + 7458272395000000 beta4^2 nu^2 + 77949526227037500 beta4^2 nu + 1556008848355500 beta4^2 - 570468750000 beta4 nu^5 - 62523375000000 beta4 nu^4 - 1525013572500000 beta4 nu^3 - 91350803887500 beta4 nu^2 - 1826016160125 beta4 nu - 12170108313 beta4 > 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 233220400000 beta4^2 nu + 6812461141500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [95812500000 beta4^2 nu^3 + 11662936250000 beta4^2 nu^2 + 340856277475000 beta4^2 nu + 6812461141500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [125000 nu^3 - 9117500 nu^2 - 1332614850 nu - 26648649 > 0 \/ 50 nu - 3649 /= 0 ] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [95812500000 beta4^2 nu^3 + 16325811250000 beta4^2 nu^2 + 681432667475000 beta4^2 nu + 13622123791500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 38325000 beta4 nu + 3731066500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3193750000 beta4^2 nu^2 + 326529000000 beta4^2 nu + 6814326802500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [63875000 beta4 nu + 1866427500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 6996228750000 beta4^2 nu^2 + 340669685825000 beta4^2 nu + 6810595480500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 2235887500 beta4^2 nu^2 + 326490680250 beta4^2 nu + 13622123919285 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2395312500000 beta4^2 nu^4 + 641336937500000 beta4^2 nu^3 + 51096955717500000 beta4^2 nu^2 + 1244466152451025000 beta4^2 nu + 24868889397045750 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 - 12180105663750000 beta4 nu^3 - 730206480525000 beta4 nu^2 - 14600130852750 beta4 nu - 97320877101 beta4 > 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 6810595480500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 31030000 beta4^2 nu + 1599320550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 438050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [1750 beta4^2 nu + 383285 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 23352700000 beta4^2 nu + 466670750 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [2463750000 beta4^2 nu^2 + 66711050000 beta4^2 nu + 1333235500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 31025000 beta4^2 nu + 2665120500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 31025000 beta4^2 nu + 1332870500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1551250000 beta4^2 nu^2 + 133287050000 beta4^2 nu + 2665120500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4^2 nu + 1095050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 730050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7500 beta4^2 nu + 365150 beta4^2 - 182550 beta4 nu - 3651 beta4 <= 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]]] \/ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 182550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4^2 nu + 912550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 547550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7500 beta4^2 nu + 182650 beta4^2 - 182550 beta4 nu - 3651 beta4 <= 0 /\ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ]]] \/ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 438100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 182550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4^2 nu + 912550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2500 beta4 nu + 912550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 < 0 /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 2798236000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 2798236000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 46730950000 beta4^2 nu + 933597000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 933597000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 < 0 /\ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 4666707500000 beta4^2 nu^2 + 85284060400000 beta4^2 nu + 1703815036000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 6998145000000 beta4^2 nu^2 + 170474786650000 beta4^2 nu + 3406696986000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 > 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 116648525000 beta4^2 nu + 1704281579000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 833203800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 187500 beta4 nu^3 + 11417500 beta4 nu^2 + 166987725 beta4 nu + 3335189 beta4 < 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]] \/ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4^2 nu + 1095050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 730050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [7500 beta4^2 nu + 365150 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7500 beta4 nu + 365150 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 19461509095000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 912600 beta4 nu + 79953251 beta4 < 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 182550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4^2 nu + 912550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 547550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [7500 beta4^2 nu + 182650 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [91250000000 beta4^2 nu^3 + 13327975000000 beta4^2 nu^2 + 486804259500000 beta4^2 nu + 9730754730000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 399821000000 beta4^2 nu + 9733419960000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [2500 beta4^2 nu + 912550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 182550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [12500000 beta4^2 nu^3 + 1825750000 beta4^2 nu^2 + 66685515000 beta4^2 nu + 1332980100 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 2665595100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [25000000 beta4^2 nu^3 + 2739000000 beta4^2 nu^2 + 66722030000 beta4^2 nu + 1333345200 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 < 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 666490050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [91250000000 beta4^2 nu^3 + 26650475000000 beta4^2 nu^2 + 1946150909500000 beta4^2 nu + 38912358730000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [91250000000 beta4^2 nu^3 + 33311725000000 beta4^2 nu^2 + 2918959859500000 beta4^2 nu + 58365873230000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 799496000000 beta4^2 nu + 38917688460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 19461509095000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1496500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2131600000000 beta4^2 - 666307500000 beta4 nu - 13326150000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2920000 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 291816040000000000 beta4^2 nu + 5835787900000000 beta4^2 - 666307500000000 beta4 nu^3 - 73000649700000000 beta4 nu^2 - 2919226419000000 beta4 nu - 29189598960000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 999735075 beta4 nu - 9996438 beta4 < 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 9992604850 beta4 nu - 199844799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2920000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2737500000 beta4^2 nu^2 + 666234500000 beta4^2 nu + 38915023595000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [62500 beta4^2 nu^2 + 36502500 beta4^2 nu + 3997480025 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 1250 beta4 nu + 547525 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 19450849635000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 7299 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [68437500000 beta4^2 nu^3 + 16657231250000 beta4^2 nu^2 + 973208707125000 beta4^2 nu + 19457511797500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ [27375000 beta4 nu + 2665047500 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 350000 beta4^2 nu^2 + 69364000 beta4^2 nu + 3198787140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 2665595100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 1999105050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 3650000000 beta4^2 nu + 399748000000 beta4^2 - 1825500000 beta4 nu^2 - 266596020000 beta4 nu - 5331190200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 48667092500000000 beta4^2 nu + 972942175000000 beta4^2 - 666307500000000 beta4 nu^3 - 24360202200000000 beta4 nu^2 - 973608519000000 beta4 nu - 9733419960000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2555000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1131500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [45625000 beta4^2 nu + 912500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [532900000000 beta4^2 - 333153750000 beta4 nu - 6663075000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1460000 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [638750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]]] /\ [333062500000000 beta4^2 nu^2 + 72954010000000000 beta4^2 nu + 1458946975000000 beta4^2 - 333153750000000 beta4 nu^3 - 36500324850000000 beta4 nu^2 - 1459613209500000 beta4 nu - 14594799480000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 166567750000 beta4^2 nu + 3330990000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [18250000 beta4 nu + 3330990000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 - 16634875000 beta4^2 nu - 332880000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 25 nu - 912 = 0 ]]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1387000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ [666125000000 beta4^2 - 399784500000 beta4 nu - 7995690000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [333062500000000 beta4^2 nu^2 + 97267572500000000 beta4^2 nu + 1945218225000000 beta4^2 - 333153750000000 beta4 nu^3 - 48660436725000000 beta4 nu^2 - 1946017684500000 beta4 nu - 19458844230000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [45625000000 beta4^2 nu^3 + 2737500000 beta4^2 nu^2 - 243135570250000 beta4^2 nu - 4862712135000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 < 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 4862712135000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 < 0 /\ 350000 beta4^2 nu^2 + 69364000 beta4^2 nu + 3198787140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 2665595100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu + 399748000000 beta4^2 - 1825500000 beta4 nu^2 - 266596020000 beta4 nu - 5331190200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 9997350000000 beta4^2 nu^2 + 243535409500000 beta4^2 nu + 4866709980000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 999187500000000 beta4^2 nu^2 + 48667092500000000 beta4^2 nu + 972942175000000 beta4^2 - 666307500000000 beta4 nu^3 - 24360202200000000 beta4 nu^2 - 973608519000000 beta4 nu - 9733419960000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1606000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [91250000 beta4^2 nu + 1825000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 60850 nu - 1217 = 0 ]] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 60850 nu - 1217 = 0 ]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [666125000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ [1825000 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [932575000000 beta4^2 - 222102500000 beta4 nu - 4442050000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ [2555000 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 48667092500000000 beta4^2 nu + 972942175000000 beta4^2 - 333153750000000 beta4 nu^3 - 8126730475000000 beta4 nu^2 - 324669434500000 beta4 nu - 3245361730000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 97294217500000000 beta4^2 nu + 1945484675000000 beta4^2 - 333153750000000 beta4 nu^3 - 16233471725000000 beta4 nu^2 - 648939084500000 beta4 nu - 6488058230000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 6662345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [54750000 beta4 nu + 6662345000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [2737500000 beta4^2 nu^2 + 666234500000 beta4^2 nu + 38915023595000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 2737500000 beta4^2 nu^2 - 972542445250000 beta4^2 nu - 19450849635000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 486404420235000 beta4 nu^2 + 19456178269800 beta4 nu + 194561786349 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 19450849635000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 - 133188500000 beta4^2 nu - 38904364135000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 14599 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [68437500000 beta4^2 nu^3 + 13326606250000 beta4^2 nu^2 + 486804232125000 beta4^2 nu + 9730754547500 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 < 0 /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 5329365000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 7993865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 7993865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 5330095000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1131500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [2555000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2555000 beta4 - 182550 nu - 3651 = 0 ] /\ [532900000000 beta4^2 - 333153750000 beta4 nu - 6663075000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 912500 beta4 - 182550 nu - 3651 = 0 ]] /\ [333062500000000 beta4^2 nu^2 + 72954010000000000 beta4^2 nu + 1458946975000000 beta4^2 - 333153750000000 beta4 nu^3 - 36500324850000000 beta4 nu^2 - 1459613209500000 beta4 nu - 14594799480000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 99955250000 beta4^2 nu + 1998740000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1998740000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [2737500000 beta4^2 nu^2 + 666234500000 beta4^2 nu + 38915023595000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ [62500 beta4^2 nu^2 + 36502500 beta4^2 nu + 3997480025 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 1250 beta4 nu + 547525 beta4 - 182550 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 19450849635000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [68437500000 beta4^2 nu^3 + 16657231250000 beta4^2 nu^2 + 973208707125000 beta4^2 nu + 19457511797500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ [27375000 beta4 nu + 2665047500 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 666234500000 beta4^2 nu + 38915023595000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 33311725000000 beta4^2 nu^2 + 2918959859500000 beta4^2 nu + 58365873230000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 < 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 19450849635000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 < 0 ]]]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 799496000000 beta4^2 nu + 38917688460000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 < 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 91272500 beta4 nu^2 + 2002025450 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 27367500 beta4 nu^2 - 2665594850 beta4 nu - 53300949 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 912600 beta4 nu + 79953251 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 7993864850 beta4 nu - 159873649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 729900 nu - 14599 < 0 /\ 50 nu - 3649 = 0 ]] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 5329365000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 5329365000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 2665595000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [91250000000 beta4^2 nu^3 + 26650475000000 beta4^2 nu^2 + 1946150909500000 beta4^2 nu + 38912358730000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 729900 nu - 14599 < 0 /\ 50 nu - 3649 = 0 ]] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [91250000000 beta4^2 nu^3 + 33311725000000 beta4^2 nu^2 + 2918959859500000 beta4^2 nu + 58365873230000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 799496000000 beta4^2 nu + 38917688460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 19461509095000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 - 266377000000 beta4^2 nu - 77808728270000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 106587299 < 0 ]]]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 27367500 beta4 nu^2 - 2665594850 beta4 nu - 53300949 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 912600 beta4 nu + 79953251 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 7993864850 beta4 nu - 159873649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 912600 beta4 nu + 79953251 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 7993864850 beta4 nu - 159873649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [532900000000 beta4^2 - 333153750000 beta4 nu - 6663075000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ [638750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]]] /\ [333062500000000 beta4^2 nu^2 + 72954010000000000 beta4^2 nu + 1458946975000000 beta4^2 - 333153750000000 beta4 nu^3 - 36500324850000000 beta4 nu^2 - 1459613209500000 beta4 nu - 14594799480000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 166567750000 beta4^2 nu + 3330990000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [18250000 beta4 nu + 3330990000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [456250000 beta4^2 nu^2 - 16634875000 beta4^2 nu - 332880000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [532900000000 beta4^2 - 333153750000 beta4 nu - 6663075000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1460000 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [584000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 584000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [333062500000000 beta4^2 nu^2 + 72954010000000000 beta4^2 nu + 1458946975000000 beta4^2 - 333153750000000 beta4 nu^3 - 36500324850000000 beta4 nu^2 - 1459613209500000 beta4 nu - 14594799480000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 99937000000 beta4^2 nu + 1998557500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 999735075 beta4 nu - 9996438 beta4 < 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [456250000 beta4^2 nu^2 - 16634875000 beta4^2 nu - 332880000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 ]]]]] \/ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 9992604850 beta4 nu - 199844799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 319425 beta4 nu + 9998263 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1496500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2131600000000 beta4^2 - 666307500000 beta4 nu - 13326150000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2920000 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 291816040000000000 beta4^2 nu + 5835787900000000 beta4^2 - 666307500000000 beta4 nu^3 - 73000649700000000 beta4 nu^2 - 2919226419000000 beta4 nu - 29189598960000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 999735075 beta4 nu - 9996438 beta4 < 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 9992604850 beta4 nu - 199844799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 319425 beta4 nu + 9998263 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2920000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 ] /\ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 49275000 beta4 nu + 5329985500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [63875000000 beta4^2 nu^3 + 23318207500000 beta4^2 nu^2 + 2043271901650000 beta4^2 nu + 40856111261000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 > 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2555000000 beta4^2 nu^2 + 559647200000 beta4^2 nu + 27242381922000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 > 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [2500 nu^2 - 729900 nu - 14599 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2463750000 beta4^2 nu^2 + 266548550000 beta4^2 nu + 5329985500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 5329985500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 7994230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 beta4^2 nu + 620550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 1095100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 18655332500000 beta4^2 nu^2 + 1362305636650000 beta4^2 nu + 27238651111000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 23318207500000 beta4^2 nu^2 + 2043271901650000 beta4^2 nu + 40856111261000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 559647200000 beta4^2 nu + 27242381922000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2463750000 beta4^2 nu^2 + 453063550000 beta4^2 nu + 13624655285500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1496500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2131600000000 beta4^2 - 666307500000 beta4 nu - 13326150000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2920000 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 291816040000000000 beta4^2 nu + 5835787900000000 beta4^2 - 666307500000000 beta4 nu^3 - 73000649700000000 beta4 nu^2 - 2919226419000000 beta4 nu - 29189598960000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 999735075 beta4 nu - 9996438 beta4 < 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 9992604850 beta4 nu - 199844799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2920000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 620550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 547550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ [2463750000 beta4^2 nu^2 + 453063550000 beta4^2 nu + 13624655285500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 - 266377000000 beta4^2 nu - 77808728270000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 106587299 > 0 ]]]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 27367500 beta4 nu^2 - 2665594850 beta4 nu - 53300949 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 912600 beta4 nu + 79953251 beta4 < 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 7993864850 beta4 nu - 159873649 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4 - 60850 nu - 1217 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 194561790000000000 beta4^2 nu + 3890702900000000 beta4^2 - 666307500000000 beta4 nu^3 - 48680425950000000 beta4 nu^2 - 1946417469000000 beta4 nu - 19461509460000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]]] \/ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 5329729850 beta4 nu - 106587299 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [175000 beta4^2 nu^2 + 19169500 beta4^2 nu + 466670820 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 31944500 beta4^2 nu + 933213820 beta4^2 - 13691250 beta4 nu^2 - 500278275 beta4 nu - 10000089 beta4 < 0 \/ 7000 beta4 nu + 1022140 beta4 - 547650 nu - 10953 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [319375000 beta4^2 nu^2 - 34958787500 beta4^2 nu - 1702648678500 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 7299 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [511000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]] \/ [10128750000 beta4^2 nu^2 + 446708900000 beta4^2 nu + 4871642626500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 /\ 375000 beta4^2 nu^2 + 31040000 beta4^2 nu + 533520650 beta4^2 - 9127500 beta4 nu^2 - 222467600 beta4 nu - 4445701 beta4 > 0 /\ 38325000 beta4^2 nu + 933341500 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1575000 beta4^2 nu^2 + 191688000 beta4^2 nu + 3734133130 beta4^2 - 82147500 beta4 nu^2 - 2002208400 beta4 nu - 40011309 beta4 < 0 \/ 2682750000 beta4^2 nu + 130614155000 beta4^2 - 1916775000 beta4 nu^2 - 140001246000 beta4 nu - 2799258210 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10500 beta4 nu + 1022210 beta4 - 547650 nu - 10953 = 0 ] /\ [119765625000 beta4^2 nu^3 + 6418639062500 beta4^2 nu^2 + 85354070593750 beta4^2 nu + 1704514914375 beta4^2 - 34228125000 beta4 nu^4 - 2084949187500 beta4 nu^3 - 30525294491250 beta4 nu^2 - 1218510935925 beta4 nu - 12176775039 beta4 < 0 \/ 652802500000000 beta4^2 nu^2 + 11939757725000000 beta4^2 nu + 238534033500000 beta4^2 - 583019062500000 beta4 nu^3 - 8547059456250000 beta4 nu^2 - 341182755375000 beta4 nu - 3409495477500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [15968750 beta4 nu + 466606875 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]] \/ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 7299 = 0 ]]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 89432000 beta4^2 nu + 9327538570 beta4^2 - 27382500 beta4 nu^2 - 3998940300 beta4 nu - 79967853 beta4 < 0 \/ 3500 beta4 nu + 1277570 beta4 - 547650 nu - 10953 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [7984375000 beta4^2 nu^3 + 1749057187500 beta4^2 nu^2 + 85167421456250 beta4^2 nu + 1702648870125 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ [3193750 beta4 nu + 233207625 beta4 - 1521250 nu^2 - 55586475 nu - 1111121 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 25 nu - 912 = 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 539623300000 beta4^2 nu + 43775204345500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 2797980500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 /\ 250000 beta4^2 nu^2 + 122285000 beta4^2 nu + 14790420600 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 67530000 beta4^2 nu + 8794200550 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [175000 beta4^2 nu^2 + 114982000 beta4^2 nu + 16788649570 beta4^2 - 27382500 beta4 nu^2 - 5997862800 beta4 nu - 119946303 beta4 < 0 \/ 894250000 beta4^2 nu + 261138885000 beta4^2 - 638925000 beta4 nu^2 - 233233182000 beta4 nu - 4664408070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 1533070 beta4 - 547650 nu - 10953 = 0 ] /\ [23953125000 beta4^2 nu^3 + 7578609062500 beta4^2 nu^2 + 510887928118750 beta4^2 nu + 10214727310375 beta4^2 - 11409375000 beta4 nu^4 - 2916008062500 beta4 nu^3 - 91375772163750 beta4 nu^2 - 3651532041975 beta4 nu - 36503658213 beta4 < 0 \/ 326401250000000 beta4^2 nu^2 + 35753992925000000 beta4^2 nu + 714949298000000 beta4^2 - 349811437500000 beta4 nu^3 - 25557223623750000 beta4 nu^2 - 1021869171225000 beta4 nu - 10217292466500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [9581250 beta4 nu + 932766625 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]] \/ [95812500000 beta4^2 nu^3 + 2337186250000 beta4^2 nu^2 - 510491440025000 beta4^2 nu - 12434441200408500 beta4^2 - 68456250000 beta4 nu^4 - 1671245250000 beta4 nu^3 + 364703245830000 beta4 nu^2 + 8891471801886900 beta4 nu + 177683541380397 beta4 < 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 /\ 375000 beta4^2 nu^2 + 31040000 beta4^2 nu + 533520650 beta4^2 - 9127500 beta4 nu^2 - 222467600 beta4 nu - 4445701 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [10128750000 beta4^2 nu^2 + 446708900000 beta4^2 nu + 4871642626500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [10128750000 beta4^2 nu^2 + 446708900000 beta4^2 nu + 4871642626500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4790625000000 beta4^2 nu^4 + 116955125000000 beta4^2 nu^3 - 25522234815000000 beta4^2 nu^2 - 622232551460450000 beta4^2 nu - 12434441200408500 beta4^2 - 3422812500000 beta4 nu^5 - 83630718750000 beta4 nu^4 + 18233491046250000 beta4 nu^3 + 444938293340175000 beta4 nu^2 + 17775648870906750 beta4 nu + 177683541380397 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1916250000 beta4^2 nu^2 - 233067100000 beta4^2 nu - 6812459608500 beta4^2 - 1369125000 beta4 nu^3 + 166494727500 beta4 nu^2 + 4870706182050 beta4 nu + 97347514797 beta4 > 0 \/ 2500 nu^2 - 182400 nu - 26648649 < 0 ]]] /\ [13125000 beta4^2 nu^3 + 2236412500 beta4^2 nu^2 + 116661315750 beta4^2 nu + 1704281706855 beta4^2 - 456375000 beta4 nu^3 - 44447882500 beta4 nu^2 - 812451492650 beta4 nu - 16231254351 beta4 < 0 \/ 2682750000 beta4^2 nu + 130614155000 beta4^2 - 1916775000 beta4 nu^2 - 140001246000 beta4 nu - 2799258210 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 127785 beta4 - 60850 nu - 1217 = 0 ] /\ [11976562500000 beta4^2 nu^4 + 1341534687500000 beta4^2 nu^3 + 38374324275000000 beta4^2 nu^2 + 312139124450125000 beta4^2 nu + 6227443489653750 beta4^2 - 3422812500000 beta4 nu^5 - 333496031250000 beta4 nu^4 - 6106721928750000 beta4 nu^3 - 365603199075000 beta4 nu^2 - 7306730783250 beta4 nu - 48693763053 beta4 < 0 \/ 652802500000000 beta4^2 nu^2 + 11939757725000000 beta4^2 nu + 238534033500000 beta4^2 - 583019062500000 beta4 nu^3 - 8547059456250000 beta4 nu^2 - 341182755375000 beta4 nu - 3409495477500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 31937500 beta4 nu + 466926250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [31937500000 beta4^2 nu^3 + 6996228750000 beta4^2 nu^2 - 169915126675000 beta4^2 nu - 37276092413269500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 + 121301225610000 beta4 nu^2 + 26635503053502300 beta4 nu + 532661500590399 beta4 > 0 /\ 125000 beta4^2 nu^2 + 67530000 beta4^2 nu + 8794200550 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [1551250000 beta4^2 nu^2 + 539623300000 beta4^2 nu + 43775204345500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [31025000 beta4 nu + 3997370500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 2797980500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 > 0 ] /\ [250000 beta4^2 nu^2 + 122285000 beta4^2 nu + 14790420600 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1350600 beta4 - 182550 nu - 3651 = 0 ] /\ [1596875000000 beta4^2 nu^4 + 349843375000000 beta4^2 nu^3 - 8488760105000000 beta4^2 nu^2 - 1863974535790150000 beta4^2 nu - 37276092413269500 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 + 6060062148750000 beta4 nu^3 + 1331896453900725000 beta4 nu^2 + 53268578083022250 beta4 nu + 532661500590399 beta4 > 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu - 20422459669500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 + 14590801087350 beta4 nu + 291829355199 beta4 > 0 \/ 2500 nu^2 - 182400 nu - 26648649 < 0 ]]] /\ [4375000 beta4^2 nu^3 + 2874637500 beta4^2 nu^2 + 536345605250 beta4^2 nu + 25539966387285 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 894250000 beta4^2 nu + 261138885000 beta4^2 - 638925000 beta4 nu^2 - 233233182000 beta4 nu - 4664408070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 638785 beta4 - 182550 nu - 3651 = 0 ] /\ [798437500000 beta4^2 nu^4 + 291493562500000 beta4^2 nu^3 + 29801601760000000 beta4^2 nu^2 + 933008997116175000 beta4^2 nu + 18648261633440250 beta4^2 - 380312500000 beta4 nu^5 - 111089281250000 beta4 nu^4 - 6088941558750000 beta4 nu^3 - 365069909675000 beta4 nu^2 - 7299621069250 beta4 nu - 48658216917 beta4 < 0 \/ 326401250000000 beta4^2 nu^2 + 35753992925000000 beta4^2 nu + 714949298000000 beta4^2 - 349811437500000 beta4 nu^3 - 25557223623750000 beta4 nu^2 - 1021869171225000 beta4 nu - 10217292466500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 6387500 beta4 nu + 466415250 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [4790625000000 beta4^2 nu^4 + 1282673875000000 beta4^2 nu^3 + 42625683310000000 beta4^2 nu^2 - 1861931077347950000 beta4^2 nu - 37255661559658500 beta4^2 - 3422812500000 beta4 nu^5 - 916515093750000 beta4 nu^4 - 30473587203750000 beta4 nu^3 + 1329706034442675000 beta4 nu^2 + 53224780356606750 beta4 nu + 532369551288897 beta4 < 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 < 0 /\ [3376250000 beta4^2 nu^2 + 66747550000 beta4^2 nu + 1333600500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [31025000 beta4^2 nu + 1332870500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [123187500000 beta4^2 nu^3 + 15661328750000 beta4^2 nu^2 + 486897555325000 beta4^2 nu + 9731687560500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 /\ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [31025000 beta4^2 nu + 2665120500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [31025000 beta4 nu + 2665120500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [123187500000 beta4^2 nu^3 + 22322578750000 beta4^2 nu^2 + 973435255325000 beta4^2 nu + 19459777060500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 \/ 49275000 beta4 nu + 5329985500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2463750000 beta4^2 nu^2 + 66711050000 beta4^2 nu + 1333235500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [4288750000 beta4^2 nu^2 + 446475300000 beta4^2 nu + 9734352790500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [125000 beta4^2 nu^2 + 67530000 beta4^2 nu + 4264550550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [3376250000 beta4^2 nu^2 + 313213800000 beta4^2 nu + 4868975425500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ [4288750000 beta4^2 nu^2 + 313250300000 beta4^2 nu + 6263290500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [1715500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [85775000 beta4^2 nu + 6263290500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [821250000 beta4^2 nu^2 - 59918400000 beta4^2 nu - 8754081196500 beta4^2 - 152125000 beta4 nu^3 + 11095997500 beta4 nu^2 + 1621792272450 beta4 nu + 32431405833 beta4 > 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 - 182400 nu - 26648649 < 0 ]]]] /\ [1149750000 beta4^2 nu + 407691495000 beta4^2 - 212975000 beta4 nu^2 - 135491044000 beta4 nu - 2709735690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1750 beta4^2 nu + 1113285 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1750 beta4 nu + 1113285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3285000000 beta4^2 nu + 563607450000 beta4^2 - 608500000 beta4 nu^2 - 164380190000 beta4 nu - 3287360400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [85775000 beta4^2 nu + 13457440500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 \/ 85775000 beta4 nu + 13457440500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1019171250000000 beta4^2 nu^2 + 15358311225000000 beta4^2 nu + 306758556000000 beta4^2 - 338706312500000 beta4 nu^3 - 2857681816250000 beta4 nu^2 - 113900825075000 beta4 nu - 1137653425500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2783125000 beta4^2 nu^2 + 23425700000 beta4^2 nu + 467400750 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 55662500 beta4 nu + 467400750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1408854375000000 beta4^2 nu^2 + 43820766675000000 beta4^2 nu + 875851791750000 beta4^2 - 410889625000000 beta4 nu^3 - 8131394627500000 beta4 nu^2 - 324762717550000 beta4 nu - 3245983617000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [9216250000 beta4^2 nu^2 + 313447400000 beta4^2 nu + 6265261500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 \/ [184325000 beta4 nu + 6265261500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu + 851674246500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 - 34958787500 beta4^2 nu - 1702648678500 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 182400 nu - 26648649 < 0 ]]]] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 958387500 beta4^2 nu^2 + 64152861500 beta4^2 nu + 1277744705160 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu + 851674246500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [1596875000000 beta4^2 nu^4 + 204128531250000 beta4^2 nu^3 + 7458272395000000 beta4^2 nu^2 + 77949526227037500 beta4^2 nu + 1556008848355500 beta4^2 - 570468750000 beta4 nu^5 - 62523375000000 beta4 nu^4 - 1525013572500000 beta4 nu^3 - 91350803887500 beta4 nu^2 - 1826016160125 beta4 nu - 12170108313 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [95812500000 beta4^2 nu^3 + 11662936250000 beta4^2 nu^2 + 340856277475000 beta4^2 nu + 6812461141500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 nu^3 - 9117500 nu^2 - 1332614850 nu - 26648649 < 0 /\ 50 nu - 3649 = 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [95812500000 beta4^2 nu^3 + 16325811250000 beta4^2 nu^2 + 681432667475000 beta4^2 nu + 13622123791500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 \/ 38325000 beta4 nu + 3731066500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3193750000 beta4^2 nu^2 + 326529000000 beta4^2 nu + 6814326802500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [63875000 beta4 nu + 1866427500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [31025000 beta4 nu + 2665120500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 6810595480500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [31937500000 beta4^2 nu^3 + 6996228750000 beta4^2 nu^2 + 340669685825000 beta4^2 nu + 6810595480500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 182400 nu - 26648649 < 0 ]]]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 2235887500 beta4^2 nu^2 + 326490680250 beta4^2 nu + 13622123919285 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2395312500000 beta4^2 nu^4 + 641336937500000 beta4^2 nu^3 + 51096955717500000 beta4^2 nu^2 + 1244466152451025000 beta4^2 nu + 24868889397045750 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 - 12180105663750000 beta4 nu^3 - 730206480525000 beta4 nu^2 - 14600130852750 beta4 nu - 97320877101 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 6810595480500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 < 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7984375000 beta4^2 nu^3 + 1749057187500 beta4^2 nu^2 + 85167421456250 beta4^2 nu + 1702648870125 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ [3193750 beta4 nu + 233207625 beta4 - 1521250 nu^2 - 55586475 nu - 1111121 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 89432000 beta4^2 nu + 9327538570 beta4^2 - 27382500 beta4 nu^2 - 3998940300 beta4 nu - 79967853 beta4 < 0 \/ 3500 beta4 nu + 1277570 beta4 - 547650 nu - 10953 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 7299 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 25 nu - 912 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [7984375000 beta4^2 nu^3 + 1749057187500 beta4^2 nu^2 + 85167421456250 beta4^2 nu + 1702648870125 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ [3193750 beta4 nu + 233207625 beta4 - 1521250 nu^2 - 55586475 nu - 1111121 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [350000 beta4^2 nu^2 + 89439000 beta4^2 nu + 4664663640 beta4^2 - 27382500 beta4 nu^2 - 2000017800 beta4 nu - 39989403 beta4 < 0 \/ 1788500000 beta4^2 nu + 195876520000 beta4^2 - 1277850000 beta4 nu^2 - 186617214000 beta4 nu - 3731833140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 7000 beta4 nu + 1277640 beta4 - 547650 nu - 10953 = 0 ] /\ [31937500000 beta4^2 nu^3 + 4081931875000 beta4^2 nu^2 + 127809442075000 beta4^2 nu + 2554556324250 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 \/ 489601875000000 beta4^2 nu^2 + 23846875325000000 beta4^2 nu + 476741665750000 beta4^2 - 466415250000000 beta4 nu^3 - 17052141540000000 beta4 nu^2 - 681525963300000 beta4 nu - 6813393972000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [12775000 beta4 nu + 699686750 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]] \/ [2445500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1022000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1022000 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [163200625000000 beta4^2 nu^2 + 35747464900000000 beta4^2 nu + 714884017750000 beta4^2 - 233207625000000 beta4 nu^3 - 25550227395000000 beta4 nu^2 - 1021729246650000 beta4 nu - 10216359636000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 46641525000 beta4^2 nu + 932702750 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [6387500 beta4 nu + 932702750 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 25 nu - 912 = 0 ]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000 beta4^2 - 279849150000 beta4 nu - 5596983000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1788500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 1788500 beta4 - 547650 nu - 10953 = 0 ] /\ [163200625000000 beta4^2 nu^2 + 47661110525000000 beta4^2 nu + 953156930250000 beta4^2 - 233207625000000 beta4 nu^3 - 34062305707500000 beta4 nu^2 - 1362212379150000 beta4 nu - 13621190961000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 319375000 beta4^2 nu^2 + 58298712500 beta4^2 nu + 1165846500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [6387500 beta4 nu + 1165846500 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]] \/ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 170194899175000 beta4^2 nu - 3403898494500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 < 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 3403898494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 < 0 /\ 500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [175000 beta4^2 nu^2 + 38332000 beta4^2 nu + 1865916570 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1788500000 beta4^2 nu + 195876520000 beta4^2 - 1277850000 beta4 nu^2 - 186617214000 beta4 nu - 3731833140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [15968750000 beta4^2 nu^3 + 583817500000 beta4^2 nu^2 - 42525400837500 beta4^2 nu - 850741416000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 + 30375265773750 beta4 nu^2 + 1215511091775 beta4 nu + 12156778512 beta4 < 0 \/ 1250 nu^2 - 45575 nu - 912 > 0 ]]] /\ [63875000000 beta4^2 nu^3 + 6998145000000 beta4^2 nu^2 + 170474786650000 beta4^2 nu + 3406696986000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 489601875000000 beta4^2 nu^2 + 23846875325000000 beta4^2 nu + 476741665750000 beta4^2 - 466415250000000 beta4 nu^3 - 17052141540000000 beta4 nu^2 - 681525963300000 beta4 nu - 6813393972000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [85775000 beta4^2 nu + 1715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [491600250000 beta4^2 - 151029700000 beta4 nu - 3020594000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1496500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [803346750000 beta4^2 - 208776350000 beta4 nu - 4175527000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [1350500 beta4 - 182550 nu - 3651 = 0 /\ [2445500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [410625000 beta4^2 nu^2 - 14971387500 beta4^2 nu - 299592000 beta4^2 - 76062500 beta4 nu^3 + 2771717500 beta4 nu^2 + 110959975 beta4 nu + 1109904 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 ]]]] /\ [809341875000000 beta4^2 nu^2 + 30667462425000000 beta4^2 nu + 613025511750000 beta4^2 - 299838375000000 beta4 nu^3 - 5692709177500000 beta4 nu^2 - 227348561050000 beta4 nu - 2272286257000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [809341875000000 beta4^2 nu^2 + 87561198675000000 beta4^2 nu + 1750900236750000 beta4^2 - 299838375000000 beta4 nu^3 - 16231472802500000 beta4 nu^2 - 648899106050000 beta4 nu - 6487791707000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[49275000 beta4 nu + 5329985500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 6262560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [49275000 beta4 nu + 6262560500 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 49275000 beta4 nu + 5329985500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 680779711675000 beta4^2 nu - 13615594744500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 486404420235000 beta4 nu^2 + 19456178269800 beta4 nu + 194561786349 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 38328500 beta4^2 nu + 3731066535 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 - 93231950000 beta4^2 nu - 27233054894500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 14599 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 ]]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 9328624375000 beta4^2 nu^2 + 340762962487500 beta4^2 nu + 6811528183250 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 5595705500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 5595705500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 3731066500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 3731066500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2445500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2445500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [638750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [163200625000000 beta4^2 nu^2 + 35747464900000000 beta4^2 nu + 714884017750000 beta4^2 - 233207625000000 beta4 nu^3 - 25550227395000000 beta4 nu^2 - 1021729246650000 beta4 nu - 10216359636000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 69968675000 beta4^2 nu + 1399118000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1399118000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [95812500000 beta4^2 nu^3 + 9331498750000 beta4^2 nu^2 + 170568082475000 beta4^2 nu + 3407629816500 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 > 0 /\ 95812500000 beta4^2 nu^3 + 2337186250000 beta4^2 nu^2 - 510491440025000 beta4^2 nu - 12434441200408500 beta4^2 - 68456250000 beta4 nu^4 - 1671245250000 beta4 nu^3 + 364703245830000 beta4 nu^2 + 8891471801886900 beta4 nu + 177683541380397 beta4 < 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 /\ 375000 beta4^2 nu^2 + 31040000 beta4^2 nu + 533520650 beta4^2 - 9127500 beta4 nu^2 - 222467600 beta4 nu - 4445701 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [10128750000 beta4^2 nu^2 + 446708900000 beta4^2 nu + 4871642626500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [10128750000 beta4^2 nu^2 + 446708900000 beta4^2 nu + 4871642626500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [4790625000000 beta4^2 nu^4 + 116955125000000 beta4^2 nu^3 - 25522234815000000 beta4^2 nu^2 - 622232551460450000 beta4^2 nu - 12434441200408500 beta4^2 - 3422812500000 beta4 nu^5 - 83630718750000 beta4 nu^4 + 18233491046250000 beta4 nu^3 + 444938293340175000 beta4 nu^2 + 17775648870906750 beta4 nu + 177683541380397 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1916250000 beta4^2 nu^2 - 372953350000 beta4^2 nu - 10219156083500 beta4^2 - 1369125000 beta4 nu^3 + 266440852500 beta4 nu^2 + 7306726402050 beta4 nu + 146027940747 beta4 < 0 \/ 2500 nu^2 - 364900 nu - 39974799 > 0 ]]] /\ [13125000 beta4^2 nu^3 + 2236412500 beta4^2 nu^2 + 116661315750 beta4^2 nu + 1704281706855 beta4^2 - 456375000 beta4 nu^3 - 44447882500 beta4 nu^2 - 812451492650 beta4 nu - 16231254351 beta4 < 0 \/ 2682750000 beta4^2 nu + 130614155000 beta4^2 - 1916775000 beta4 nu^2 - 140001246000 beta4 nu - 2799258210 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 127785 beta4 - 60850 nu - 1217 = 0 ] /\ [11976562500000 beta4^2 nu^4 + 1341534687500000 beta4^2 nu^3 + 38374324275000000 beta4^2 nu^2 + 312139124450125000 beta4^2 nu + 6227443489653750 beta4^2 - 3422812500000 beta4 nu^5 - 333496031250000 beta4 nu^4 - 6106721928750000 beta4 nu^3 - 365603199075000 beta4 nu^2 - 7306730783250 beta4 nu - 48693763053 beta4 < 0 \/ 652802500000000 beta4^2 nu^2 + 11939757725000000 beta4^2 nu + 238534033500000 beta4^2 - 583019062500000 beta4 nu^3 - 8547059456250000 beta4 nu^2 - 341182755375000 beta4 nu - 3409495477500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 31937500 beta4 nu + 466926250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [31937500000 beta4^2 nu^3 + 9327666250000 beta4^2 nu^2 + 510957880825000 beta4^2 nu + 10215426805500 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 /\ 31937500000 beta4^2 nu^3 + 6996228750000 beta4^2 nu^2 - 169915126675000 beta4^2 nu - 37276092413269500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 + 121301225610000 beta4 nu^2 + 26635503053502300 beta4 nu + 532661500590399 beta4 > 0 /\ 125000 beta4^2 nu^2 + 67530000 beta4^2 nu + 8794200550 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [1551250000 beta4^2 nu^2 + 539623300000 beta4^2 nu + 43775204345500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [31025000 beta4 nu + 3997370500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 2797980500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 > 0 ] /\ [250000 beta4^2 nu^2 + 122285000 beta4^2 nu + 14790420600 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1350600 beta4 - 182550 nu - 3651 = 0 ] /\ [1596875000000 beta4^2 nu^4 + 349843375000000 beta4^2 nu^3 - 8488760105000000 beta4^2 nu^2 - 1863974535790150000 beta4^2 nu - 37276092413269500 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 + 6060062148750000 beta4 nu^3 + 1331896453900725000 beta4 nu^2 + 53268578083022250 beta4 nu + 532661500590399 beta4 > 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 30635088494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 21888200827350 beta4 nu + 437764023849 beta4 < 0 \/ 2500 nu^2 - 364900 nu - 39974799 > 0 ]]] /\ [4375000 beta4^2 nu^3 + 2874637500 beta4^2 nu^2 + 536345605250 beta4^2 nu + 25539966387285 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 894250000 beta4^2 nu + 261138885000 beta4^2 - 638925000 beta4 nu^2 - 233233182000 beta4 nu - 4664408070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 638785 beta4 - 182550 nu - 3651 = 0 ] /\ [798437500000 beta4^2 nu^4 + 291493562500000 beta4^2 nu^3 + 29801601760000000 beta4^2 nu^2 + 933008997116175000 beta4^2 nu + 18648261633440250 beta4^2 - 380312500000 beta4 nu^5 - 111089281250000 beta4 nu^4 - 6088941558750000 beta4 nu^3 - 365069909675000 beta4 nu^2 - 7299621069250 beta4 nu - 48658216917 beta4 < 0 \/ 326401250000000 beta4^2 nu^2 + 35753992925000000 beta4^2 nu + 714949298000000 beta4^2 - 349811437500000 beta4 nu^3 - 25557223623750000 beta4 nu^2 - 1021869171225000 beta4 nu - 10217292466500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 6387500 beta4 nu + 466415250 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [4790625000000 beta4^2 nu^4 + 1282673875000000 beta4^2 nu^3 + 42625683310000000 beta4^2 nu^2 - 1861931077347950000 beta4^2 nu - 37255661559658500 beta4^2 - 3422812500000 beta4 nu^5 - 916515093750000 beta4 nu^4 - 30473587203750000 beta4 nu^3 + 1329706034442675000 beta4 nu^2 + 53224780356606750 beta4 nu + 532369551288897 beta4 < 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [125000 beta4^2 nu^2 + 67530000 beta4^2 nu + 4264550550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ [3376250000 beta4^2 nu^2 + 313213800000 beta4^2 nu + 4868975425500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [85775000 beta4^2 nu + 6263290500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ [4288750000 beta4^2 nu^2 + 313250300000 beta4^2 nu + 6263290500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [1715500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [821250000 beta4^2 nu^2 - 119869650000 beta4^2 nu - 13131721471500 beta4^2 - 152125000 beta4 nu^3 + 22201122500 beta4 nu^2 + 2432910602450 beta4 nu + 48649330383 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 - 364900 nu - 39974799 > 0 ]]]] /\ [1149750000 beta4^2 nu + 407691495000 beta4^2 - 212975000 beta4 nu^2 - 135491044000 beta4 nu - 2709735690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1750 beta4^2 nu + 1113285 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1750 beta4 nu + 1113285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3285000000 beta4^2 nu + 563607450000 beta4^2 - 608500000 beta4 nu^2 - 164380190000 beta4 nu - 3287360400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [85775000 beta4^2 nu + 13457440500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 \/ 85775000 beta4 nu + 13457440500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [1019171250000000 beta4^2 nu^2 + 15358311225000000 beta4^2 nu + 306758556000000 beta4^2 - 338706312500000 beta4 nu^3 - 2857681816250000 beta4 nu^2 - 113900825075000 beta4 nu - 1137653425500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2783125000 beta4^2 nu^2 + 23425700000 beta4^2 nu + 467400750 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 55662500 beta4 nu + 467400750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1408854375000000 beta4^2 nu^2 + 43820766675000000 beta4^2 nu + 875851791750000 beta4^2 - 410889625000000 beta4 nu^3 - 8131394627500000 beta4 nu^2 - 324762717550000 beta4 nu - 3245983617000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [9216250000 beta4^2 nu^2 + 313447400000 beta4^2 nu + 6265261500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 < 0 \/ [184325000 beta4 nu + 6265261500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu + 851674246500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 - 58273162500 beta4^2 nu - 2554089653500 beta4^2 - 228187500 beta4 nu^3 + 41630527500 beta4 nu^2 + 1825682276175 beta4 nu + 36496991487 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 39974799 > 0 ]]]] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 958387500 beta4^2 nu^2 + 64152861500 beta4^2 nu + 1277744705160 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [319375000 beta4^2 nu^2 + 34984337500 beta4^2 nu + 851674246500 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [1596875000000 beta4^2 nu^4 + 204128531250000 beta4^2 nu^3 + 7458272395000000 beta4^2 nu^2 + 77949526227037500 beta4^2 nu + 1556008848355500 beta4^2 - 570468750000 beta4 nu^5 - 62523375000000 beta4 nu^4 - 1525013572500000 beta4 nu^3 - 91350803887500 beta4 nu^2 - 1826016160125 beta4 nu - 12170108313 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [31937500000 beta4^2 nu^3 + 6996228750000 beta4^2 nu^2 + 340669685825000 beta4^2 nu + 6810595480500 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [31025000 beta4 nu + 2665120500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 6810595480500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 - 46603200000 beta4^2 nu - 20424324819500 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 14593466317350 beta4 nu + 291856007499 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 39974799 > 0 ]]]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 2235887500 beta4^2 nu^2 + 326490680250 beta4^2 nu + 13622123919285 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2395312500000 beta4^2 nu^4 + 641336937500000 beta4^2 nu^3 + 51096955717500000 beta4^2 nu^2 + 1244466152451025000 beta4^2 nu + 24868889397045750 beta4^2 - 1140937500000 beta4 nu^5 - 249979406250000 beta4 nu^4 - 12180105663750000 beta4 nu^3 - 730206480525000 beta4 nu^2 - 14600130852750 beta4 nu - 97320877101 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 6810595480500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [7984375000 beta4^2 nu^3 + 479062500 beta4^2 nu^2 - 10637174012500 beta4^2 nu - 212743608000 beta4^2 - 5704687500 beta4 nu^4 - 456375000 beta4 nu^3 + 7600056230625 beta4 nu^2 + 304002614325 beta4 nu + 3040027056 beta4 < 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 < 0 /\ 125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [87500 beta4^2 nu^2 + 12778500 beta4^2 nu + 349971160 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 1750494375000 beta4^2 nu^2 + 21344348637500 beta4^2 nu + 426187030500 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 \/ 489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [85775000 beta4^2 nu + 1715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [407668500000 beta4^2 - 135482525000 beta4 nu - 2709650500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1241000 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1113250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1113250 beta4 - 182550 nu - 3651 = 0 ]]] /\ [563541750000 beta4^2 - 164355850000 beta4 nu - 3287117000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1715500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [3686500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 3686500 beta4 - 547650 nu - 10953 = 0 ]]] /\ [809341875000000 beta4^2 nu^2 + 15349918050000000 beta4^2 nu + 306674624250000 beta4^2 - 299838375000000 beta4 nu^3 - 2855349740000000 beta4 nu^2 - 113854183550000 beta4 nu - 1137342482000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2463750000 beta4^2 nu^2 + 23412925000 beta4^2 nu + 467273000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 49275000 beta4 nu + 467273000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [809341875000000 beta4^2 nu^2 + 43796786175000000 beta4^2 nu + 875611986750000 beta4^2 - 299838375000000 beta4 nu^3 - 8124731552500000 beta4 nu^2 - 324629456050000 beta4 nu - 3245095207000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1565886500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [24637500 beta4 nu + 1565886500 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 125000 beta4^2 nu^2 + 31030000 beta4^2 nu + 1599320550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 3403898494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 170194899175000 beta4^2 nu - 3403898494500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 25553500 beta4^2 nu + 1399373535 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 - 93231950000 beta4^2 nu - 10213561144500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 7298731807350 beta4 nu + 145947991149 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 10949 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 4665749375000 beta4^2 nu^2 + 85284041237500 beta4^2 nu + 1703814908250 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1715500 beta4 - 182550 nu - 3651 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 89432000 beta4^2 nu + 9327538570 beta4^2 - 27382500 beta4 nu^2 - 3998940300 beta4 nu - 79967853 beta4 < 0 \/ 3500 beta4 nu + 1277570 beta4 - 547650 nu - 10953 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7984375000 beta4^2 nu^3 + 1749057187500 beta4^2 nu^2 + 85167421456250 beta4^2 nu + 1702648870125 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ [3193750 beta4 nu + 233207625 beta4 - 1521250 nu^2 - 55586475 nu - 1111121 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [63875000000 beta4^2 nu^3 + 23318207500000 beta4^2 nu^2 + 2043271901650000 beta4^2 nu + 40856111261000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 < 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2555000000 beta4^2 nu^2 + 559647200000 beta4^2 nu + 27242381922000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 < 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 45675 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 91272500 beta4 nu^2 + 2002025450 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 89432000 beta4^2 nu + 9327538570 beta4^2 - 27382500 beta4 nu^2 - 3998940300 beta4 nu - 79967853 beta4 < 0 \/ 3500 beta4 nu + 1277570 beta4 - 547650 nu - 10953 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7984375000 beta4^2 nu^3 + 1749057187500 beta4^2 nu^2 + 85167421456250 beta4^2 nu + 1702648870125 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ [3193750 beta4 nu + 233207625 beta4 - 1521250 nu^2 - 55586475 nu - 1111121 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [31937500000 beta4^2 nu^3 + 4664791250000 beta4^2 nu^2 - 510398259175000 beta4^2 nu - 10209830844500 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 + 364603409235000 beta4 nu^2 + 14588135674800 beta4 nu + 145894686549 beta4 < 0 /\ 638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 2797980500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu - 10209830844500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 + 7293401347350 beta4 nu + 145894686549 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [125000 beta4^2 nu^2 + 67530000 beta4^2 nu + 8794200550 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [2500 beta4 nu + 803050 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [125000 beta4^2 nu^2 + 67530000 beta4^2 nu + 8794200550 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 803050 beta4 - 182550 nu - 3651 = 0 ] /\ [821250000 beta4^2 nu^2 + 313111600000 beta4^2 nu + 29182536903500 beta4^2 - 152125000 beta4 nu^3 - 33324502500 beta4 nu^2 - 1332797550 beta4 nu - 13327367 beta4 > 0 \/ 16425000 beta4 nu + 2664828500 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [4375000 beta4^2 nu^3 + 2555262500 beta4^2 nu^2 + 349817830250 beta4^2 nu + 6995334535 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 894250000 beta4^2 nu + 261138885000 beta4^2 - 638925000 beta4 nu^2 - 233233182000 beta4 nu - 4664408070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 638785 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu - 20422459669500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 + 14590801087350 beta4 nu + 291829355199 beta4 > 0 \/ 2500 nu^2 - 364900 nu - 7299 > 0 ]]] /\ [1916250000 beta4^2 nu^2 + 373106650000 beta4^2 nu - 10204234883500 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 + 7285404562050 beta4 nu + 145814722347 beta4 > 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [326401250000000 beta4^2 nu^2 + 35753992925000000 beta4^2 nu + 714949298000000 beta4^2 - 349811437500000 beta4 nu^3 - 25557223623750000 beta4 nu^2 - 1021869171225000 beta4 nu - 10217292466500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 319375000 beta4^2 nu^2 + 93270275000 beta4^2 nu + 5107713402750 beta4^2 - 152125000 beta4 nu^3 - 33324502500 beta4 nu^2 - 1332797550 beta4 nu - 13327367 beta4 > 0 \/ 6387500 beta4 nu + 466415250 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 113303300000 beta4^2 nu + 2265445500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 31025000 beta4^2 nu + 2265445500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 2931935550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 803050 beta4 - 182550 nu - 3651 = 0 ] /\ [3376250000 beta4^2 nu^2 + 379826300000 beta4^2 nu + 9733020175500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 67525000 beta4 nu + 2665850500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3102500000 beta4^2 nu + 611564800000 beta4^2 - 912750000 beta4 nu^2 - 293211810000 beta4 nu - 5863871100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [123187500000 beta4^2 nu^3 + 29316891250000 beta4^2 nu^2 + 1484299840325000 beta4^2 nu + 29674271035500 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 49275000 beta4 nu + 8127710500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [2171750000 beta4^2 nu + 543601435000 beta4^2 - 638925000 beta4 nu^2 - 273211632000 beta4 nu - 5463977070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 2190262500 beta4^2 nu^2 + 136643230250 beta4^2 nu + 2731988535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 1750 beta4 nu + 748285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1551250000 beta4^2 nu^2 - 113179200000 beta4^2 nu - 16535486704500 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 4865376817350 beta4 nu + 97294217499 beta4 > 0 \/ [620500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [1528756875000000 beta4^2 nu^2 + 41394206525000000 beta4^2 nu + 827272627750000 beta4^2 - 732938250000000 beta4 nu^3 - 12204088170000000 beta4 nu^2 - 487284000900000 beta4 nu - 4869908256000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [5566250000 beta4^2 nu^2 + 586412650000 beta4^2 nu + 13141049776500 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [111325000 beta4 nu + 3599301500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [1358895000000000 beta4^2 nu^2 + 28987495175000000 beta4^2 nu + 579206345500000 beta4^2 - 682965187500000 beta4 nu^3 - 8553056223750000 beta4 nu^2 - 341302690725000 beta4 nu - 3410295046500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1870625000 beta4^2 nu^2 + 159944825000 beta4^2 nu + 1705147523250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 37412500 beta4 nu + 467035750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2500 nu^2 - 729900 nu - 14599 > 0 /\ 350 nu - 72993 < 0 /\ [2463750000 beta4^2 nu^2 + 133323550000 beta4^2 nu + 2665485500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [4288750000 beta4^2 nu^2 + 266621550000 beta4^2 nu + 5330715500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [85775000 beta4 nu + 5330715500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3376250000 beta4^2 nu^2 + 133360050000 beta4^2 nu + 2665850500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [67525000 beta4 nu + 2665850500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2463750000 beta4^2 nu^2 + 133323550000 beta4^2 nu + 2665485500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [49275000 beta4^2 nu + 2665485500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [85775000 beta4^2 nu + 5330715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [49275000 beta4^2 nu + 5329985500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 5329985500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [85775000 beta4^2 nu + 10659715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 85775000 beta4 nu + 10659715500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [4288750000 beta4^2 nu^2 + 133396550000 beta4^2 nu + 2666215500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7938750000 beta4^2 nu^2 + 266767550000 beta4^2 nu + 5332175500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [158775000 beta4 nu + 5332175500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 438100 beta4 - 182550 nu - 3651 = 0 ] /\ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 < 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 639012500 beta4^2 nu^2 + 17511336500 beta4^2 nu + 349971160 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 - 34958787500 beta4^2 nu - 1702648678500 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 34997112500 beta4^2 nu + 426187030500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ [250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ [5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 ] /\ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 49275000 beta4 nu + 5329985500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1916512500 beta4^2 nu^2 + 186591655250 beta4^2 nu + 3731066535 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 186553325000 beta4^2 nu + 6811528183250 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ [125000 beta4^2 nu^2 + 31030000 beta4^2 nu + 1599320550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 438050 beta4 - 182550 nu - 3651 = 0 ] /\ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1277762500 beta4^2 nu^2 + 69994230250 beta4^2 nu + 1399373535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 - 46603200000 beta4^2 nu - 6808729819500 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 4865376817350 beta4 nu + 97294217499 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [1916250000 beta4^2 nu^2 + 186591650000 beta4^2 nu + 3407629816500 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 93295825000 beta4^2 nu + 1703814908250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ] /\ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 - 49941125000 beta4^2 nu - 2432355255000 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]] \/ [50 nu - 3649 <= 0 /\ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 /\ [15000 beta4^2 nu + 365300 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [5000 beta4^2 nu + 547600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ]] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [375000 beta4 nu^3 - 45602500 beta4 nu^2 - 1334074550 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3832500000 beta4^2 nu^2 + 93410800000 beta4^2 nu + 1866683000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2190000000 beta4^2 nu^2 + 46716350000 beta4^2 nu + 933451000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 364900 nu - 7299 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [2737500000 beta4^2 nu^2 + 666234500000 beta4^2 nu + 38915023595000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 799496000000 beta4^2 nu + 38917688460000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 < 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 33311725000000 beta4^2 nu^2 + 2918959859500000 beta4^2 nu + 58365873230000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 < 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 19450849635000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 91272500 beta4 nu^2 + 2002025450 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2190000000 beta4^2 nu^2 + 46716350000 beta4^2 nu + 933451000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 364900 nu - 7299 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 125000 beta4^2 nu^2 + 31030000 beta4^2 nu + 1599320550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 - 46603200000 beta4^2 nu - 6808729819500 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 4865376817350 beta4 nu + 97294217499 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [3376250000 beta4^2 nu^2 + 379826300000 beta4^2 nu + 9733020175500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 2931935550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ [1528756875000000 beta4^2 nu^2 + 41394206525000000 beta4^2 nu + 827272627750000 beta4^2 - 732938250000000 beta4 nu^3 - 12204088170000000 beta4 nu^2 - 487284000900000 beta4 nu - 4869908256000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [5566250000 beta4^2 nu^2 + 586412650000 beta4^2 nu + 13141049776500 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ [111325000 beta4 nu + 3599301500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [3102500000 beta4^2 nu + 611564800000 beta4^2 - 912750000 beta4 nu^2 - 293211810000 beta4 nu - 5863871100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [123187500000 beta4^2 nu^3 + 29316891250000 beta4^2 nu^2 + 1484299840325000 beta4^2 nu + 29674271035500 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 < 0 \/ 49275000 beta4 nu + 8127710500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [31025000 beta4^2 nu + 2265445500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 113303300000 beta4^2 nu + 2265445500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [31025000 beta4^2 nu + 2265445500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [1551250000 beta4^2 nu^2 + 113303300000 beta4^2 nu + 2265445500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2171750000 beta4^2 nu + 543601435000 beta4^2 - 638925000 beta4 nu^2 - 273211632000 beta4 nu - 5463977070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 2190262500 beta4^2 nu^2 + 136643230250 beta4^2 nu + 2731988535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 748285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1551250000 beta4^2 nu^2 - 113179200000 beta4^2 nu - 16535486704500 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 4865376817350 beta4 nu + 97294217499 beta4 > 0 \/ [620500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 < 0 ]]]] /\ [1358895000000000 beta4^2 nu^2 + 28987495175000000 beta4^2 nu + 579206345500000 beta4^2 - 682965187500000 beta4 nu^3 - 8553056223750000 beta4 nu^2 - 341302690725000 beta4 nu - 3410295046500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1870625000 beta4^2 nu^2 + 159944825000 beta4^2 nu + 1705147523250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 37412500 beta4 nu + 467035750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3193750000 beta4^2 nu^2 + 93385250000 beta4^2 nu + 1866427500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [63875000 beta4 nu + 1866427500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2190000000 beta4^2 nu^2 + 46716350000 beta4^2 nu + 933451000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 3731066500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 3731066500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 93334150000 beta4^2 nu + 1865916500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 364900 nu - 7299 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 125000 beta4^2 nu^2 + 31030000 beta4^2 nu + 1599320550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ [1916250000 beta4^2 nu^2 + 186591650000 beta4^2 nu + 3407629816500 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1277762500 beta4^2 nu^2 + 69994230250 beta4^2 nu + 1399373535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 - 46603200000 beta4^2 nu - 6808729819500 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 4865376817350 beta4 nu + 97294217499 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 < 0 ]]]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 93295825000 beta4^2 nu + 1703814908250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ [5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1916512500 beta4^2 nu^2 + 186591655250 beta4^2 nu + 3731066535 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 < 0 ]]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 186553325000 beta4^2 nu + 6811528183250 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 639012500 beta4^2 nu^2 + 17511336500 beta4^2 nu + 349971160 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 - 34958787500 beta4^2 nu - 1702648678500 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 < 0 ]]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 34997112500 beta4^2 nu + 426187030500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [62500 beta4 nu^3 - 6840000 beta4 nu^2 - 333336175 beta4 nu - 6663987 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 2664499850 beta4 nu - 53289999 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 125000 beta4^2 nu^2 + 31030000 beta4^2 nu + 1599320550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 - 46603200000 beta4^2 nu - 6808729819500 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 4865376817350 beta4 nu + 97294217499 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ [125000 beta4^2 nu^2 + 31030000 beta4^2 nu + 1599320550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 438050 beta4 - 182550 nu - 3651 = 0 ] /\ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [63875000000 beta4^2 nu^3 + 13992457500000 beta4^2 nu^2 + 681339371650000 beta4^2 nu + 13621190961000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 - 46603200000 beta4^2 nu - 6808729819500 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 4865376817350 beta4 nu + 97294217499 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2555000000 beta4^2 nu^2 + 279874700000 beta4^2 nu + 6813393972000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [[1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 729900 nu - 14599 > 0 \/ 50 nu - 14599 = 0 ] /\ [2463750000 beta4^2 nu^2 + 133323550000 beta4^2 nu + 2665485500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7300000000 beta4^2 nu^2 + 266742000000 beta4^2 nu + 5331920000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 5331920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 666490050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 >= 0 /\ 1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 72977500 beta4 nu^2 - 2001294550 beta4 nu - 39996697 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 45602500 beta4 nu^2 - 1334074550 beta4 nu - 26663247 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 45675 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ] /\ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [456250000 beta4^2 nu^2 - 83247375000 beta4^2 nu - 3648699505000 beta4^2 - 228187500 beta4 nu^3 + 41630527500 beta4 nu^2 + 1825682276175 beta4 nu + 36496991487 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 547400 nu - 10949 > 0 ]]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [456250000 beta4^2 nu^2 - 49941125000 beta4^2 nu - 2432355255000 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [5000 beta4^2 nu + 547600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 /\ [15000 beta4^2 nu + 365300 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 72977500 beta4 nu^2 - 2001294550 beta4 nu - 39996697 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 45602500 beta4 nu^2 - 1334074550 beta4 nu - 26663247 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [62500 beta4 nu^3 - 11402500 beta4 nu^2 - 500049925 beta4 nu - 9996437 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [62500 beta4 nu^3 - 6840000 beta4 nu^2 - 333336175 beta4 nu - 6663987 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [[1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2190000000 beta4^2 nu^2 + 46716350000 beta4^2 nu + 933451000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 255400 nu - 5109 > 0 \/ 50 nu - 5109 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3832500000 beta4^2 nu^2 + 93410800000 beta4^2 nu + 1866683000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 72977500 beta4 nu^2 - 2001294550 beta4 nu - 39996697 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 45602500 beta4 nu^2 - 1334074550 beta4 nu - 26663247 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 4666707500000 beta4^2 nu^2 + 85284060400000 beta4^2 nu + 1703815036000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 6998145000000 beta4^2 nu^2 + 170474786650000 beta4^2 nu + 3406696986000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 > 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 116648525000 beta4^2 nu + 1704281579000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 833203800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 99991750000 beta4^2 nu + 1217677230000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [73000000 beta4 nu + 1333710000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [912500000 beta4^2 nu^2 - 99882250000 beta4^2 nu - 4864710510000 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 136825 nu - 6663987 < 0 ]]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [912500000 beta4^2 nu^2 - 166494750000 beta4^2 nu - 7297399010000 beta4^2 - 228187500 beta4 nu^3 + 41630527500 beta4 nu^2 + 1825682276175 beta4 nu + 36496991487 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 228075 nu - 9996437 < 0 ]]]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 4563750 beta4 nu^2 - 499913175 beta4 nu - 9996438 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 62500 nu^3 + 6847500 nu^2 + 166805075 nu + 3333363 > 0 ]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 912750000 beta4 nu^3 - 16712452500 beta4 nu^2 - 667402800 beta4 nu - 6670377 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 45602500 beta4 nu^2 - 1334074550 beta4 nu - 26663247 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 72977500 beta4 nu^2 - 2001294550 beta4 nu - 39996697 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 45675 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 45675 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 5995124850 beta4 nu - 119902499 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 18655332500000 beta4^2 nu^2 + 1362305636650000 beta4^2 nu + 27238651111000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 23318207500000 beta4^2 nu^2 + 2043271901650000 beta4^2 nu + 40856111261000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 559647200000 beta4^2 nu + 27242381922000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [2463750000 beta4^2 nu^2 + 453063550000 beta4^2 nu + 13624655285500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 - 133152000000 beta4^2 nu - 58355213770000 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 14593466317350 beta4 nu + 291856007499 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 182400 nu - 79938649 < 0 ]]]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 - 242935732750000 beta4^2 nu - 4860713760000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 62500 nu^3 + 6847500 nu^2 - 332788675 nu - 6658512 > 0 ]]]] /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 > 0 ]] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 45675 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 5995124850 beta4 nu - 119902499 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2190000000 beta4^2 nu^2 + 46716350000 beta4^2 nu + 933451000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 139937350000 beta4^2 nu + 2798236000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 2798236000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 933597000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 51100000 beta4 nu + 933597000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [1277500000 beta4^2 nu^2 + 139937350000 beta4^2 nu + 2798236000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4^2 nu + 933597000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 nu^2 - 127550 nu - 2553 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [2190000000 beta4^2 nu^2 + 46716350000 beta4^2 nu + 933451000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 547400 nu - 10949 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5000 nu^2 - 127550 nu - 2553 > 0 \/ 100 nu - 2553 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 + 136925 nu + 3333363 < 0 /\ 50 nu - 3649 < 0 /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [63875000000 beta4^2 nu^3 + 11661020000000 beta4^2 nu^2 + 511051176650000 beta4^2 nu + 10216359636000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 /\ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [2555000000 beta4^2 nu^2 + 233245950000 beta4^2 nu + 3408562647000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ [2500 nu^2 - 255400 nu - 5109 > 0 \/ 50 nu - 5109 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [31937500000 beta4^2 nu^3 + 11659103750000 beta4^2 nu^2 + 681246075825000 beta4^2 nu + 13620258130500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [1916250000 beta4^2 nu^2 + 233220400000 beta4^2 nu + 6812461141500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ [2500 nu^2 - 255400 nu - 5109 > 0 \/ 50 nu - 5109 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [31937500000 beta4^2 nu^3 + 9327666250000 beta4^2 nu^2 + 510957880825000 beta4^2 nu + 10215426805500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [1916250000 beta4^2 nu^2 + 186591650000 beta4^2 nu + 3407629816500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [2190000000 beta4^2 nu^2 + 46716350000 beta4^2 nu + 933451000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 547400 nu - 10949 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ [5000 nu^2 - 127550 nu - 2553 > 0 \/ 100 nu - 2553 = 0 ] /\ [2500 nu^2 - 255400 nu - 5109 > 0 \/ 50 nu - 5109 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 255400 nu - 5109 > 0 \/ 50 nu - 5109 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 912600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 62500 nu^3 + 6847500 nu^2 + 166805075 nu + 3333363 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [250000 beta4^2 nu^2 + 45635000 beta4^2 nu + 1999287600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 /\ [25000000 beta4^2 nu^3 + 2282750000 beta4^2 nu^2 + 33397530000 beta4^2 nu + 667037700 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 10000 beta4 nu + 182700 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4^2 nu + 1095050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 547600 nu + 26655951 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [125000 beta4^2 nu^2 + 45630000 beta4^2 nu + 2665412550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [18750000 beta4^2 nu^3 + 2282375000 beta4^2 nu^2 + 66703772500 beta4^2 nu + 1333162650 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 7500 beta4 nu + 365150 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 182550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4^2 nu + 912550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 1999105050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [18750000 beta4^2 nu^3 + 1826125000 beta4^2 nu^2 + 33379272500 beta4^2 nu + 666855150 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 547600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 730050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 182550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4^2 nu + 912550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2500 beta4 nu + 912550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 >= 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ [456250000 beta4^2 nu^2 + 49977625000 beta4^2 nu + 1216677495000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 609005328825 beta4 nu - 12170108313 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 91250000 beta4 nu + 2666325000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ] /\ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [456250000 beta4^2 nu^2 - 83247375000 beta4^2 nu - 3648699505000 beta4^2 - 228187500 beta4 nu^3 + 41630527500 beta4 nu^2 + 1825682276175 beta4 nu + 36496991487 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 547400 nu - 10949 > 0 ]]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [22812500000 beta4^2 nu^3 - 831287500000 beta4^2 nu^2 - 303952810125000 beta4^2 nu - 8880529036005000 beta4^2 - 11409375000 beta4 nu^4 + 415529437500 beta4 nu^3 + 152026357586250 beta4 nu^2 + 4444521389678025 beta4 nu + 88829620576587 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 125000 nu^3 - 9117500 nu^2 - 1332614850 nu - 26648649 < 0 ]]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2500 nu^2 + 182600 nu + 3651 < 0 /\ [2190000000 beta4^2 nu^2 + 46716350000 beta4^2 nu + 933451000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 255400 nu - 5109 > 0 \/ 50 nu - 5109 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 nu^3 - 9117500 nu^2 - 1332614850 nu - 26648649 > 0 /\ 50 nu - 3649 = 0 ]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3832500000 beta4^2 nu^2 + 93410800000 beta4^2 nu + 1866683000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [375000 beta4 nu^3 + 36522500 beta4 nu^2 + 667585450 beta4 nu + 13337103 beta4 < 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 72977500 beta4 nu^2 - 2001294550 beta4 nu - 39996697 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [18750000 beta4 nu^4 - 911000000 beta4 nu^3 - 233198455000 beta4 nu^2 - 4872039344400 beta4 nu - 97347514797 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 < 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [62500 beta4 nu^3 - 11402500 beta4 nu^2 - 500049925 beta4 nu - 9996437 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [3125000 beta4 nu^4 - 113812500 beta4 nu^3 - 41639648750 beta4 nu^2 - 1217343574275 beta4 nu - 24330216537 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 375000 beta4 nu^3 + 36522500 beta4 nu^2 + 667585450 beta4 nu + 13337103 beta4 < 0 /\ 187500 beta4 nu^3 + 25105000 beta4 nu^2 + 1000191475 beta4 nu + 12176775039 beta4 < 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [375000 beta4 nu^3 - 72977500 beta4 nu^2 - 2001294550 beta4 nu - 39996697 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [18750000 beta4 nu^4 - 911000000 beta4 nu^3 - 233198455000 beta4 nu^2 - 4872039344400 beta4 nu - 97347514797 beta4 > 0 \/ 50 nu - 3649 /= 0 ]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 + 136925 nu + 3333363 < 0 /\ 50 nu - 3649 < 0 /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 11661020000000 beta4^2 nu^2 + 511051176650000 beta4^2 nu + 10216359636000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 25550000 beta4 nu + 2798236000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 233245950000 beta4^2 nu + 3408562647000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 51100000 beta4 nu + 933597000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4^2 nu + 912600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 62500 nu^3 + 6847500 nu^2 + 166805075 nu + 3333363 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 45635000 beta4^2 nu + 1999287600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 /\ [25000000 beta4^2 nu^3 + 2282750000 beta4^2 nu^2 + 33397530000 beta4^2 nu + 667037700 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 10000 beta4 nu + 182700 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1250 nu^2 + 136925 nu + 3333363 < 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 255400 nu - 5109 > 0 \/ 50 nu - 5109 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1703815036000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 4666707500000 beta4^2 nu^2 + 85284060400000 beta4^2 nu + 1703815036000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 6998145000000 beta4^2 nu^2 + 170474786650000 beta4^2 nu + 3406696986000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 116648525000 beta4^2 nu + 1704281579000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [5000 beta4^2 nu + 912600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 62500 nu^3 + 6847500 nu^2 + 166805075 nu + 3333363 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [12500000 beta4^2 nu^3 + 913250000 beta4^2 nu^2 + 16689640000 beta4^2 nu + 333427600 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 27385000 beta4^2 nu + 666672600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 /\ [18750000 beta4^2 nu^3 + 1141750000 beta4^2 nu^2 + 16698772500 beta4^2 nu + 333518900 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 187500 beta4 nu^3 + 25105000 beta4 nu^2 + 1000191475 beta4 nu + 12176775039 beta4 < 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 25 beta4 nu + 913 beta4 < 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 + 36522500 beta4 nu^2 + 667585450 beta4 nu + 13337103 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 72977500 beta4 nu^2 - 2001294550 beta4 nu - 39996697 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [9375000 beta4 nu^4 + 2624187500 beta4 nu^3 + 133382428750 beta4 nu^2 + 1828849335925 beta4 nu + 36523654739 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 < 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 25 beta4 nu + 913 beta4 < 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [62500 beta4 nu^3 - 11402500 beta4 nu^2 - 500049925 beta4 nu - 9996437 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 >= 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 >= 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 >= 0 /\ 6250000 beta4 nu^4 + 2738000000 beta4 nu^3 + 366533015000 beta4 nu^2 + 14602795535200 beta4 nu + 291909319401 beta4 < 0 /\ 125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 < 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 5995124850 beta4 nu - 119902499 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 15972500 beta4 nu^2 + 333701325 beta4 nu - 36463676112 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 >= 0 /\ 125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 < 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 3997114850 beta4 nu - 79938649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 + 166987575 beta4 nu - 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 319802050000 beta4^2 nu + 13621990420500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 9729422115000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [45625000000 beta4^2 nu^3 + 9994612500000 beta4^2 nu^2 + 486670979750000 beta4^2 nu + 9729422115000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 666198000000 beta4^2 nu + 58365873230000 beta4^2 - 456375000 beta4 nu^3 - 199919632500 beta4 nu^2 - 19464175237650 beta4 nu - 389203540551 beta4 < 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [912500000 beta4^2 nu^2 - 66576000000 beta4^2 nu - 29177606885000 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 14593466317350 beta4 nu + 291856007499 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [182500000000 beta4^2 nu^3 + 39978450000000 beta4^2 nu^2 + 1946683919000000 beta4^2 nu + 38917688460000 beta4^2 - 68456250000 beta4 nu^4 - 13331626500000 beta4 nu^3 - 487204208295000 beta4 nu^2 - 19472172570600 beta4 nu - 194668410153 beta4 < 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1140625000000 beta4^2 nu^4 + 208255312500000 beta4^2 nu^3 + 3051687893750000 beta4^2 nu^2 - 443600697979125000 beta4^2 nu - 8873232968880000 beta4^2 - 570468750000 beta4 nu^5 - 104167593750000 beta4 nu^4 - 1528345110000000 beta4 nu^3 + 221830590968737500 beta4 nu^2 + 8875054319974875 beta4 nu + 88756639916112 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 62500 nu^3 + 2285000 nu^2 - 166439925 nu - 3329712 < 0 ]]]]] \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 < 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 5995124850 beta4 nu - 119902499 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 15972500 beta4 nu^2 + 333701325 beta4 nu - 36463676112 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 beta4 nu^2 - 364900 beta4 nu - 7299 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 6250000 beta4 nu^4 + 2738000000 beta4 nu^3 + 366533015000 beta4 nu^2 + 14602795535200 beta4 nu + 291909319401 beta4 < 0 /\ 125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 < 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 5995124850 beta4 nu - 119902499 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 15972500 beta4 nu^2 + 333701325 beta4 nu - 36463676112 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ [2500 nu^2 - 255400 nu - 5109 > 0 \/ 50 nu - 5109 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [31937500000 beta4^2 nu^3 + 11659103750000 beta4^2 nu^2 + 681246075825000 beta4^2 nu + 13620258130500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 233220400000 beta4^2 nu + 6812461141500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4^2 nu + 1095050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 547600 nu + 26655951 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [125000 beta4^2 nu^2 + 45630000 beta4^2 nu + 2665412550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [18750000 beta4^2 nu^3 + 2282375000 beta4^2 nu^2 + 66703772500 beta4^2 nu + 1333162650 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 7500 beta4 nu + 365150 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 18655332500000 beta4^2 nu^2 + 1362305636650000 beta4^2 nu + 27238651111000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 23318207500000 beta4^2 nu^2 + 2043271901650000 beta4^2 nu + 40856111261000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 559647200000 beta4^2 nu + 27242381922000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 10660190100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 22818750000 beta4 nu^4 - 4999131750000 beta4 nu^3 - 243502130640000 beta4 nu^2 - 9734086997700 beta4 nu - 97320877101 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 125000 nu^3 + 27382500 nu^2 + 1333345150 nu + 26655951 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [2463750000 beta4^2 nu^2 + 453063550000 beta4^2 nu + 13624655285500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 - 133152000000 beta4^2 nu - 58355213770000 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 14593466317350 beta4 nu + 291856007499 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 182400 nu - 79938649 < 0 ]]]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 4868043142650 beta4 nu - 97320877101 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 547600 nu + 26655951 < 0 ]]]] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 6250000 beta4 nu^4 + 2738000000 beta4 nu^3 + 366533015000 beta4 nu^2 + 14602795535200 beta4 nu + 291909319401 beta4 < 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 5995124850 beta4 nu - 119902499 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [125000 beta4 nu^3 + 36507500 beta4 nu^2 + 1999835150 beta4 nu + 39982101 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 < 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [62500 beta4 nu^3 - 11402500 beta4 nu^2 - 500049925 beta4 nu - 9996437 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [3125000 beta4 nu^4 - 113812500 beta4 nu^3 - 41639648750 beta4 nu^2 - 1217343574275 beta4 nu - 24330216537 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 < 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 3997114850 beta4 nu - 79938649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [62500 beta4 nu^3 + 11410000 beta4 nu^2 + 166987575 beta4 nu - 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ [2500 nu^2 - 255400 nu - 5109 > 0 \/ 50 nu - 5109 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [31937500000 beta4^2 nu^3 + 9327666250000 beta4^2 nu^2 + 510957880825000 beta4^2 nu + 10215426805500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 186591650000 beta4^2 nu + 3407629816500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 182550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4^2 nu + 912550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 1999105050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [18750000 beta4^2 nu^3 + 1826125000 beta4^2 nu^2 + 33379272500 beta4^2 nu + 666855150 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 255400 nu - 5109 > 0 \/ 50 nu - 5109 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [63875000000 beta4^2 nu^3 + 9329582500000 beta4^2 nu^2 + 340762981650000 beta4^2 nu + 6811528311000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000000 beta4^2 nu^3 + 13992457500000 beta4^2 nu^2 + 681339371650000 beta4^2 nu + 13621190961000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 279874700000 beta4^2 nu + 6813393972000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [2500 beta4^2 nu + 912550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 182550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [12500000 beta4^2 nu^3 + 1825750000 beta4^2 nu^2 + 66685515000 beta4^2 nu + 1332980100 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 2665595100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [25000000 beta4^2 nu^3 + 2739000000 beta4^2 nu^2 + 66722030000 beta4^2 nu + 1333345200 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [62500 beta4 nu^3 - 11402500 beta4 nu^2 - 500049925 beta4 nu - 9996437 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [62500 beta4 nu^3 + 6847500 beta4 nu^2 + 166805075 beta4 nu + 3333363 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 < 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 3997114850 beta4 nu - 79938649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 666490050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 3405764155500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 72977500 beta4 nu^2 - 2001294550 beta4 nu - 39996697 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 45602500 beta4 nu^2 - 1334074550 beta4 nu - 26663247 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 31944500 beta4^2 nu + 933213820 beta4^2 - 13691250 beta4 nu^2 - 500278275 beta4 nu - 10000089 beta4 < 0 \/ 7000 beta4 nu + 1022140 beta4 - 547650 nu - 10953 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [319375000 beta4^2 nu^2 - 34958787500 beta4^2 nu - 1702648678500 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [511000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ [125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 438100 beta4 - 182550 nu - 3651 = 0 ] /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 - 34958787500 beta4^2 nu - 1702648678500 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 58324262500 beta4^2 nu + 852140789500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [[1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 364900 nu - 7299 > 0 \/ 50 nu - 7299 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2463750000 beta4^2 nu^2 + 66711050000 beta4^2 nu + 1333235500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 438100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 438100 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 /\ [15000 beta4^2 nu + 365300 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 45602500 beta4 nu^2 - 1334074550 beta4 nu - 26663247 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [62500 beta4 nu^3 - 6840000 beta4 nu^2 - 333336175 beta4 nu - 6663987 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 >= 0 /\ 1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 72977500 beta4 nu^2 - 2001294550 beta4 nu - 39996697 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 45602500 beta4 nu^2 - 1334074550 beta4 nu - 26663247 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 45675 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 - 30475266663750 beta4 nu^2 - 1217510744475 beta4 nu - 12170108313 beta4 < 0 /\ 912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 833203800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [912500000 beta4^2 nu^2 - 99882250000 beta4^2 nu - 4864710510000 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [912500000 beta4^2 nu^2 - 166494750000 beta4^2 nu - 7297399010000 beta4^2 - 228187500 beta4 nu^3 + 41630527500 beta4 nu^2 + 1825682276175 beta4 nu + 36496991487 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 547400 nu - 10949 > 0 ]]]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 166640750000 beta4^2 nu + 2434687970000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [5000 beta4^2 nu + 912600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 /\ [15000 beta4^2 nu + 365300 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [7500 beta4 nu^2 + 730300 beta4 nu + 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 45602500 beta4 nu^2 - 1334074550 beta4 nu - 26663247 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [375000 beta4 nu^3 - 72977500 beta4 nu^2 - 2001294550 beta4 nu - 39996697 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1250 beta4 nu^2 + 136925 beta4 nu + 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [62500 beta4 nu^3 - 6840000 beta4 nu^2 - 333336175 beta4 nu - 6663987 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [62500 beta4 nu^3 - 11402500 beta4 nu^2 - 500049925 beta4 nu - 9996437 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [[1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 255400 nu - 5109 > 0 \/ 50 nu - 5109 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3832500000 beta4^2 nu^2 + 93410800000 beta4^2 nu + 1866683000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 45675 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 89432000 beta4^2 nu + 9327538570 beta4^2 - 27382500 beta4 nu^2 - 3998940300 beta4 nu - 79967853 beta4 < 0 \/ 3500 beta4 nu + 1277570 beta4 - 547650 nu - 10953 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7984375000 beta4^2 nu^3 + 1749057187500 beta4^2 nu^2 + 85167421456250 beta4^2 nu + 1702648870125 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ [3193750 beta4 nu + 233207625 beta4 - 1521250 nu^2 - 55586475 nu - 1111121 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 < 0 ]]]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [63875000000 beta4^2 nu^3 + 23318207500000 beta4^2 nu^2 + 2043271901650000 beta4^2 nu + 40856111261000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 < 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2555000000 beta4^2 nu^2 + 559647200000 beta4^2 nu + 27242381922000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 < 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 45675 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 91272500 beta4 nu^2 + 2002025450 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ [125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 1095050 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 19461509095000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 + 73000000 beta4^2 nu - 38901699270000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [182500000000 beta4^2 nu^3 + 66623450000000 beta4^2 nu^2 + 5837919719000000 beta4^2 nu + 116731746460000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 > 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 1598992000000 beta4^2 nu + 77835376920000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 > 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [[912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 364900 nu - 7299 > 0 \/ 50 nu - 7299 = 0 ] /\ [17500 nu^2 - 1824300 nu - 36493 > 0 \/ 350 nu - 36493 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 7994230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 beta4^2 nu + 1095050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 1095050 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 1095100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 2664499850 beta4 nu - 53289999 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 31944500 beta4^2 nu + 933213820 beta4^2 - 13691250 beta4 nu^2 - 500278275 beta4 nu - 10000089 beta4 < 0 \/ 7000 beta4 nu + 1022140 beta4 - 547650 nu - 10953 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [319375000 beta4^2 nu^2 - 34958787500 beta4^2 nu - 1702648678500 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [511000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 139937350000 beta4^2 nu + 2798236000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 2798236000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 933597000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 51100000 beta4 nu + 933597000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 89432000 beta4^2 nu + 9327538570 beta4^2 - 27382500 beta4 nu^2 - 3998940300 beta4 nu - 79967853 beta4 < 0 \/ 3500 beta4 nu + 1277570 beta4 - 547650 nu - 10953 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7984375000 beta4^2 nu^3 + 1749057187500 beta4^2 nu^2 + 85167421456250 beta4^2 nu + 1702648870125 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ [3193750 beta4 nu + 233207625 beta4 - 1521250 nu^2 - 55586475 nu - 1111121 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [31937500000 beta4^2 nu^3 + 4664791250000 beta4^2 nu^2 - 510398259175000 beta4^2 nu - 10209830844500 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 + 364603409235000 beta4 nu^2 + 14588135674800 beta4 nu + 145894686549 beta4 < 0 /\ 638750000 beta4^2 nu^2 + 139911800000 beta4^2 nu + 2797980500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 < 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu - 10209830844500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 + 7293401347350 beta4 nu + 145894686549 beta4 < 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [250000 beta4^2 nu^2 + 122285000 beta4^2 nu + 14790420600 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [5000 beta4 nu + 1350600 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [125000 beta4^2 nu^2 + 67530000 beta4^2 nu + 8794200550 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 803050 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 539623300000 beta4^2 nu + 43775204345500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 31025000 beta4 nu + 3997370500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu - 20422459669500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 + 14590801087350 beta4 nu + 291829355199 beta4 > 0 \/ 2500 nu^2 - 364900 nu - 7299 > 0 ]]] /\ [4375000 beta4^2 nu^3 + 2555262500 beta4^2 nu^2 + 349817830250 beta4^2 nu + 6995334535 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 894250000 beta4^2 nu + 261138885000 beta4^2 - 638925000 beta4 nu^2 - 233233182000 beta4 nu - 4664408070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 1750 beta4 nu + 638785 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 35753992925000000 beta4^2 nu + 714949298000000 beta4^2 - 349811437500000 beta4 nu^3 - 25557223623750000 beta4 nu^2 - 1021869171225000 beta4 nu - 10217292466500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 319375000 beta4^2 nu^2 + 93270275000 beta4^2 nu + 5107713402750 beta4^2 - 152125000 beta4 nu^3 - 33324502500 beta4 nu^2 - 1332797550 beta4 nu - 13327367 beta4 > 0 \/ 6387500 beta4 nu + 466415250 beta4 - 3042500 nu^2 - 121700 nu - 1217 = 0 ] /\ [1916250000 beta4^2 nu^2 + 373106650000 beta4^2 nu - 10204234883500 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 + 7285404562050 beta4 nu + 145814722347 beta4 > 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 /\ 16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ [125000 beta4^2 nu^2 + 67530000 beta4^2 nu + 4264550550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 1168050 beta4 - 182550 nu - 3651 = 0 ] /\ [3376250000 beta4^2 nu^2 + 313213800000 beta4^2 nu + 4868975425500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [821250000 beta4^2 nu^2 - 59918400000 beta4^2 nu - 8754081196500 beta4^2 - 152125000 beta4 nu^3 + 11095997500 beta4 nu^2 + 1621792272450 beta4 nu + 32431405833 beta4 > 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [1149750000 beta4^2 nu + 407691495000 beta4^2 - 212975000 beta4 nu^2 - 135491044000 beta4 nu - 2709735690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [4375000 beta4^2 nu^3 + 3102762500 beta4^2 nu^2 + 203292230250 beta4^2 nu + 4064603535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 1750 beta4 nu + 1113285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3285000000 beta4^2 nu + 563607450000 beta4^2 - 608500000 beta4 nu^2 - 164380190000 beta4 nu - 3287360400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [214437500000 beta4^2 nu^3 + 49306116250000 beta4^2 nu^2 + 2457641799825000 beta4^2 nu + 49133115265500 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 85775000 beta4 nu + 13457440500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [1019171250000000 beta4^2 nu^2 + 15358311225000000 beta4^2 nu + 306758556000000 beta4^2 - 338706312500000 beta4 nu^3 - 2857681816250000 beta4 nu^2 - 113900825075000 beta4 nu - 1137653425500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2783125000 beta4^2 nu^2 + 226593825000 beta4^2 nu + 1706480138250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 55662500 beta4 nu + 467400750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1408854375000000 beta4^2 nu^2 + 43820766675000000 beta4^2 nu + 875851791750000 beta4^2 - 410889625000000 beta4 nu^3 - 8131394627500000 beta4 nu^2 - 324762717550000 beta4 nu - 3245983617000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [9216250000 beta4^2 nu^2 + 986233650000 beta4^2 nu + 22874469736500 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [184325000 beta4 nu + 6265261500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 < 0 /\ [1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2463750000 beta4^2 nu^2 + 133323550000 beta4^2 nu + 2665485500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3376250000 beta4^2 nu^2 + 66747550000 beta4^2 nu + 1333600500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [67525000 beta4 nu + 1333600500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [31025000 beta4^2 nu + 1332870500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [49275000 beta4^2 nu + 2665485500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [31025000 beta4^2 nu + 2665120500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [31025000 beta4 nu + 2665120500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [49275000 beta4^2 nu + 5329985500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 49275000 beta4 nu + 5329985500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2463750000 beta4^2 nu^2 + 66711050000 beta4^2 nu + 1333235500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [4288750000 beta4^2 nu^2 + 133396550000 beta4^2 nu + 2666215500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 438100 beta4 - 182550 nu - 3651 = 0 ] /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 - 34958787500 beta4^2 nu - 1702648678500 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 639012500 beta4^2 nu^2 + 17511336500 beta4^2 nu + 349971160 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 < 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 34997112500 beta4^2 nu + 426187030500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ [500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ [10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 31025000 beta4 nu + 2665120500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1916512500 beta4^2 nu^2 + 186591655250 beta4^2 nu + 3731066535 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 186553325000 beta4^2 nu + 6811528183250 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ [125000 beta4^2 nu^2 + 31030000 beta4^2 nu + 1599320550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 438050 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 - 46603200000 beta4^2 nu - 6808729819500 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 4865376817350 beta4 nu + 97294217499 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1277762500 beta4^2 nu^2 + 69994230250 beta4^2 nu + 1399373535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 93295825000 beta4^2 nu + 1703814908250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 186591650000 beta4^2 nu + 3407629816500 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [62500 beta4 nu^3 - 6840000 beta4 nu^2 - 333336175 beta4 nu - 6663987 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 18250000 beta4^2 nu + 666490000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [3996750000000000 beta4^2 nu^2 + 97414120000000000 beta4^2 nu + 1946683700000000 beta4^2 - 1332615000000000 beta4 nu^3 - 24400180650000000 beta4 nu^2 - 974408088000000 beta4 nu - 9738750420000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 166640750000 beta4^2 nu + 2434687970000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [14600000000 beta4^2 nu + 1066092000000 beta4^2 - 3651000000 beta4 nu^2 - 399930540000 beta4 nu - 7997150400 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 4998675000000 beta4^2 nu^2 + 121767704750000 beta4^2 nu + 2433354990000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 833203800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 79997050000 beta4^2 nu + 852574008000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 - 99882250000 beta4^2 nu - 4864710510000 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 \/ 50 nu - 3649 /= 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]] \/ [50 nu - 3649 <= 0 /\ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 /\ [15000 beta4^2 nu + 365300 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [5000 beta4^2 nu + 912600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ]] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [62500 beta4 nu^3 - 6840000 beta4 nu^2 - 333336175 beta4 nu - 6663987 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [16425000000 beta4^2 nu^2 + 800007000000 beta4^2 nu + 9741418570000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [375000 beta4 nu^3 - 45602500 beta4 nu^2 - 1334074550 beta4 nu - 26663247 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3832500000 beta4^2 nu^2 + 93410800000 beta4^2 nu + 1866683000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 364900 nu - 7299 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 19461509095000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 1598992000000 beta4^2 nu + 77835376920000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [182500000000 beta4^2 nu^3 + 66623450000000 beta4^2 nu^2 + 5837919719000000 beta4^2 nu + 116731746460000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 + 73000000 beta4^2 nu - 38901699270000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 91272500 beta4 nu^2 + 2002025450 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 364900 nu - 7299 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 125000 beta4^2 nu^2 + 31030000 beta4^2 nu + 1599320550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 - 46603200000 beta4^2 nu - 6808729819500 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 4865376817350 beta4 nu + 97294217499 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [3376250000 beta4^2 nu^2 + 313213800000 beta4^2 nu + 4868975425500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 125000 beta4^2 nu^2 + 67530000 beta4^2 nu + 4264550550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ [1408854375000000 beta4^2 nu^2 + 43820766675000000 beta4^2 nu + 875851791750000 beta4^2 - 410889625000000 beta4 nu^3 - 8131394627500000 beta4 nu^2 - 324762717550000 beta4 nu - 3245983617000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [9216250000 beta4^2 nu^2 + 986233650000 beta4^2 nu + 22874469736500 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ [184325000 beta4 nu + 6265261500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [3285000000 beta4^2 nu + 563607450000 beta4^2 - 608500000 beta4 nu^2 - 164380190000 beta4 nu - 3287360400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [214437500000 beta4^2 nu^3 + 49306116250000 beta4^2 nu^2 + 2457641799825000 beta4^2 nu + 49133115265500 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 < 0 \/ 85775000 beta4 nu + 13457440500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [16425000 beta4^2 nu + 1199353500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [85775000 beta4^2 nu + 1715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [821250000 beta4^2 nu^2 + 59984100000 beta4^2 nu + 1199353500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [821250000 beta4^2 nu^2 - 59918400000 beta4^2 nu - 8754081196500 beta4^2 - 152125000 beta4 nu^3 + 11095997500 beta4 nu^2 + 1621792272450 beta4 nu + 32431405833 beta4 > 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 - 364900 nu - 7299 < 0 ]]]] /\ [1149750000 beta4^2 nu + 407691495000 beta4^2 - 212975000 beta4 nu^2 - 135491044000 beta4 nu - 2709735690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 1241070 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [4375000 beta4^2 nu^3 + 3102762500 beta4^2 nu^2 + 203292230250 beta4^2 nu + 4064603535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 1113285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1019171250000000 beta4^2 nu^2 + 15358311225000000 beta4^2 nu + 306758556000000 beta4^2 - 338706312500000 beta4 nu^3 - 2857681816250000 beta4 nu^2 - 113900825075000 beta4 nu - 1137653425500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2783125000 beta4^2 nu^2 + 226593825000 beta4^2 nu + 1706480138250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 55662500 beta4 nu + 467400750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3193750000 beta4^2 nu^2 + 93385250000 beta4^2 nu + 1866427500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [63875000 beta4 nu + 1866427500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [3102500000 beta4^2 nu^2 + 46752850000 beta4^2 nu + 933816000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [62050000 beta4 nu + 933816000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 3731066500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 3731066500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 93334150000 beta4^2 nu + 1865916500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 364900 nu - 7299 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 125000 beta4^2 nu^2 + 31030000 beta4^2 nu + 1599320550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ [1916250000 beta4^2 nu^2 + 186591650000 beta4^2 nu + 3407629816500 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 - 46603200000 beta4^2 nu - 6808729819500 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 4865376817350 beta4 nu + 97294217499 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 < 0 ]]]] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1277762500 beta4^2 nu^2 + 69994230250 beta4^2 nu + 1399373535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 93295825000 beta4^2 nu + 1703814908250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ [10000 beta4 nu + 1715700 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 < 0 ]]]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1916512500 beta4^2 nu^2 + 186591655250 beta4^2 nu + 3731066535 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 186553325000 beta4^2 nu + 6811528183250 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [85775000 beta4 nu + 2666215500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 - 34958787500 beta4^2 nu - 1702648678500 beta4^2 - 228187500 beta4 nu^3 + 24972840000 beta4 nu^2 + 1217010374925 beta4 nu + 24330216537 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 < 0 ]]]] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 639012500 beta4^2 nu^2 + 17511336500 beta4^2 nu + 349971160 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 34997112500 beta4^2 nu + 426187030500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [62500 beta4 nu^3 - 6840000 beta4 nu^2 - 333336175 beta4 nu - 6663987 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 2664499850 beta4 nu - 53289999 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 125000 beta4^2 nu^2 + 31030000 beta4^2 nu + 1599320550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 - 46603200000 beta4^2 nu - 6808729819500 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 4865376817350 beta4 nu + 97294217499 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ [125000 beta4^2 nu^2 + 31030000 beta4^2 nu + 1599320550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 438050 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [638750000 beta4^2 nu^2 - 46603200000 beta4^2 nu - 6808729819500 beta4^2 - 456375000 beta4 nu^3 + 33287992500 beta4 nu^2 + 4865376817350 beta4 nu + 97294217499 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [63875000000 beta4^2 nu^3 + 13992457500000 beta4^2 nu^2 + 681339371650000 beta4^2 nu + 13621190961000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2555000000 beta4^2 nu^2 + 279874700000 beta4^2 nu + 6813393972000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [[912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 364900 nu - 7299 > 0 \/ 50 nu - 7299 = 0 ] /\ [1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 182550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 438050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 438050 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 666490050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 <= 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 45675 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 >= 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 5995124850 beta4 nu - 119902499 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 >= 0 /\ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4^2 nu + 730050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 5995124850 beta4 nu - 119902499 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 3730811000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 3730811000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 255400 nu - 5109 > 0 \/ 50 nu - 5109 = 0 ] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 279823600000 beta4^2 nu + 5595961000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 <= 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 45675 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 <= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 >= 0 /\ 50 nu - 3649 = 0 ]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 89432000 beta4^2 nu + 9327538570 beta4^2 - 27382500 beta4 nu^2 - 3998940300 beta4 nu - 79967853 beta4 < 0 \/ 3500 beta4 nu + 1277570 beta4 - 547650 nu - 10953 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7984375000 beta4^2 nu^3 + 1749057187500 beta4^2 nu^2 + 85167421456250 beta4^2 nu + 1702648870125 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ [3193750 beta4 nu + 233207625 beta4 - 1521250 nu^2 - 55586475 nu - 1111121 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [2500 beta4^2 nu + 620550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 133287050000 beta4^2 nu + 2665120500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 364900 nu - 7299 > 0 \/ 50 nu - 7299 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 7994230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 2664499850 beta4 nu - 53289999 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 136925 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 <= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 < 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 >= 0 /\ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 >= 0 /\ 50 nu - 3649 = 0 ]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7984375000 beta4^2 nu^3 + 1749057187500 beta4^2 nu^2 + 85167421456250 beta4^2 nu + 1702648870125 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ [3193750 beta4 nu + 233207625 beta4 - 1521250 nu^2 - 55586475 nu - 1111121 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [163200625000000 beta4^2 nu^2 + 35747464900000000 beta4^2 nu + 714884017750000 beta4^2 - 233207625000000 beta4 nu^3 - 25550227395000000 beta4 nu^2 - 1021729246650000 beta4 nu - 10216359636000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [319375000 beta4^2 nu^2 + 46641525000 beta4^2 nu + 932702750 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [6387500 beta4 nu + 932702750 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 170194899175000 beta4^2 nu - 3403898494500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 > 0 /\ 1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 3403898494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ [175000 beta4^2 nu^2 + 38332000 beta4^2 nu + 1865916570 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 1788500000 beta4^2 nu + 195876520000 beta4^2 - 1277850000 beta4 nu^2 - 186617214000 beta4 nu - 3731833140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [63875000000 beta4^2 nu^3 + 6998145000000 beta4^2 nu^2 + 170474786650000 beta4^2 nu + 3406696986000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 \/ 489601875000000 beta4^2 nu^2 + 23846875325000000 beta4^2 nu + 476741665750000 beta4^2 - 466415250000000 beta4 nu^3 - 17052141540000000 beta4 nu^2 - 681525963300000 beta4 nu - 6813393972000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [15968750000 beta4^2 nu^3 + 583817500000 beta4^2 nu^2 - 42525400837500 beta4^2 nu - 850741416000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 + 30375265773750 beta4 nu^2 + 1215511091775 beta4 nu + 12156778512 beta4 < 0 \/ 1250 nu^2 - 45575 nu - 912 < 0 ]]]] \/ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 680779711675000 beta4^2 nu - 13615594744500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 486404420235000 beta4 nu^2 + 19456178269800 beta4 nu + 194561786349 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 38328500 beta4^2 nu + 3731066535 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 - 93231950000 beta4^2 nu - 27233054894500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 14599 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 9328624375000 beta4^2 nu^2 + 340762962487500 beta4^2 nu + 6811528183250 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 45575 nu - 912 < 0 ]]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 638750 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 2500 nu^2 + 365100 nu + 7301 > 0 ] /\ [163200625000000 beta4^2 nu^2 + 35747464900000000 beta4^2 nu + 714884017750000 beta4^2 - 233207625000000 beta4 nu^3 - 25550227395000000 beta4 nu^2 - 1021729246650000 beta4 nu - 10216359636000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 638750000 beta4^2 nu^2 + 69968675000 beta4^2 nu + 1399118000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1399118000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 \/ 1250 nu^2 - 45575 nu - 912 < 0 ]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[255500 beta4 - 60850 nu - 1217 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 365100 nu + 7301 > 0 ] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 45575 nu - 912 < 0 ]]]]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4^2 nu + 730050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 279823600000 beta4^2 nu + 5595961000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 3730811000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 3730811000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 547550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 1095100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 < 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [962550625000000 beta4^2 nu^2 + 82704614525000000 beta4^2 nu + 1653707270250000 beta4^2 - 566361375000000 beta4 nu^3 - 24354205432500000 beta4 nu^2 - 973488583650000 beta4 nu - 9732620391000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[31025000 beta4 nu + 2665120500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 3597695500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [31025000 beta4 nu + 3597695500 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [837985250000 beta4^2 - 359806050000 beta4 nu - 7196121000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1350500 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [702095750000 beta4^2 - 319827600000 beta4 nu - 6396552000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1131500 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [962550625000000 beta4^2 nu^2 + 57904780775000000 beta4^2 nu + 1157710595250000 beta4^2 - 566361375000000 beta4 nu^3 - 17058138307500000 beta4 nu^2 - 681645898650000 beta4 nu - 6814193541000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[31025000 beta4 nu + 1865770500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 46690800000 beta4^2 nu + 933195500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [775625000 beta4^2 nu^2 - 28279287500 beta4^2 nu - 565896000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 \/ [620500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 ]]]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 3731066500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 3731066500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 5595705500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 5595705500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 31025000 beta4 nu + 1865770500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1350500 beta4 - 182550 nu - 3651 = 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [638750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [163200625000000 beta4^2 nu^2 + 35747464900000000 beta4^2 nu + 714884017750000 beta4^2 - 233207625000000 beta4 nu^3 - 25550227395000000 beta4 nu^2 - 1021729246650000 beta4 nu - 10216359636000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 69968675000 beta4^2 nu + 1399118000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1399118000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 - 93231950000 beta4^2 nu - 27233054894500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 14599 = 0 ]]] /\ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 31025000 beta4 nu + 2665120500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 38328500 beta4^2 nu + 3731066535 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 680779711675000 beta4^2 nu - 13615594744500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 486404420235000 beta4 nu^2 + 19456178269800 beta4 nu + 194561786349 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 9328624375000 beta4^2 nu^2 + 340762962487500 beta4^2 nu + 6811528183250 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 ]]]]] \/ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [182500 beta4 - 60850 nu - 1217 = 0 /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 666234500000 beta4^2 nu + 38915023595000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 33311725000000 beta4^2 nu^2 + 2918959859500000 beta4^2 nu + 58365873230000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 19450849635000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 ]]]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 799496000000 beta4^2 nu + 38917688460000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [[1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 5330095000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 729900 nu - 14599 > 0 \/ 50 nu - 14599 = 0 ] /\ [17500 nu^2 - 3649300 nu - 72993 > 0 \/ 350 nu - 72993 = 0 ] /\ [36500000 beta4^2 nu + 7994230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 beta4^2 nu + 730050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 1095100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 2664499850 beta4 nu - 53289999 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 < 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [91250000000 beta4^2 nu^3 + 26650475000000 beta4^2 nu^2 + 1946150909500000 beta4^2 nu + 38912358730000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [91250000000 beta4^2 nu^3 + 33311725000000 beta4^2 nu^2 + 2918959859500000 beta4^2 nu + 58365873230000 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 799496000000 beta4^2 nu + 38917688460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 19461509095000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 + 73000000 beta4^2 nu - 38901699270000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 100 nu - 53289999 < 0 ]]]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 547550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 1095100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [50 beta4 nu + beta4 > 0 /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1022000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1496500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2131600000000 beta4^2 - 666307500000 beta4 nu - 13326150000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2920000 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [912500000 beta4^2 nu^2 - 33269750000 beta4^2 nu - 665760000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 291816040000000000 beta4^2 nu + 5835787900000000 beta4^2 - 666307500000000 beta4 nu^3 - 73000649700000000 beta4 nu^2 - 2919226419000000 beta4 nu - 29189598960000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 999735075 beta4 nu - 9996438 beta4 < 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 9992604850 beta4 nu - 199844799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2920000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [375000 beta4^2 nu^2 + 18265000 beta4^2 nu + 365150 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7500 beta4 nu + 365150 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 730050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] \/ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 547550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 beta4^2 nu + 1095050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [2500 beta4^2 nu + 730050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [375000 beta4^2 nu^2 + 18265000 beta4^2 nu + 365150 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7500 beta4 nu + 365150 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [175000 beta4^2 nu^2 + 87607000 beta4^2 nu + 9061052070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 73005000 beta4^2 nu + 7994960050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ [2737500000 beta4^2 nu^2 + 533009500000 beta4^2 nu + 19461509095000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [50 nu - 3649 < 0 \/ [50 nu - 3649 = 0 /\ [1825000000 beta4^2 nu^2 - 266377000000 beta4^2 nu - 77808728270000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 < 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 - 364900 nu - 106587299 > 0 ]]]] /\ [7300000000 beta4^2 nu + 1598846000000 beta4^2 - 1825500000 beta4 nu^2 - 533119020000 beta4 nu - 10661650200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [73000000 beta4^2 nu + 15988460000 beta4^2 - 9127500 beta4 nu^2 - 2665595100 beta4 nu - 53308251 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2664500000000000 beta4^2 nu^2 + 194615080000000000 beta4^2 nu + 3891235800000000 beta4^2 - 999461250000000 beta4 nu^3 - 48700415175000000 beta4 nu^2 - 1946817253500000 beta4 nu - 19464174690000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [7300000000 beta4^2 nu^2 + 533192000000 beta4^2 nu + 10660920000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 - 2666872950 beta4 nu - 26663253 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 < 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 27367500 beta4 nu^2 - 2665594850 beta4 nu - 53300949 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 27382500 beta4 nu^2 + 1333345150 beta4 nu + 26655951 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 912600 beta4 nu + 79953251 beta4 < 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]] /\ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 7993864850 beta4 nu - 159873649 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 146022500 beta4 nu^2 + 15326715450 beta4 nu + 292069225903 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [182500 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [532900000000 beta4^2 - 177682000000 beta4 nu - 3553640000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4 - 60850 nu - 1217 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1332250000000000 beta4^2 nu^2 + 194561790000000000 beta4^2 nu + 3890702900000000 beta4^2 - 666307500000000 beta4 nu^3 - 48680425950000000 beta4 nu^2 - 1946417469000000 beta4 nu - 19461509460000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 5329729850 beta4 nu - 106587299 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 <= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 45675 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 <= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [175000 beta4^2 nu^2 + 89432000 beta4^2 nu + 9327538570 beta4^2 - 27382500 beta4 nu^2 - 3998940300 beta4 nu - 79967853 beta4 < 0 \/ 3500 beta4 nu + 1277570 beta4 - 547650 nu - 10953 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 >= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7984375000 beta4^2 nu^3 + 1749057187500 beta4^2 nu^2 + 85167421456250 beta4^2 nu + 1702648870125 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ [3193750 beta4 nu + 233207625 beta4 - 1521250 nu^2 - 55586475 nu - 1111121 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [2500 beta4^2 nu + 620550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [2463750000 beta4^2 nu^2 + 266548550000 beta4^2 nu + 5329985500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 729900 nu - 14599 > 0 \/ 50 nu - 14599 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 10659460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 7994230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 799496000000 beta4^2 nu + 15988460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 15988460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [146000000 beta4^2 nu + 10660920000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 10660920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 2664499850 beta4 nu - 53289999 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 136925 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 1999104850 beta4 nu - 39974799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 1332614850 beta4 nu - 26648649 beta4 <= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 45675 beta4 nu - 3329712 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 >= 0 /\ 500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 5995124850 beta4 nu - 119902499 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 >= 0 /\ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2500 beta4^2 nu + 1095050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 5995124850 beta4 nu - 119902499 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [2500 beta4 nu^2 + 547600 beta4 nu + 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 9117500 beta4 nu^2 - 3997114850 beta4 nu - 79938649 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 136925 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 3730811000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 3730811000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 255400 nu - 5109 > 0 \/ 50 nu - 5109 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 547400 nu - 10949 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 279823600000 beta4^2 nu + 5595961000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 730100 beta4 nu + 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 7500 beta4 nu^2 - 5995124850 beta4 nu - 119902499 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1022000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [163200625000000 beta4^2 nu^2 + 35747464900000000 beta4^2 nu + 714884017750000 beta4^2 - 233207625000000 beta4 nu^3 - 25550227395000000 beta4 nu^2 - 1021729246650000 beta4 nu - 10216359636000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [319375000 beta4^2 nu^2 + 46641525000 beta4^2 nu + 932702750 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [6387500 beta4 nu + 932702750 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1022000 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [408800 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 408800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [163200625000000 beta4^2 nu^2 + 35747464900000000 beta4^2 nu + 714884017750000 beta4^2 - 233207625000000 beta4 nu^3 - 25550227395000000 beta4 nu^2 - 1021729246650000 beta4 nu - 10216359636000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 69955900000 beta4^2 nu + 1398990250 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 999735075 beta4 nu - 9996438 beta4 < 0 \/ [6387500 beta4 nu + 1398990250 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 ]]]]] \/ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 9992604850 beta4 nu - 199844799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1022000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 + 9132500 beta4 nu^2 - 3996384850 beta4 nu - 79931349 beta4 <= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 547550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 1095100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]]] \/ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [50 nu - 3649 < 0 \/ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 >= 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7984375000 beta4^2 nu^3 + 1749057187500 beta4^2 nu^2 + 85167421456250 beta4^2 nu + 1702648870125 beta4^2 - 3803125000 beta4 nu^4 - 694374562500 beta4 nu^3 - 20308506471250 beta4 nu^2 - 811507131075 beta4 nu - 8112294421 beta4 < 0 \/ [3193750 beta4 nu + 233207625 beta4 - 1521250 nu^2 - 55586475 nu - 1111121 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 < 0 /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 >= 0 /\ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 /\ 2445500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [163200625000000 beta4^2 nu^2 + 35747464900000000 beta4^2 nu + 714884017750000 beta4^2 - 233207625000000 beta4 nu^3 - 25550227395000000 beta4 nu^2 - 1021729246650000 beta4 nu - 10216359636000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [319375000 beta4^2 nu^2 + 46641525000 beta4^2 nu + 932702750 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [6387500 beta4 nu + 932702750 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 /\ 50 nu - 3649 = 0 ]]] \/ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 170194899175000 beta4^2 nu - 3403898494500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 > 0 /\ 2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 3403898494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ [175000 beta4^2 nu^2 + 38332000 beta4^2 nu + 1865916570 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 1788500000 beta4^2 nu + 195876520000 beta4^2 - 1277850000 beta4 nu^2 - 186617214000 beta4 nu - 3731833140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [15968750000 beta4^2 nu^3 + 583817500000 beta4^2 nu^2 - 42525400837500 beta4^2 nu - 850741416000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 + 30375265773750 beta4 nu^2 + 1215511091775 beta4 nu + 12156778512 beta4 < 0 \/ 1250 nu^2 - 45575 nu - 912 < 0 ]]] /\ [63875000000 beta4^2 nu^3 + 6998145000000 beta4^2 nu^2 + 170474786650000 beta4^2 nu + 3406696986000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 > 0 \/ 489601875000000 beta4^2 nu^2 + 23846875325000000 beta4^2 nu + 476741665750000 beta4^2 - 466415250000000 beta4 nu^3 - 17052141540000000 beta4 nu^2 - 681525963300000 beta4 nu - 6813393972000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 680779711675000 beta4^2 nu - 13615594744500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 486404420235000 beta4 nu^2 + 19456178269800 beta4 nu + 194561786349 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 38328500 beta4^2 nu + 3731066535 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 - 93231950000 beta4^2 nu - 27233054894500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 14599 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 45575 nu - 912 < 0 ]]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 9328624375000 beta4^2 nu^2 + 340762962487500 beta4^2 nu + 6811528183250 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 > 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 2445500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 638750 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 \/ 1250 nu^2 - 45575 nu - 912 < 0 ]]] /\ [163200625000000 beta4^2 nu^2 + 35747464900000000 beta4^2 nu + 714884017750000 beta4^2 - 233207625000000 beta4 nu^3 - 25550227395000000 beta4 nu^2 - 1021729246650000 beta4 nu - 10216359636000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 638750000 beta4^2 nu^2 + 69968675000 beta4^2 nu + 1399118000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1399118000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 2500 nu^2 + 365100 nu + 7301 > 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[255500 beta4 - 60850 nu - 1217 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 45575 nu - 912 < 0 ]]]] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 365100 nu + 7301 > 0 ]] \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 >= 0 /\ 125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 136925 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4^2 nu + 1095050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 136925 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [500000 beta4^2 nu^2 + 219020000 beta4^2 nu + 23984880200 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 228175 beta4 nu - 9987312 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 279823600000 beta4^2 nu + 5595961000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 3730811000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 3730811000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 547550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 1095100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]]] \/ [50 beta4 nu + beta4 > 0 /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 < 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [809341875000000 beta4^2 nu^2 + 87561198675000000 beta4^2 nu + 1750900236750000 beta4^2 - 299838375000000 beta4 nu^3 - 16231472802500000 beta4 nu^2 - 648899106050000 beta4 nu - 6487791707000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[49275000 beta4 nu + 5329985500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 6262560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [49275000 beta4 nu + 6262560500 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [803346750000 beta4^2 - 208776350000 beta4 nu - 4175527000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [1350500 beta4 - 182550 nu - 3651 = 0 /\ [2445500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [491600250000 beta4^2 - 151029700000 beta4 nu - 3020594000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1496500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1241000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1241000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [85775000 beta4^2 nu + 1715500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [410625000 beta4^2 nu^2 - 14971387500 beta4^2 nu - 299592000 beta4^2 - 76062500 beta4 nu^3 + 2771717500 beta4 nu^2 + 110959975 beta4 nu + 1109904 beta4 < 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 ]]]] /\ [809341875000000 beta4^2 nu^2 + 30667462425000000 beta4^2 nu + 613025511750000 beta4^2 - 299838375000000 beta4 nu^3 - 5692709177500000 beta4 nu^2 - 227348561050000 beta4 nu - 2272286257000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2463750000 beta4^2 nu^2 + 46727300000 beta4^2 nu + 933560500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 49275000 beta4 nu + 933560500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 3731066500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 3731066500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 5595705500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 5595705500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2463750000 beta4^2 nu^2 + 93356050000 beta4^2 nu + 1866135500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 49275000 beta4 nu + 1866135500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2445500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 2445500 beta4 - 182550 nu - 3651 = 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [638750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [163200625000000 beta4^2 nu^2 + 35747464900000000 beta4^2 nu + 714884017750000 beta4^2 - 233207625000000 beta4 nu^3 - 25550227395000000 beta4 nu^2 - 1021729246650000 beta4 nu - 10216359636000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 69968675000 beta4^2 nu + 1399118000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1399118000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 - 93231950000 beta4^2 nu - 27233054894500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 14599 = 0 ]]] /\ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 49275000 beta4 nu + 5329985500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 38328500 beta4^2 nu + 3731066535 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 680779711675000 beta4^2 nu - 13615594744500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 486404420235000 beta4 nu^2 + 19456178269800 beta4 nu + 194561786349 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 nu - 3649 = 0 /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 - 85027506462500 beta4^2 nu - 1701249816000 beta4^2 - 11409375000 beta4 nu^4 - 1250239312500 beta4 nu^3 + 60725572398750 beta4 nu^2 + 2430522818025 beta4 nu + 24310227312 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 ]]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 9328624375000 beta4^2 nu^2 + 340762962487500 beta4^2 nu + 6811528183250 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 beta4 nu^2 + 136925 beta4 nu - 6658512 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 - 11644412500 beta4^2 nu - 233016000 beta4^2 - 228187500 beta4 nu^3 + 8315152500 beta4 nu^2 + 332879925 beta4 nu + 3329712 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [182500 beta4 - 60850 nu - 1217 = 0 /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]]] \/ [50 beta4 nu + beta4 > 0 /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [25 beta4 nu - 912 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [949000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [25550000 beta4^2 nu + 511000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4 - 60850 nu - 1217 = 0 ]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4 - 60850 nu - 1217 = 0 ]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [38325000 beta4^2 nu + 933341500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [76650000 beta4^2 nu + 1866683000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [2044000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2044000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [228125000 beta4^2 nu^2 + 8335687500 beta4^2 nu + 166622500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 4562500 beta4^2 nu + 166622500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 22822500 beta4^2 nu + 500050100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 547700 beta4 - 182550 nu - 3651 = 0 ] /\ [866875000 beta4^2 nu^2 + 54989987500 beta4^2 nu + 852074140500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu + 66630750000 beta4^2 - 912750000 beta4 nu^2 - 99982635000 beta4 nu - 1999287600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [11406250000 beta4^2 nu^3 + 1249668750000 beta4^2 nu^2 + 30441926187500 beta4^2 nu + 608338747500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [249796875000000 beta4^2 nu^2 + 6088382500000000 beta4^2 nu + 121667731250000 beta4^2 - 333153750000000 beta4 nu^3 - 6100045162500000 beta4 nu^2 - 243602022000000 beta4 nu - 2434687605000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [684375000 beta4^2 nu^2 + 41660187500 beta4^2 nu + 608671992500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3832500000 beta4^2 nu^2 + 93410800000 beta4^2 nu + 1866683000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [10000 beta4^2 nu + 547700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 547700 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [30000 beta4^2 nu + 730600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [949000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [2044000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2044000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [25550000 beta4^2 nu + 511000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4 - 60850 nu - 1217 = 0 ]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4 - 60850 nu - 1217 = 0 ]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [38325000 beta4^2 nu + 933341500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [76650000 beta4^2 nu + 1866683000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3832500000 beta4^2 nu^2 + 93410800000 beta4^2 nu + 1866683000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 547700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 < 0 /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]] \/ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1022000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 511000 beta4 - 60850 nu - 1217 = 0 ]]]] \/ [228125000 beta4^2 nu^2 + 8335687500 beta4^2 nu + 166622500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 4562500 beta4^2 nu + 166622500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 17344500 beta4^2 nu + 400021820 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 ] /\ [1140625000 beta4^2 nu^2 + 74984687500 beta4^2 nu + 1217177362500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu + 66630750000 beta4^2 - 912750000 beta4 nu^2 - 99982635000 beta4 nu - 1999287600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [11406250000 beta4^2 nu^3 + 1249668750000 beta4^2 nu^2 + 30441926187500 beta4^2 nu + 608338747500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [249796875000000 beta4^2 nu^2 + 6088382500000000 beta4^2 nu + 121667731250000 beta4^2 - 333153750000000 beta4 nu^3 - 6100045162500000 beta4 nu^2 - 243602022000000 beta4 nu - 2434687605000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [684375000 beta4^2 nu^2 + 41660187500 beta4^2 nu + 608671992500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [7000 beta4^2 nu + 438140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 511420 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [21000 beta4 nu + 511420 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 599603750000 beta4^2 nu + 38913691162500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 82135000 beta4^2 nu + 6662892600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 60232000 beta4^2 nu + 5063754570 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu + 99927875000 beta4^2 - 456375000 beta4 nu^2 - 133279755000 beta4 nu - 2665412550 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 16655862500000 beta4^2 nu^2 + 1459479929750000 beta4^2 nu + 29182936615000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [166531250000000 beta4^2 nu^2 + 12163442500000000 beta4^2 nu + 243202237500000 beta4^2 - 249865312500000 beta4 nu^3 - 12175103793750000 beta4 nu^2 - 486704313375000 beta4 nu - 4866043672500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 91272500 beta4 nu^2 + 2002025450 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [228125000 beta4^2 nu^2 + 8335687500 beta4^2 nu + 166622500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 4562500 beta4^2 nu + 166622500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [249796875000000 beta4^2 nu^2 + 6088382500000000 beta4^2 nu + 121667731250000 beta4^2 - 333153750000000 beta4 nu^3 - 6100045162500000 beta4 nu^2 - 243602022000000 beta4 nu - 2434687605000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [684375000 beta4^2 nu^2 + 41660187500 beta4^2 nu + 608671992500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [912500000 beta4^2 nu + 66630750000 beta4^2 - 912750000 beta4 nu^2 - 99982635000 beta4 nu - 1999287600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [11406250000 beta4^2 nu^3 + 1249668750000 beta4^2 nu^2 + 30441926187500 beta4^2 nu + 608338747500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [175000 beta4^2 nu^2 + 17344500 beta4^2 nu + 400021820 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 ] /\ [1140625000 beta4^2 nu^2 + 74984687500 beta4^2 nu + 1217177362500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 511420 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [21000 beta4 nu + 511420 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [7000 beta4^2 nu + 438140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 599603750000 beta4^2 nu + 38913691162500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 82135000 beta4^2 nu + 6662892600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 60232000 beta4^2 nu + 5063754570 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ 50 nu - 3649 <= 0 /\ [166531250000000 beta4^2 nu^2 + 12163442500000000 beta4^2 nu + 243202237500000 beta4^2 - 249865312500000 beta4 nu^3 - 12175103793750000 beta4 nu^2 - 486704313375000 beta4 nu - 4866043672500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [456250000 beta4^2 nu + 99927875000 beta4^2 - 456375000 beta4 nu^2 - 133279755000 beta4 nu - 2665412550 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 16655862500000 beta4^2 nu^2 + 1459479929750000 beta4^2 nu + 29182936615000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3193750000 beta4^2 nu^2 + 366496500000 beta4^2 nu + 9732753652500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 175000 beta4^2 nu^2 + 52932000 beta4^2 nu + 2932008570 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [333062500000000 beta4^2 nu^2 + 6091713125000000 beta4^2 nu + 121701037500000 beta4^2 - 194339687500000 beta4 nu^3 - 2038345693750000 beta4 nu^2 - 81300620125000 beta4 nu - 812228842500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [4562500000 beta4^2 nu^2 + 466470000000 beta4^2 nu + 9734752575000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [456250000 beta4^2 nu + 133234125000 beta4^2 - 152125000 beta4 nu^2 - 77741960000 beta4 nu - 1554778350 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [91250000000 beta4^2 nu^3 + 23319850000000 beta4^2 nu^2 + 1216610809500000 beta4^2 nu + 24322888980000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 < 0 \/ 36500000 beta4 nu + 6661980000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [912500000 beta4^2 nu + 166549500000 beta4^2 - 304250000 beta4 nu^2 - 88853170000 beta4 nu - 1776941700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [6250000 beta4^2 nu^3 + 2281625000 beta4^2 nu^2 + 133316257500 beta4^2 nu + 2665412550 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [416328125000000 beta4^2 nu^2 + 12173434375000000 beta4^2 nu + 243302156250000 beta4^2 - 222102500000000 beta4 nu^3 - 4066696775000000 beta4 nu^2 - 162401348000000 beta4 nu - 1623125070000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [1825000000 beta4^2 nu^2 + 166604250000 beta4^2 nu + 2434687605000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [4562500000 beta4^2 nu^2 + 133407500000 beta4^2 nu + 2666325000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 5330095000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4^2 nu + 2665595000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 666234500000 beta4^2 nu + 38915023595000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ [2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 2737875000 beta4^2 nu^2 + 266559507500 beta4^2 nu + 5330095050 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 266504750000 beta4^2 nu + 9730754547500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 912875000 beta4^2 nu^2 + 25016195000 beta4^2 nu + 499958800 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 175000 beta4^2 nu^2 + 43807000 beta4^2 nu + 2265701070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 43807000 beta4^2 nu + 2265701070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 399821000000 beta4^2 nu + 9733419960000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 933086070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu + 666855000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [7000 beta4^2 nu + 620640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 511420 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [21000 beta4 nu + 511420 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 620700 beta4 - 182550 nu - 3651 = 0 ] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 58324262500 beta4^2 nu + 852140789500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1551250000 beta4^2 nu^2 + 33368300000 beta4^2 nu + 666745500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [10000 beta4^2 nu + 620700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 620700 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [30000 beta4^2 nu + 730600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [27375000 beta4^2 nu + 666672500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 58324262500 beta4^2 nu + 852140789500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 620700 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [30000 beta4^2 nu + 730600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [10000 beta4^2 nu + 620700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 620700 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [1551250000 beta4^2 nu^2 + 33368300000 beta4^2 nu + 666745500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 620700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 < 0 /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [4343500000 beta4^2 nu + 385107120000 beta4^2 - 1277850000 beta4 nu^2 - 226595664000 beta4 nu - 4531402140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [43800000 beta4^2 nu + 2265701000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 43800000 beta4 nu + 2265701000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ]]] /\ [702095750000 beta4^2 - 319827600000 beta4 nu - 6396552000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1131500 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [748250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 748250 beta4 - 182550 nu - 3651 = 0 ]]] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [837985250000 beta4^2 - 359806050000 beta4 nu - 7196121000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ [1350500 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [14600000 beta4^2 nu + 292000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [6205000000 beta4^2 nu + 385144350000 beta4^2 - 1825500000 beta4 nu^2 - 226617570000 beta4 nu - 4531621200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 620700 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 620600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 < 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 54790000 beta4^2 nu + 1095400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 20000 beta4 nu + 1095400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [30000 beta4^2 nu + 365600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 30000 beta4 nu + 365600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [10000 beta4^2 nu + 620700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 620700 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 365400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [1131500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1131500 beta4 - 182550 nu - 3651 = 0 ] /\ [532900000000 beta4^2 - 333153750000 beta4 nu - 6663075000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 912500 beta4 - 182550 nu - 3651 = 0 ]] /\ [5475000000 beta4^2 nu + 133334500000 beta4^2 - 2738250000 beta4 nu^2 - 133371030000 beta4 nu - 2666325300 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [7500 beta4^2 nu + 365150 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7500 beta4 nu + 365150 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 16689625000 beta4^2 nu - 607505635000 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 100 nu - 1823 = 0 ]]] /\ [175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [11406250000 beta4^2 nu^3 + 684375000 beta4^2 nu^2 - 15195962875000 beta4^2 nu - 303919440000 beta4^2 - 5704687500 beta4 nu^4 - 456375000 beta4 nu^3 + 7600056230625 beta4 nu^2 + 304002614325 beta4 nu + 3040027056 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [228125000 beta4^2 nu^2 + 9125000 beta4^2 nu - 303919440000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 912875000 beta4^2 nu^2 + 25016195000 beta4^2 nu + 499958800 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]] \/ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [182500 beta4 - 60850 nu - 1217 = 0 /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]]]] \/ [50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]] \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ] /\ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [22812500000 beta4^2 nu^3 + 2499337500000 beta4^2 nu^2 + 60883852375000 beta4^2 nu + 1216677495000 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 83320375000 beta4^2 nu + 1217343985000 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2190000000 beta4^2 nu^2 + 46716350000 beta4^2 nu + 933451000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3832500000 beta4^2 nu^2 + 93410800000 beta4^2 nu + 1866683000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [5000 beta4^2 nu + 547600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 /\ [15000 beta4^2 nu + 365300 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 438100 beta4 - 182550 nu - 3651 = 0 ] /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 58324262500 beta4^2 nu + 852140789500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2463750000 beta4^2 nu^2 + 66711050000 beta4^2 nu + 1333235500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [5000 beta4^2 nu + 438100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 438100 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 /\ [15000 beta4^2 nu + 365300 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 666234500000 beta4^2 nu + 38915023595000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 33311725000000 beta4^2 nu^2 + 2918959859500000 beta4^2 nu + 58365873230000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 < 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 799496000000 beta4^2 nu + 38917688460000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 < 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 91272500 beta4 nu^2 + 2002025450 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [63875000000 beta4^2 nu^3 + 23318207500000 beta4^2 nu^2 + 2043271901650000 beta4^2 nu + 40856111261000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 < 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2555000000 beta4^2 nu^2 + 559647200000 beta4^2 nu + 27242381922000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 < 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 91272500 beta4 nu^2 + 2002025450 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 58324262500 beta4^2 nu + 852140789500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [15968750000 beta4^2 nu^3 + 1749536250000 beta4^2 nu^2 + 42618696662500 beta4^2 nu + 851674246500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 438100 beta4 - 182550 nu - 3651 = 0 ] /\ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [375000 beta4^2 nu^2 + 9140000 beta4^2 nu + 182650 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 /\ [15000 beta4^2 nu + 365300 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [5000 beta4^2 nu + 438100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 438100 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [5000 beta4^2 nu + 182600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [1125000 beta4^2 nu^2 + 54795000 beta4^2 nu + 667220450 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 7500 beta4 nu + 182650 beta4 - 182550 nu - 3651 = 0 ] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ 50 nu - 3649 <= 0 /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2555000000 beta4^2 nu^2 + 559647200000 beta4^2 nu + 27242381922000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 < 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [63875000000 beta4^2 nu^3 + 23318207500000 beta4^2 nu^2 + 2043271901650000 beta4^2 nu + 40856111261000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 < 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 91272500 beta4 nu^2 + 2002025450 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2463750000 beta4^2 nu^2 + 66711050000 beta4^2 nu + 1333235500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3376250000 beta4^2 nu^2 + 379826300000 beta4^2 nu + 9733020175500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 2931935550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [1358895000000000 beta4^2 nu^2 + 28987495175000000 beta4^2 nu + 579206345500000 beta4^2 - 682965187500000 beta4 nu^3 - 8553056223750000 beta4 nu^2 - 341302690725000 beta4 nu - 3410295046500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [5292500000 beta4^2 nu^2 + 546434200000 beta4^2 nu + 11681436567000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ [105850000 beta4 nu + 3199517000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2171750000 beta4^2 nu + 543601435000 beta4^2 - 638925000 beta4 nu^2 - 273211632000 beta4 nu - 5463977070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [109500000000 beta4^2 nu^3 + 27317695000000 beta4^2 nu^2 + 1411279201400000 beta4^2 nu + 28214657826000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 < 0 \/ 43800000 beta4 nu + 7727926000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [31025000 beta4^2 nu + 2265445500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 113303300000 beta4^2 nu + 2265445500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 113303300000 beta4^2 nu + 2265445500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [31025000 beta4^2 nu + 2265445500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ [14600000 beta4^2 nu + 292000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3102500000 beta4^2 nu + 611564800000 beta4^2 - 912750000 beta4 nu^2 - 293211810000 beta4 nu - 5863871100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 2464125000 beta4^2 nu^2 + 146646057500 beta4^2 nu + 2931935550 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 803050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1528756875000000 beta4^2 nu^2 + 41394206525000000 beta4^2 nu + 827272627750000 beta4^2 - 732938250000000 beta4 nu^3 - 12204088170000000 beta4 nu^2 - 487284000900000 beta4 nu - 4869908256000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [2007500000 beta4^2 nu^2 + 179934050000 beta4^2 nu + 2434954128000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 40150000 beta4 nu + 666928000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [4562500000 beta4^2 nu^2 + 133407500000 beta4^2 nu + 2666325000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2463750000 beta4^2 nu^2 + 66711050000 beta4^2 nu + 1333235500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 5330095000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4^2 nu + 2665595000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 1999105050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 1825375000 beta4^2 nu^2 + 99991757500 beta4^2 nu + 1999105050 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2434021297500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2737500000 beta4^2 nu^2 + 666234500000 beta4^2 nu + 38915023595000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ [3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 2737875000 beta4^2 nu^2 + 266559507500 beta4^2 nu + 5330095050 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 266504750000 beta4^2 nu + 9730754547500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 912875000 beta4^2 nu^2 + 25016195000 beta4^2 nu + 499958800 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 1999105050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 1999105050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 399821000000 beta4^2 nu + 9733419960000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [2500 nu^2 - 729900 nu - 14599 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7300000000 beta4^2 nu^2 + 266742000000 beta4^2 nu + 5331920000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 5331920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 182550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 beta4^2 nu + 182550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 9135000 beta4^2 nu + 182600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [125000 beta4^2 nu^2 + 9130000 beta4^2 nu + 166713800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 182600 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 666490050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 182550 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [228125000 beta4^2 nu^2 + 8335687500 beta4^2 nu + 166622500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 4562500 beta4^2 nu + 166622500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [249796875000000 beta4^2 nu^2 + 6088382500000000 beta4^2 nu + 121667731250000 beta4^2 - 333153750000000 beta4 nu^3 - 6100045162500000 beta4 nu^2 - 243602022000000 beta4 nu - 2434687605000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [684375000 beta4^2 nu^2 + 41660187500 beta4^2 nu + 608671992500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [912500000 beta4^2 nu + 66630750000 beta4^2 - 912750000 beta4 nu^2 - 99982635000 beta4 nu - 1999287600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [11406250000 beta4^2 nu^3 + 1249668750000 beta4^2 nu^2 + 30441926187500 beta4^2 nu + 608338747500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [250000 beta4^2 nu^2 + 22822500 beta4^2 nu + 500050100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 547700 beta4 - 182550 nu - 3651 = 0 ] /\ [866875000 beta4^2 nu^2 + 54989987500 beta4^2 nu + 852074140500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [228125000 beta4^2 nu^2 + 8335687500 beta4^2 nu + 166622500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 4562500 beta4^2 nu + 166622500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [249796875000000 beta4^2 nu^2 + 6088382500000000 beta4^2 nu + 121667731250000 beta4^2 - 333153750000000 beta4 nu^3 - 6100045162500000 beta4 nu^2 - 243602022000000 beta4 nu - 2434687605000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [684375000 beta4^2 nu^2 + 41660187500 beta4^2 nu + 608671992500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [912500000 beta4^2 nu + 66630750000 beta4^2 - 912750000 beta4 nu^2 - 99982635000 beta4 nu - 1999287600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [11406250000 beta4^2 nu^3 + 1249668750000 beta4^2 nu^2 + 30441926187500 beta4^2 nu + 608338747500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [866875000 beta4^2 nu^2 + 54989987500 beta4^2 nu + 852074140500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 22822500 beta4^2 nu + 500050100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 547700 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [30000 beta4^2 nu + 730600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [10000 beta4^2 nu + 547700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 547700 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2250000 beta4^2 nu^2 + 109590000 beta4^2 nu + 1334440900 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]] \/ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4^2 nu + 547700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [1058500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu + 99937000000 beta4^2 - 304250000 beta4 nu^2 - 66642920000 beta4 nu - 1332736700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [36500000 beta4^2 nu + 1999105000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 36500000 beta4 nu + 1999105000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ]]] /\ [166531250000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[912500 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [638750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [233143750000 beta4^2 - 111051250000 beta4 nu - 2221025000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1277500 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [1825000000 beta4^2 nu + 99955250000 beta4^2 - 608500000 beta4 nu^2 - 66655090000 beta4 nu - 1332858400 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[10000 beta4 nu + 547700 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [5000 beta4^2 nu + 547600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 < 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 54790000 beta4^2 nu + 1095400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 20000 beta4 nu + 1095400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [750000 beta4^2 nu^2 + 18280000 beta4^2 nu + 365300 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [30000 beta4^2 nu + 365600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 30000 beta4 nu + 365600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [10000 beta4^2 nu + 547700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 547700 beta4 - 182550 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 365400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1131500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [532900000000 beta4^2 - 333153750000 beta4 nu - 6663075000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [5475000000 beta4^2 nu + 133334500000 beta4^2 - 2738250000 beta4 nu^2 - 133371030000 beta4 nu - 2666325300 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [15000 beta4 nu + 365300 beta4 - 182550 nu - 3651 = 0 /\ [7500 beta4^2 nu + 365150 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7500 beta4 nu + 365150 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 16689625000 beta4^2 nu - 607505635000 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 100 nu - 1823 = 0 ]]] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [11406250000 beta4^2 nu^3 + 684375000 beta4^2 nu^2 - 15195962875000 beta4^2 nu - 303919440000 beta4^2 - 5704687500 beta4 nu^4 - 456375000 beta4 nu^3 + 7600056230625 beta4 nu^2 + 304002614325 beta4 nu + 3040027056 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [228125000 beta4^2 nu^2 + 9125000 beta4^2 nu - 303919440000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 912875000 beta4^2 nu^2 + 25016195000 beta4^2 nu + 499958800 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [5475000000 beta4^2 nu^2 + 133444000000 beta4^2 nu + 2666690000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [109500000 beta4 nu + 2666690000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [228125000 beta4^2 nu^2 + 8335687500 beta4^2 nu + 166622500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 4562500 beta4^2 nu + 166622500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 /\ 50 nu - 3649 <= 0 /\ [249796875000000 beta4^2 nu^2 + 6088382500000000 beta4^2 nu + 121667731250000 beta4^2 - 333153750000000 beta4 nu^3 - 6100045162500000 beta4 nu^2 - 243602022000000 beta4 nu - 2434687605000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [684375000 beta4^2 nu^2 + 41660187500 beta4^2 nu + 608671992500 beta4^2 - 456375000 beta4 nu^3 - 25013913750 beta4 nu^2 - 305002805775 beta4 nu - 6090054201 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [912500000 beta4^2 nu + 66630750000 beta4^2 - 912750000 beta4 nu^2 - 99982635000 beta4 nu - 1999287600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [11406250000 beta4^2 nu^3 + 1249668750000 beta4^2 nu^2 + 30441926187500 beta4^2 nu + 608338747500 beta4^2 - 5704687500 beta4 nu^4 - 833340750000 beta4 nu^3 - 22850196519375 beta4 nu^2 - 913008034425 beta4 nu - 9126747894 beta4 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [1140625000 beta4^2 nu^2 + 74984687500 beta4^2 nu + 1217177362500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 17344500 beta4^2 nu + 400021820 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 511420 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [21000 beta4 nu + 511420 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [7000 beta4^2 nu + 438140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 ]]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [700000 beta4^2 nu^2 + 25578000 beta4^2 nu + 511280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]] /\ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1575000 beta4^2 nu^2 + 76713000 beta4^2 nu + 934108630 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 \/ 10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 599603750000 beta4^2 nu + 38913691162500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 82135000 beta4^2 nu + 6662892600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 60232000 beta4^2 nu + 5063754570 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 /\ 50 nu - 3649 <= 0 /\ [166531250000000 beta4^2 nu^2 + 12163442500000000 beta4^2 nu + 243202237500000 beta4^2 - 249865312500000 beta4 nu^3 - 12175103793750000 beta4 nu^2 - 486704313375000 beta4 nu - 4866043672500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 19458844230000 beta4^2 - 1369125000 beta4 nu^3 - 266605147500 beta4 nu^2 - 9738752062950 beta4 nu - 194668410153 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [456250000 beta4^2 nu + 99927875000 beta4^2 - 456375000 beta4 nu^2 - 133279755000 beta4 nu - 2665412550 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 16655862500000 beta4^2 nu^2 + 1459479929750000 beta4^2 nu + 29182936615000 beta4^2 - 22818750000 beta4 nu^4 - 9996438000000 beta4 nu^3 - 973408681515000 beta4 nu^2 - 38924352265200 beta4 nu - 389203540551 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 799423000000 beta4^2 nu + 87544812730000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [375000 beta4 nu^3 + 91272500 beta4 nu^2 + 2002025450 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3650000000 beta4^2 nu^2 + 533046000000 beta4^2 nu + 19461509460000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 620570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [17500 nu^2 - 3649300 nu - 72993 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7300000000 beta4^2 nu^2 + 266742000000 beta4^2 nu + 5331920000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 5331920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 43807000 beta4^2 nu + 2265701070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3193750000 beta4^2 nu^2 + 366496500000 beta4^2 nu + 9732753652500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 175000 beta4^2 nu^2 + 52932000 beta4^2 nu + 2932008570 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [333062500000000 beta4^2 nu^2 + 6091713125000000 beta4^2 nu + 121701037500000 beta4^2 - 194339687500000 beta4 nu^3 - 2038345693750000 beta4 nu^2 - 81300620125000 beta4 nu - 812228842500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [4562500000 beta4^2 nu^2 + 466470000000 beta4^2 nu + 9734752575000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [456250000 beta4^2 nu + 133234125000 beta4^2 - 152125000 beta4 nu^2 - 77741960000 beta4 nu - 1554778350 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [91250000000 beta4^2 nu^3 + 23319850000000 beta4^2 nu^2 + 1216610809500000 beta4^2 nu + 24322888980000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 < 0 \/ 36500000 beta4 nu + 6661980000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [912500000 beta4^2 nu + 166549500000 beta4^2 - 304250000 beta4 nu^2 - 88853170000 beta4 nu - 1776941700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [6250000 beta4^2 nu^3 + 2281625000 beta4^2 nu^2 + 133316257500 beta4^2 nu + 2665412550 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [416328125000000 beta4^2 nu^2 + 12173434375000000 beta4^2 nu + 243302156250000 beta4^2 - 222102500000000 beta4 nu^3 - 4066696775000000 beta4 nu^2 - 162401348000000 beta4 nu - 1623125070000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [1825000000 beta4^2 nu^2 + 166604250000 beta4^2 nu + 2434687605000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 66722000000 beta4^2 nu + 1333345000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [4562500000 beta4^2 nu^2 + 133407500000 beta4^2 nu + 2666325000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2281250000 beta4^2 nu^2 + 66703750000 beta4^2 nu + 1333162500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 5330095000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4^2 nu + 2665595000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 175000 beta4^2 nu^2 + 43807000 beta4^2 nu + 2265701070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 266559500000 beta4^2 nu + 4868042595000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 1825375000 beta4^2 nu^2 + 99991757500 beta4^2 nu + 1999105050 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2434021297500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2737500000 beta4^2 nu^2 + 666234500000 beta4^2 nu + 38915023595000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ [2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 2737875000 beta4^2 nu^2 + 266559507500 beta4^2 nu + 5330095050 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 266504750000 beta4^2 nu + 9730754547500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2281250000 beta4^2 nu^2 + 149969375000 beta4^2 nu + 2434354725000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 175000 beta4^2 nu^2 + 21907000 beta4^2 nu + 566644320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 912875000 beta4^2 nu^2 + 25016195000 beta4^2 nu + 499958800 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [38325000 beta4^2 nu + 933341500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 949000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 7000 beta4^2 nu + 438140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [730000000 beta4^2 nu + 63962600000 beta4^2 - 304250000 beta4 nu^2 - 53316770000 beta4 nu - 1066213700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[5000 beta4 nu + 438100 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [31025000 beta4^2 nu + 1599320500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 31025000 beta4 nu + 1599320500 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 ]]] /\ [117238000000 beta4^2 - 75514850000 beta4 nu - 1510297000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[803000 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [529250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 529250 beta4 - 182550 nu - 3651 = 0 ]]] /\ [7300000 beta4^2 nu + 146000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [146000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [7300000 beta4^2 nu + 146000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 146000 beta4 - 60850 nu - 1217 = 0 ]] /\ [146000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 146000 beta4 - 60850 nu - 1217 = 0 ]] /\ [1022000000 beta4^2 nu + 63968440000 beta4^2 - 425950000 beta4 nu^2 - 53321638000 beta4 nu - 1066262380 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [3500 beta4^2 nu + 438070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 438070 beta4 - 182550 nu - 3651 = 0 ]]] /\ [138554000000 beta4^2 - 84398950000 beta4 nu - 1687979000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[949000 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [693500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 693500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [38325000 beta4^2 nu + 933341500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000 beta4^2 nu + 1866427500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 63875000 beta4 nu + 1866427500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [1788500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1788500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [949000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 949000 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [63875000 beta4^2 nu + 1277500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 60850 nu - 1217 = 0 ]]] \/ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 38353000 beta4^2 nu + 766780 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 766780 beta4 - 182550 nu - 3651 = 0 ]]] /\ [525000 beta4^2 nu^2 + 12796000 beta4^2 nu + 255710 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [21000 beta4^2 nu + 255920 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 21000 beta4 nu + 255920 beta4 - 182550 nu - 3651 = 0 ]]] /\ [7000 beta4^2 nu + 438140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 438140 beta4 - 182550 nu - 3651 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 50 nu - 3649 /= 0 ] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [2682750000 beta4^2 nu + 65333905000 beta4^2 - 1916775000 beta4 nu^2 - 93359721000 beta4 nu - 1866427710 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10500 beta4 nu + 255710 beta4 - 182550 nu - 3651 = 0 /\ [5250 beta4^2 nu + 255605 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5250 beta4 nu + 255605 beta4 - 182550 nu - 3651 = 0 ]]] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [638750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 11682737500 beta4^2 nu - 425253944500 beta4^2 - 456375000 beta4 nu^3 - 8356226250 beta4 nu^2 + 303669095475 beta4 nu + 6076720749 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 100 nu - 1823 = 0 ]]] /\ [125000 beta4^2 nu^2 + 15517500 beta4^2 nu + 399985300 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 5000 beta4 nu + 438100 beta4 - 182550 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [7984375000 beta4^2 nu^3 + 479062500 beta4^2 nu^2 - 10637174012500 beta4^2 nu - 212743608000 beta4^2 - 5704687500 beta4 nu^4 - 456375000 beta4 nu^3 + 7600056230625 beta4 nu^2 + 304002614325 beta4 nu + 3040027056 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [159687500 beta4^2 nu^2 + 6387500 beta4^2 nu - 212743608000 beta4^2 - 114093750 beta4 nu^3 - 6845625 beta4 nu^2 + 152001261525 beta4 nu + 3040027056 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 639012500 beta4^2 nu^2 + 17511336500 beta4^2 nu + 349971160 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 34997112500 beta4^2 nu + 426187030500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 693570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2920000000 beta4^2 nu^2 + 346501800000 beta4^2 nu + 9732353868000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 58410000 beta4^2 nu + 2932118100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [226482500000000 beta4^2 nu^2 + 4871771800000000 beta4^2 nu + 97344843000000 beta4^2 - 161024312500000 beta4 nu^3 - 2036346771250000 beta4 nu^2 - 81260641675000 beta4 nu - 811962319500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [3741250000 beta4^2 nu^2 + 386502150000 beta4^2 nu + 8274339796500 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ [74825000 beta4 nu + 2266321500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [365000000 beta4^2 nu + 90600300000 beta4^2 - 152125000 beta4 nu^2 - 64415810000 beta4 nu - 1288255350 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [77562500000 beta4^2 nu^3 + 19322278750000 beta4^2 nu^2 + 997628860575000 beta4^2 nu + 19944848920500 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 < 0 \/ 31025000 beta4 nu + 5462845500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [7300000 beta4^2 nu + 533046000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [365000000 beta4^2 nu^2 + 26659600000 beta4^2 nu + 533046000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [7300000 beta4^2 nu + 533046000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 146000 beta4 - 60850 nu - 1217 = 0 ]] /\ [365000000 beta4^2 nu^2 + 26659600000 beta4^2 nu + 533046000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 146000 beta4 - 60850 nu - 1217 = 0 ]] /\ [511000000 beta4^2 nu + 101261220000 beta4^2 - 212975000 beta4 nu^2 - 68860294000 beta4 nu - 1377120690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [4375000 beta4^2 nu^3 + 1734012500 beta4^2 nu^2 + 103318730250 beta4^2 nu + 2065681035 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 565785 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [253127500000000 beta4^2 nu^2 + 6817922600000000 beta4^2 nu + 136257201000000 beta4^2 - 172129437500000 beta4 nu^3 - 2847687203750000 beta4 nu^2 - 113700932825000 beta4 nu - 1136320810500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [1414375000 beta4^2 nu^2 + 126620325000 beta4^2 nu + 1704481215750 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 28287500 beta4 nu + 466853250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1250 nu^2 - 63825 nu - 1277 > 0 /\ 50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3193750000 beta4^2 nu^2 + 93385250000 beta4^2 nu + 1866427500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [63875000 beta4 nu + 1866427500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 3731066500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 3731066500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 93334150000 beta4^2 nu + 1865916500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 766780 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 766780 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [3500 beta4^2 nu + 693570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 63889000 beta4^2 nu + 1277640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 1277640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 766640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 186591650000 beta4^2 nu + 3407629816500 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 1250 nu^2 + 45675 nu + 913 > 0 ] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1277762500 beta4^2 nu^2 + 69994230250 beta4^2 nu + 1399373535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 93295825000 beta4^2 nu + 1703814908250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2463750000 beta4^2 nu^2 + 626256050000 beta4^2 nu + 38914224135500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ [2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1916512500 beta4^2 nu^2 + 186591655250 beta4^2 nu + 3731066535 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 186553325000 beta4^2 nu + 6811528183250 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [2144375000 beta4^2 nu^2 + 144967962500 beta4^2 nu + 2434254751500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 250000 beta4^2 nu^2 + 24647500 beta4^2 nu + 566699100 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 639012500 beta4^2 nu^2 + 17511336500 beta4^2 nu + 349971160 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 34997112500 beta4^2 nu + 426187030500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 620570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [3102500000 beta4^2 nu + 385082300000 beta4^2 - 912750000 beta4 nu^2 - 226581060000 beta4 nu - 4531256100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ] /\ [2171750000 beta4^2 nu + 385063685000 beta4^2 - 638925000 beta4 nu^2 - 226570107000 beta4 nu - 4531146570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 ] /\ [203834250000 beta4^2 - 97725100000 beta4 nu - 1954502000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [181186000000 beta4^2 - 91062025000 beta4 nu - 1821240500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 170194899175000 beta4^2 nu - 3403898494500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 3403898494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1277762500 beta4^2 nu^2 + 69994230250 beta4^2 nu + 1399373535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1916250000 beta4^2 nu^2 + 93334150000 beta4^2 nu - 3402032833500 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 150 nu - 3647 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 93295825000 beta4^2 nu + 1703814908250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [49275000 beta4^2 nu + 1333235500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]] \/ [500000 beta4^2 nu^2 + 31045000 beta4^2 nu + 620700 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 985600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 803100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 31035000 beta4^2 nu + 620600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 620600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ]] \/ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 620500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [3102500000 beta4^2 nu + 385082300000 beta4^2 - 912750000 beta4 nu^2 - 226581060000 beta4 nu - 4531256100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ] /\ [2171750000 beta4^2 nu + 385063685000 beta4^2 - 638925000 beta4 nu^2 - 226570107000 beta4 nu - 4531146570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 ] /\ [203834250000 beta4^2 - 97725100000 beta4 nu - 1954502000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [181186000000 beta4^2 - 91062025000 beta4 nu - 1821240500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ]] \/ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2007500000 beta4^2 nu + 644849150000 beta4^2 - 456375000 beta4 nu^2 - 293193555000 beta4 nu - 5863688550 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 803050 beta4 - 182550 nu - 3651 = 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [49275000 beta4^2 nu + 5862885500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 49275000 beta4 nu + 5862885500 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [263785500000 beta4^2 - 108830225000 beta4 nu - 2176604500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[803000 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2591500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 2591500 beta4 - 547650 nu - 10953 = 0 ]]] /\ [40150000 beta4^2 nu + 803000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [40150000 beta4^2 nu + 803000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 803000 beta4 - 182550 nu - 3651 = 0 ]] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 803000 beta4 - 182550 nu - 3651 = 0 ]] /\ [4015000000 beta4^2 nu + 644889300000 beta4^2 - 912750000 beta4 nu^2 - 293211810000 beta4 nu - 5863871100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 803100 beta4 - 182550 nu - 3651 = 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4^2 nu + 803050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 803050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2810500000 beta4^2 nu + 644865210000 beta4^2 - 638925000 beta4 nu^2 - 293200857000 beta4 nu - 5863761570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 803070 beta4 - 182550 nu - 3651 = 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [1750 beta4^2 nu + 803035 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1750 beta4 nu + 803035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [937904000000 beta4^2 - 359806050000 beta4 nu - 7196121000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1168000 beta4 - 182550 nu - 3651 = 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [849975500000 beta4^2 - 339816825000 beta4 nu - 6796336500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1058500 beta4 - 182550 nu - 3651 = 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [310250 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 310250 beta4 - 60850 nu - 1217 = 0 ]]]] \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [49275000 beta4^2 nu + 1333235500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [67525000 beta4^2 nu + 2665850500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 67525000 beta4 nu + 2665850500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [1350500 beta4 - 182550 nu - 3651 = 0 /\ [693500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 693500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [67525000 beta4^2 nu + 1350500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]]] \/ [5000 beta4^2 nu + 620600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [5000 beta4^2 nu + 985600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 67545000 beta4^2 nu + 1350700 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 1350700 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 31045000 beta4^2 nu + 620700 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 620700 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 620900 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 20000 beta4 nu + 620900 beta4 - 182550 nu - 3651 = 0 ]]] /\ [5000 beta4^2 nu + 803100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 803100 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 31035000 beta4^2 nu + 620600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4^2 nu + 620700 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ]] \/ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 693500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 620500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [6205000000 beta4^2 nu + 385144350000 beta4^2 - 1825500000 beta4 nu^2 - 226617570000 beta4 nu - 4531621200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10000 beta4 nu + 620700 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 620600 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [4343500000 beta4^2 nu + 385107120000 beta4^2 - 1277850000 beta4 nu^2 - 226595664000 beta4 nu - 4531402140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 620640 beta4 - 182550 nu - 3651 = 0 /\ [3500 beta4^2 nu + 620570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 ]]] /\ [837985250000 beta4^2 - 359806050000 beta4 nu - 7196121000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1350500 beta4 - 182550 nu - 3651 = 0 /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [702095750000 beta4^2 - 319827600000 beta4 nu - 6396552000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1131500 beta4 - 182550 nu - 3651 = 0 /\ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ]]]] \/ [3376250000 beta4^2 nu^2 + 379826300000 beta4^2 nu + 9733020175500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 31025000 beta4^2 nu + 2265445500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [[620500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [4653750000 beta4^2 nu^2 + 226668650000 beta4^2 nu - 8262079738500 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 \/ 150 nu - 3647 = 0 ]]] /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 2931935550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 2500 beta4 nu + 803050 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 113303300000 beta4^2 nu + 2265445500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [77562500000 beta4^2 nu^3 + 4653750000 beta4^2 nu^2 - 413330469425000 beta4^2 nu - 8266610629500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 > 0 \/ 620500 beta4 - 182550 nu - 3651 /= 0 ] /\ [1551250000 beta4^2 nu^2 + 62050000 beta4^2 nu - 8266610629500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 > 0 \/ 620500 beta4 - 182550 nu - 3651 /= 0 ] /\ [3102500000 beta4^2 nu + 611564800000 beta4^2 - 912750000 beta4 nu^2 - 293211810000 beta4 nu - 5863871100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 2464125000 beta4^2 nu^2 + 146646057500 beta4^2 nu + 2931935550 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 803050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2171750000 beta4^2 nu + 543601435000 beta4^2 - 638925000 beta4 nu^2 - 273211632000 beta4 nu - 5463977070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 2190262500 beta4^2 nu^2 + 136643230250 beta4^2 nu + 2731988535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 748285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1528756875000000 beta4^2 nu^2 + 41394206525000000 beta4^2 nu + 827272627750000 beta4^2 - 732938250000000 beta4 nu^3 - 12204088170000000 beta4 nu^2 - 487284000900000 beta4 nu - 4869908256000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [2007500000 beta4^2 nu^2 + 179934050000 beta4^2 nu + 2434954128000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 40150000 beta4 nu + 666928000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1358895000000000 beta4^2 nu^2 + 28987495175000000 beta4^2 nu + 579206345500000 beta4^2 - 682965187500000 beta4 nu^3 - 8553056223750000 beta4 nu^2 - 341302690725000 beta4 nu - 3410295046500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1870625000 beta4^2 nu^2 + 159944825000 beta4^2 nu + 1705147523250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 37412500 beta4 nu + 467035750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]] \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ]]]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 43807000 beta4^2 nu + 2265701070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [3650000000 beta4^2 nu^2 + 399821000000 beta4^2 nu + 9733419960000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 511140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [3500 beta4^2 nu + 620570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 511280 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4 nu + 511280 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [17500 nu^2 - 3649300 nu - 72993 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu + 2665595000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7300000000 beta4^2 nu^2 + 266742000000 beta4^2 nu + 5331920000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 5331920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 233399320 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 933086070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 532973000000 beta4^2 nu + 38912358730000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ] /\ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [63875000000 beta4^2 nu^3 + 13992457500000 beta4^2 nu^2 + 681339371650000 beta4^2 nu + 13621190961000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2555000000 beta4^2 nu^2 + 279874700000 beta4^2 nu + 6813393972000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2463750000 beta4^2 nu^2 + 133323550000 beta4^2 nu + 2665485500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7300000000 beta4^2 nu^2 + 266742000000 beta4^2 nu + 5331920000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 5331920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 620600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 1460200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ]] \/ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4^2 nu + 620570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [3102500000 beta4^2 nu + 385082300000 beta4^2 - 912750000 beta4 nu^2 - 226581060000 beta4 nu - 4531256100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [49275000 beta4^2 nu + 4530635500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 49275000 beta4 nu + 4530635500 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [2171750000 beta4^2 nu + 385063685000 beta4^2 - 638925000 beta4 nu^2 - 226570107000 beta4 nu - 4531146570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1750 beta4^2 nu + 620535 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1750 beta4 nu + 620535 beta4 - 182550 nu - 3651 = 0 ]]] /\ [203834250000 beta4^2 - 97725100000 beta4 nu - 1954502000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2226500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 2226500 beta4 - 547650 nu - 10953 = 0 ]]] /\ [181186000000 beta4^2 - 91062025000 beta4 nu - 1821240500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [748250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 748250 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1788500000 beta4^2 nu + 65316020000 beta4^2 - 1277850000 beta4 nu^2 - 93334164000 beta4 nu - 1866172140 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]]] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [3500 beta4^2 nu + 255570 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 12782000 beta4^2 nu + 255570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 255640 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 3500 beta4 nu + 255570 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 620570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 12789000 beta4^2 nu + 255640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 255640 beta4 - 182550 nu - 3651 = 0 /\ [14000 beta4^2 nu + 255780 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 14000 beta4 nu + 255780 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 170194899175000 beta4^2 nu - 3403898494500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 3403898494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [4375000 beta4^2 nu^3 + 1277762500 beta4^2 nu^2 + 69994230250 beta4^2 nu + 1399373535 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1916250000 beta4^2 nu^2 + 93334150000 beta4^2 nu - 3402032833500 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 150 nu - 3647 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [958125000 beta4^2 nu^2 + 93295825000 beta4^2 nu + 1703814908250 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 ] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 /\ 50 nu - 3649 <= 0 /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [2555000000 beta4^2 nu^2 + 279874700000 beta4^2 nu + 6813393972000 beta4^2 - 1369125000 beta4 nu^3 - 133343647500 beta4 nu^2 - 2437354477950 beta4 nu - 48693763053 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [63875000000 beta4^2 nu^3 + 13992457500000 beta4^2 nu^2 + 681339371650000 beta4^2 nu + 13621190961000 beta4^2 - 22818750000 beta4 nu^4 - 6664900500000 beta4 nu^3 - 365203195515000 beta4 nu^2 - 14600130670200 beta4 nu - 145974650751 beta4 > 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [2463750000 beta4^2 nu^2 + 313177300000 beta4^2 nu + 9731687560500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 2265810600 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 nu - 3649 <= 0 /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [5000 beta4^2 nu + 620600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 1460200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [3650000000 beta4^2 nu^2 + 133371000000 beta4^2 nu + 2665960000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [7300000000 beta4^2 nu^2 + 266742000000 beta4^2 nu + 5331920000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [146000000 beta4 nu + 5331920000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2463750000 beta4^2 nu^2 + 133323550000 beta4^2 nu + 2665485500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 2665485500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 10659460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 10659460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [3650000000 beta4^2 nu^2 + 266596000000 beta4^2 nu + 5330460000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2434021480000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 333427600 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 ]] \/ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]] \/ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 620600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 133261500000 beta4^2 - 912750000 beta4 nu^2 - 133298010000 beta4 nu - 2665595100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [266450000000 beta4^2 - 199892250000 beta4 nu - 3997845000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2171750000 beta4^2 nu + 385063685000 beta4^2 - 638925000 beta4 nu^2 - 226570107000 beta4 nu - 4531146570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [43800000 beta4^2 nu + 4530526000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 43800000 beta4 nu + 4530526000 beta4 - 9127500 nu^2 - 1332980100 nu - 26655951 = 0 ]]] /\ [181186000000 beta4^2 - 91062025000 beta4 nu - 1821240500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [2117000 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 2117000 beta4 - 547650 nu - 10953 = 0 ]]] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [14600000 beta4^2 nu + 292000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [3102500000 beta4^2 nu + 385082300000 beta4^2 - 912750000 beta4 nu^2 - 226581060000 beta4 nu - 4531256100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4^2 nu + 620550 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [203834250000 beta4^2 - 97725100000 beta4 nu - 1954502000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 2665595000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]]] \/ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 54770000 beta4^2 nu + 1095200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 18270000 beta4^2 nu + 365200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 365400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 20000 beta4 nu + 365400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [5000 beta4^2 nu + 620600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 620600 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4^2 nu + 365200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [3650000000 beta4^2 nu + 133298000000 beta4^2 - 1825500000 beta4 nu^2 - 133334520000 beta4 nu - 2665960200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [10000 beta4 nu + 365200 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 365100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [2737500000 beta4^2 nu^2 + 333172000000 beta4^2 nu + 9732087345000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [2737500000 beta4^2 nu^2 + 133334500000 beta4^2 nu - 4860046905000 beta4^2 - 1369125000 beta4 nu^3 - 66712897500 beta4 nu^2 + 2429355502050 beta4 nu + 48613784247 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 150 nu - 3647 = 0 ]]] /\ [175000 beta4^2 nu^2 + 43807000 beta4^2 nu + 2265701070 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 3500 beta4 nu + 620570 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 2737500000 beta4^2 nu^2 - 243135570250000 beta4^2 nu - 4862712135000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 4862712135000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [6250000 beta4^2 nu^3 + 1825375000 beta4^2 nu^2 + 99991757500 beta4^2 nu + 1999105050 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2434021297500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 133261500000 beta4^2 - 912750000 beta4 nu^2 - 133298010000 beta4 nu - 2665595100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [266450000000 beta4^2 - 199892250000 beta4 nu - 3997845000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]] \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2920000 beta4 - 182550 nu - 3651 = 0 ]]]] \/ [50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]] \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [866875000 beta4^2 nu^2 + 54989987500 beta4^2 nu + 852074140500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 500000 beta4^2 nu^2 + 41082500 beta4^2 nu + 833477700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [228125000 beta4^2 nu^2 + 8335687500 beta4^2 nu + 166622500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [4562500 beta4^2 nu + 166622500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu + 66630750000 beta4^2 - 912750000 beta4 nu^2 - 99982635000 beta4 nu - 1999287600 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [228125000 beta4^2 nu^2 + 24988812500 beta4^2 nu + 608338747500 beta4^2 - 114093750 beta4 nu^3 - 16664533125 beta4 nu^2 - 456670639725 beta4 nu - 9126747894 beta4 < 0 \/ 9125000 beta4 nu + 666307500 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 ]]] /\ [4562500 beta4^2 nu + 166622500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [249796875000000 beta4^2 nu^2 + 6088382500000000 beta4^2 nu + 121667731250000 beta4^2 - 333153750000000 beta4 nu^3 - 6100045162500000 beta4 nu^2 - 243602022000000 beta4 nu - 2434687605000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [34218750000 beta4^2 nu^3 + 2083693750000 beta4^2 nu^2 + 30475259812500 beta4^2 nu + 608671992500 beta4^2 - 22818750000 beta4 nu^4 - 1251152062500 beta4 nu^3 - 15275154202500 beta4 nu^2 - 609505515825 beta4 nu - 6090054201 beta4 < 0 \/ [27375000 beta4 nu + 666672500 beta4 - 18255000 nu^2 - 333883950 nu - 6670377 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [228125000 beta4^2 nu^2 + 8335687500 beta4^2 nu + 166622500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [182500 beta4 - 182550 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [375000 beta4 nu^3 + 91272500 beta4 nu^2 + 2002025450 beta4 nu + 40004003 beta4 > 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1095000000 beta4^2 nu^2 + 253171300000 beta4^2 nu + 13620657988000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 82135000 beta4^2 nu + 6662892600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu + 99927875000 beta4^2 - 456375000 beta4 nu^2 - 133279755000 beta4 nu - 2665412550 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 333099000000 beta4^2 nu + 29182936615000 beta4^2 - 456375000 beta4 nu^3 - 199919632500 beta4 nu^2 - 19464175237650 beta4 nu - 389203540551 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [166531250000000 beta4^2 nu^2 + 12163442500000000 beta4^2 nu + 243202237500000 beta4^2 - 249865312500000 beta4 nu^3 - 12175103793750000 beta4 nu^2 - 486704313375000 beta4 nu - 4866043672500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 68456250000 beta4 nu^4 - 13331626500000 beta4 nu^3 - 487204208295000 beta4 nu^2 - 19472172570600 beta4 nu - 194668410153 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [182500 beta4 - 182550 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [76650000 beta4^2 nu + 1866683000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [76650000 beta4 nu + 1866683000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [2555000000 beta4^2 nu^2 + 186617200000 beta4^2 nu + 3731322000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [5000 nu^2 - 127550 nu - 2553 > 0 \/ 100 nu - 2553 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2555000000 beta4^2 nu^2 + 93359700000 beta4^2 nu + 1866172000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 >= 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1095000000 beta4^2 nu^2 + 93301300000 beta4^2 nu + 1865588000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 279823600000 beta4^2 nu + 5595961000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 3730811000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 3730811000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 912600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 < 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] \/ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3407096770500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3407096770500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1368750000 beta4^2 nu^2 + 333117250000 beta4^2 nu + 19457511797500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 60232000 beta4^2 nu + 5063754570 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [456250000 beta4^2 nu + 99927875000 beta4^2 - 456375000 beta4 nu^2 - 133279755000 beta4 nu - 2665412550 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 333099000000 beta4^2 nu + 29182936615000 beta4^2 - 456375000 beta4 nu^3 - 199919632500 beta4 nu^2 - 19464175237650 beta4 nu - 389203540551 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 2665595100 nu - 53308251 = 0 ]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [166531250000000 beta4^2 nu^2 + 12163442500000000 beta4^2 nu + 243202237500000 beta4^2 - 249865312500000 beta4 nu^3 - 12175103793750000 beta4 nu^2 - 486704313375000 beta4 nu - 4866043672500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [91250000000 beta4^2 nu^3 + 19989225000000 beta4^2 nu^2 + 973341959500000 beta4^2 nu + 19458844230000 beta4^2 - 68456250000 beta4 nu^4 - 13331626500000 beta4 nu^3 - 487204208295000 beta4 nu^2 - 19472172570600 beta4 nu - 194668410153 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 27382500 nu^2 - 1333710300 nu - 26663253 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ [182500 beta4 - 182550 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [949000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [182500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [133225000000 beta4^2 - 166576875000 beta4 nu - 3331537500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[730000 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [292000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 292000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [182500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [83265625000000 beta4^2 nu^2 + 18238502500000000 beta4^2 nu + 364736743750000 beta4^2 - 166576875000000 beta4 nu^3 - 18250162425000000 beta4 nu^2 - 729806604750000 beta4 nu - 7297399740000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 182550 nu - 3651 = 0 ] /\ [228125000 beta4^2 nu^2 + 49968500000 beta4^2 nu + 999278750 beta4^2 - 228187500 beta4 nu^3 - 25000222500 beta4 nu^2 - 999735075 beta4 nu - 9996438 beta4 < 0 \/ [4562500 beta4 nu + 999278750 beta4 - 4563750 nu^2 - 499913175 nu - 9996438 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]] /\ [9125000 beta4^2 nu + 182500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [125000 beta4 nu^3 - 18242500 beta4 nu^2 - 9992604850 beta4 nu - 199844799 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 >= 0 /\ 175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2665047500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3500 beta4^2 nu + 693570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1533140 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1533140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 1022140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [949000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [2044000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2044000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4 - 60850 nu - 1217 = 0 ]] /\ [175000 beta4^2 nu^2 + 38332000 beta4^2 nu + 766570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 76664000 beta4^2 nu + 1533140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 1533140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [25550000 beta4^2 nu + 511000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4 - 60850 nu - 1217 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2665047500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [8212500000 beta4^2 nu^2 + 400003500000 beta4^2 nu + 4870709285000 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [20000 beta4^2 nu + 1095400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 1823 <= 0 /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4^2 nu + 1460800 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 2920800 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 40000 beta4 nu + 2920800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ [3000000 beta4^2 nu^2 + 73120000 beta4^2 nu + 1461200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [60000 beta4 nu + 1461200 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1825000000 beta4^2 nu^2 + 33379250000 beta4^2 nu + 666855000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5000 nu^2 - 91050 nu - 1823 > 0 \/ 100 nu - 1823 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]] \/ [5748750000 beta4^2 nu^2 + 280002450000 beta4^2 nu + 3409496499500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4106250000 beta4^2 nu^2 + 200001750000 beta4^2 nu + 2435354642500 beta4^2 - 1369125000 beta4 nu^3 - 33397522500 beta4 nu^2 - 1334257950 beta4 nu - 13337103 beta4 > 0 /\ 4500000 beta4^2 nu^2 + 219180000 beta4^2 nu + 2668881800 beta4^2 - 27382500 beta4 nu^2 - 667402800 beta4 nu - 13337103 beta4 > 0 /\ 7500 beta4 nu^2 + 182800 beta4 nu + 3653 beta4 > 0 /\ 150 beta4 nu + 3653 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [20000 beta4^2 nu + 985900 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 1823 <= 0 /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4^2 nu + 1460800 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 2920800 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 40000 beta4 nu + 2920800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ [3000000 beta4^2 nu^2 + 73120000 beta4^2 nu + 1461200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [60000 beta4 nu + 1461200 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]]] \/ [1551250000 beta4^2 nu^2 + 33368300000 beta4^2 nu + 666745500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5000 nu^2 - 91050 nu - 1823 > 0 \/ 100 nu - 1823 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3500 beta4^2 nu + 876070 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 350 nu - 18243 <= 0 /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4^2 nu + 1022140 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ]] /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1533140 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 7000 beta4 nu + 1533140 beta4 - 182550 nu - 3651 = 0 ]]] /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 51128000 beta4^2 nu + 1022280 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [14000 beta4 nu + 1022280 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 1332797500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [17500 nu^2 - 911800 nu - 18243 > 0 \/ 350 nu - 18243 = 0 ] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [5000 beta4^2 nu + 985600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 1460200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 2190200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]] \/ [1095000000 beta4^2 nu^2 + 66656300000 beta4^2 nu + 1332688000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [20000 beta4^2 nu + 985900 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 1823 <= 0 /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ [3000000 beta4^2 nu^2 + 73120000 beta4^2 nu + 1461200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [60000 beta4 nu + 1461200 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 2920800 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 40000 beta4 nu + 2920800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4^2 nu + 1460800 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 33368300000 beta4^2 nu + 666745500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 1333345000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [5000 nu^2 - 91050 nu - 1823 > 0 \/ 100 nu - 1823 = 0 ] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]] /\ [18250000 beta4^2 nu + 666490000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1866172140 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]] \/ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 >= 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1095000000 beta4^2 nu^2 + 66656300000 beta4^2 nu + 1332688000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [9125000 beta4^2 nu + 1998557500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 199874000000 beta4^2 nu + 3997115000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 1332432500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [456250000 beta4^2 nu^2 + 199855750000 beta4^2 nu + 21886203182500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 9125000 beta4 nu + 1998557500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 985600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 < 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] \/ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2434021297500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2007500000 beta4^2 nu^2 + 179934050000 beta4^2 nu + 2434954128000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 104045000 beta4^2 nu + 4931405700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [1358895000000000 beta4^2 nu^2 + 28987495175000000 beta4^2 nu + 579206345500000 beta4^2 - 682965187500000 beta4 nu^3 - 8553056223750000 beta4 nu^2 - 341302690725000 beta4 nu - 3410295046500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [264625000000 beta4^2 nu^3 + 27327002500000 beta4^2 nu^2 + 584618262550000 beta4^2 nu + 11681436567000 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 \/ [105850000 beta4 nu + 3199517000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2171750000 beta4^2 nu + 543601435000 beta4^2 - 638925000 beta4 nu^2 - 273211632000 beta4 nu - 5463977070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [2190000000 beta4^2 nu^2 + 546310100000 beta4^2 nu + 28214657826000 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 43800000 beta4 nu + 7727926000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [1528756875000000 beta4^2 nu^2 + 41394206525000000 beta4^2 nu + 827272627750000 beta4^2 - 732938250000000 beta4 nu^3 - 12204088170000000 beta4 nu^2 - 487284000900000 beta4 nu - 4869908256000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [100375000000 beta4^2 nu^3 + 8998710000000 beta4^2 nu^2 + 121927640450000 beta4^2 nu + 2434954128000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 40150000 beta4 nu + 666928000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1551250000 beta4^2 nu^2 + 113303300000 beta4^2 nu + 2265445500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [31025000 beta4^2 nu + 2265445500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 113303300000 beta4^2 nu + 2265445500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [620500 beta4 - 182550 nu - 3651 = 0 /\ [14600000 beta4^2 nu + 292000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 \/ [292000 beta4 - 60850 nu - 1217 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [31025000 beta4^2 nu + 2265445500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [3102500000 beta4^2 nu + 611564800000 beta4^2 - 912750000 beta4 nu^2 - 293211810000 beta4 nu - 5863871100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 2931935550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 803050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 < 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 54790000 beta4^2 nu + 1095400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1095400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 1825200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 1825200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [5000 beta4^2 nu + 985600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 54770000 beta4^2 nu + 1095200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]]] \/ [1368750000 beta4^2 nu^2 + 266504750000 beta4^2 nu + 9730754547500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 164270000 beta4^2 nu + 13325785200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [365000 beta4 - 182550 nu - 3651 = 0 \/ 2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [68437500000 beta4^2 nu^3 + 13326606250000 beta4^2 nu^2 + 486804232125000 beta4^2 nu + 9730754547500 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 45645000 beta4^2 nu + 1000100200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 2500706250000 beta4^2 nu^2 + 30491926625000 beta4^2 nu + 608838615000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 608505370000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2434021297500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 1823 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 2920400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 2920400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1368750000 beta4^2 nu^2 + 33361000000 beta4^2 nu + 666672500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5000 nu^2 - 91050 nu - 1823 > 0 \/ 100 nu - 1823 = 0 ] /\ [9125000 beta4^2 nu + 1332432500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 33342750000 beta4^2 nu + 666490000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 666490000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 1332980000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 133243250000 beta4^2 nu + 9728089682500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 9125000 beta4 nu + 1332432500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [456250000 beta4^2 nu^2 + 66630750000 beta4^2 nu + 2432688682500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 9125000 beta4 nu + 666307500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4^2 nu + 730050 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 93319550000 beta4^2 nu + 1865770500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 255400 nu - 5109 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 3730811000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 3730811000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 279823600000 beta4^2 nu + 5595961000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 5595961000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 3731322000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4 nu + 3731322000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 9730754730000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4^2 nu + 620550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 133287050000 beta4^2 nu + 2665120500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 7994230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 547550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 1095100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 547550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 1095100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 >= 0 /\ 125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1551250000 beta4^2 nu^2 + 133287050000 beta4^2 nu + 2665120500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4^2 nu + 620550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 18260000 beta4^2 nu + 365100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 365100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 beta4^2 nu + 547550 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ]]] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 beta4^2 nu + 365050 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 1460000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [125000 beta4^2 nu^2 + 27380000 beta4^2 nu + 547550 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 54760000 beta4^2 nu + 1095100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 547600 nu + 10951 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 beta4 nu + beta4 > 0 /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1551250000 beta4^2 nu^2 + 133287050000 beta4^2 nu + 2665120500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 < 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [962550625000000 beta4^2 nu^2 + 57904780775000000 beta4^2 nu + 1157710595250000 beta4^2 - 566361375000000 beta4 nu^3 - 17058138307500000 beta4 nu^2 - 681645898650000 beta4 nu - 6814193541000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[31025000 beta4 nu + 1865770500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3198020500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [31025000 beta4 nu + 3198020500 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [702095750000 beta4^2 - 319827600000 beta4 nu - 6396552000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1131500 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [748250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 748250 beta4 - 182550 nu - 3651 = 0 ]]] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [837985250000 beta4^2 - 359806050000 beta4 nu - 7196121000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [328500 beta4 - 60850 nu - 1217 = 0 /\ [1350500 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [14600000 beta4^2 nu + 292000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [962550625000000 beta4^2 nu^2 + 82704614525000000 beta4^2 nu + 1653707270250000 beta4^2 - 566361375000000 beta4 nu^3 - 24354205432500000 beta4 nu^2 - 973488583650000 beta4 nu - 9732620391000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[31025000 beta4 nu + 2665120500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 2500 nu^2 - 364900 nu - 7299 > 0 /\ 50 nu - 3649 < 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 5330095000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 7993865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 7993865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1551250000 beta4^2 nu^2 + 133287050000 beta4^2 nu + 2665120500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 31025000 beta4 nu + 2665120500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 5329365000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1131500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1131500 beta4 - 182550 nu - 3651 = 0 ] /\ [532900000000 beta4^2 - 333153750000 beta4 nu - 6663075000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ 912500 beta4 - 182550 nu - 3651 = 0 ]] /\ [333062500000000 beta4^2 nu^2 + 72954010000000000 beta4^2 nu + 1458946975000000 beta4^2 - 333153750000000 beta4 nu^3 - 36500324850000000 beta4 nu^2 - 1459613209500000 beta4 nu - 14594799480000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 99955250000 beta4^2 nu + 1998740000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1998740000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 - 133188500000 beta4^2 nu - 38904364135000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 14599 = 0 ]]] /\ [1551250000 beta4^2 nu^2 + 319802050000 beta4^2 nu + 13621990420500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 31025000 beta4 nu + 1865770500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 /\ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 2737500000 beta4^2 nu^2 - 972542445250000 beta4^2 nu - 19450849635000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 486404420235000 beta4 nu^2 + 19456178269800 beta4 nu + 194561786349 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 19450849635000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [68437500000 beta4^2 nu^3 + 13326606250000 beta4^2 nu^2 + 486804232125000 beta4^2 nu + 9730754547500 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 2665230050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4 - 182550 nu - 3651 = 0 ]] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [182500 beta4 - 60850 nu - 1217 = 0 /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 365050 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [2500 beta4 nu + 365050 beta4 - 182550 nu - 3651 = 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 beta4 nu + beta4 > 0 /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 >= 0 /\ 250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [5000 beta4^2 nu + 912600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 2190200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 2190200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 1460200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [20000 beta4^2 nu + 912900 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 2553 <= 0 /\ [1500000 beta4^2 nu^2 + 36560000 beta4^2 nu + 730600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [30000 beta4 nu + 730600 beta4 - 182550 nu - 3651 = 0 /\ [3000000 beta4^2 nu^2 + 73120000 beta4^2 nu + 1461200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [60000 beta4 nu + 1461200 beta4 - 182550 nu - 3651 = 0 /\ 7500 nu^2 + 182800 nu + 3653 > 0 ]]]] /\ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ [40000 beta4^2 nu + 2920800 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 40000 beta4 nu + 2920800 beta4 - 182550 nu - 3651 = 0 ]]] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [20000 beta4^2 nu + 730400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4^2 nu + 1460800 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 < 0 ]]]]] \/ [1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 1332980100 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 6811528311000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1000000 beta4^2 nu^2 + 146040000 beta4^2 nu + 5331920400 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 ]] \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 >= 0 /\ 250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 >= 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 30640684455500 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 109510000 beta4^2 nu + 11992440100 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 >= 0 /\ 500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3407096770500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 5000 beta4^2 nu + 912600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 <= 0 /\ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ]] \/ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 /\ 1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3407096770500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2007500000 beta4^2 nu^2 + 193256550000 beta4^2 nu + 3407763078000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 100395000 beta4^2 nu + 4664882700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [333062500000000 beta4^2 nu^2 + 6091713125000000 beta4^2 nu + 121701037500000 beta4^2 - 194339687500000 beta4 nu^3 - 2038345693750000 beta4 nu^2 - 81300620125000 beta4 nu - 812228842500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [228125000000 beta4^2 nu^3 + 23328062500000 beta4^2 nu^2 + 487204098750000 beta4^2 nu + 9734752575000 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 \/ [91250000 beta4 nu + 2666325000 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [456250000 beta4^2 nu + 133234125000 beta4^2 - 152125000 beta4 nu^2 - 77741960000 beta4 nu - 1554778350 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [1825000000 beta4^2 nu^2 + 466360500000 beta4^2 nu + 24322888980000 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 36500000 beta4 nu + 6661980000 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [416328125000000 beta4^2 nu^2 + 12173434375000000 beta4^2 nu + 243302156250000 beta4^2 - 222102500000000 beta4 nu^3 - 4066696775000000 beta4 nu^2 - 162401348000000 beta4 nu - 1623125070000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[45625000 beta4 nu + 1333162500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [91250000000 beta4^2 nu^3 + 8332037500000 beta4^2 nu^2 + 121900984500000 beta4^2 nu + 2434687605000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [9125000 beta4^2 nu + 666307500 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [456250000 beta4^2 nu^2 + 33324500000 beta4^2 nu + 666307500 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [182500 beta4 - 60850 nu - 1217 = 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [730000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [912500000 beta4^2 nu + 166549500000 beta4^2 - 304250000 beta4 nu^2 - 88853170000 beta4 nu - 1776941700 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [125000 beta4^2 nu^2 + 45630000 beta4^2 nu + 2665412550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [5000 beta4^2 nu + 730100 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 1277 < 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 54790000 beta4^2 nu + 1095400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1095400 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [5000 beta4^2 nu + 1095100 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 /\ [10000 beta4^2 nu + 1825200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 10000 beta4 nu + 1825200 beta4 - 182550 nu - 3651 = 0 ]]] /\ [5000 beta4^2 nu + 912600 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 5000 beta4 nu + 912600 beta4 - 182550 nu - 3651 = 0 ] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 54770000 beta4^2 nu + 1095200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]]] \/ [1551250000 beta4^2 nu^2 + 319802050000 beta4^2 nu + 13621990420500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 164270000 beta4^2 nu + 13325785200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [365000 beta4 - 182550 nu - 3651 = 0 \/ 2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [68437500000 beta4^2 nu^3 + 13326606250000 beta4^2 nu^2 + 486804232125000 beta4^2 nu + 9730754547500 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1095000000 beta4^2 nu^2 + 63325675000 beta4^2 nu + 852240763000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 45645000 beta4^2 nu + 1000100200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 49995875000 beta4^2 nu + 608838615000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [999187500000000 beta4^2 nu^2 + 24353530000000000 beta4^2 nu + 486670925000000 beta4^2 - 666307500000000 beta4 nu^3 - 12200090325000000 beta4 nu^2 - 487204044000000 beta4 nu - 4869375210000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[54750000 beta4 nu + 1333345000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 2500706250000 beta4^2 nu^2 + 30491926625000 beta4^2 nu + 608838615000 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 \/ 36500000 beta4 nu + 666855000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [9125000 beta4^2 nu + 333245000 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [365000 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [3650000000 beta4^2 nu + 266523000000 beta4^2 - 1825500000 beta4 nu^2 - 199965270000 beta4 nu - 3998575200 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 18255000 beta4^2 nu + 499958800 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 5000 beta4 nu + 547600 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2665047500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ 50 nu - 3649 <= 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 5330460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4 nu + 5330460000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 399748000000 beta4^2 nu + 7994230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 7994230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 5329730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 >= 0 /\ 175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 >= 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2665047500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 1824300 nu - 36493 >= 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5996220050 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 /\ 2500 beta4 nu^2 + 547600 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + 10951 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [7500 beta4 nu^2 + 1825300 beta4 nu + 40004003 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 43772406365000 beta4^2 - 456375000 beta4 nu^3 - 99973507500 beta4 nu^2 - 3998392650 beta4 nu - 39982101 beta4 > 0 \/ 18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 76657000 beta4^2 nu + 8394708070 beta4^2 - 9127500 beta4 nu^2 - 1999287600 beta4 nu - 39982101 beta4 > 0 \/ 3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 beta4 nu + beta4 > 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 >= 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 50 beta4 nu + beta4 > 0 /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 365000 beta4 - 60850 nu - 1217 = 0 ] /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4^2 nu + 1022000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 511000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 51114000 beta4^2 nu + 1022140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 1022140 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2665047500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 17500 nu^2 - 1824300 nu - 36493 >= 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 < 0 /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1058500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [249796875000000 beta4^2 nu^2 + 12166773125000000 beta4^2 nu + 243235543750000 beta4^2 - 166576875000000 beta4 nu^3 - 4063365237500000 beta4 nu^2 - 162334717250000 beta4 nu - 1622680865000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2665047500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [27375000 beta4 nu + 2665047500 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [166531250000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[912500 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [638750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]]] /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [233143750000 beta4^2 - 111051250000 beta4 nu - 2221025000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[1277500 beta4 - 182550 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [182500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [9125000 beta4^2 nu + 182500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 182500 beta4 - 60850 nu - 1217 = 0 ]] /\ [249796875000000 beta4^2 nu^2 + 24323554375000000 beta4^2 nu + 486371168750000 beta4^2 - 166576875000000 beta4 nu^3 - 8116735862500000 beta4 nu^2 - 324469542250000 beta4 nu - 3244029115000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[27375000 beta4 nu + 2665047500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 182500 beta4 - 60850 nu - 1217 = 0 ] /\ [1368750000 beta4^2 nu^2 + 66667250000 beta4^2 nu + 1332797500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 17500 nu^2 - 1824300 nu - 36493 > 0 /\ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 5330095000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 5330095000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [18250000 beta4^2 nu + 3997115000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 399711500000 beta4^2 nu + 7993865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 7993865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 133279750000 beta4^2 nu + 2665047500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 27375000 beta4 nu + 2665047500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 5329365000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1131500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [456250000 beta4^2 nu^2 + 16671375000 beta4^2 nu + 333245000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ] /\ [532900000000 beta4^2 - 333153750000 beta4 nu - 6663075000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ [912500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 912500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [333062500000000 beta4^2 nu^2 + 72954010000000000 beta4^2 nu + 1458946975000000 beta4^2 - 333153750000000 beta4 nu^3 - 36500324850000000 beta4 nu^2 - 1459613209500000 beta4 nu - 14594799480000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [18250000 beta4 nu + 3997115000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 99955250000 beta4^2 nu + 1998740000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1998740000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 175000 beta4^2 nu^2 + 69357000 beta4^2 nu + 6396187070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 - 133188500000 beta4^2 nu - 38904364135000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 14599 = 0 ]]] /\ [1368750000 beta4^2 nu^2 + 266504750000 beta4^2 nu + 9730754547500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1825000000 beta4^2 nu + 399711500000 beta4^2 - 912750000 beta4 nu^2 - 266559510000 beta4 nu - 5330825100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 1095100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 54755000 beta4^2 nu + 5330095050 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 2500 beta4 nu + 730050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 19450849635000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [45625000000 beta4^2 nu^3 + 2737500000 beta4^2 nu^2 - 972542445250000 beta4^2 nu - 19450849635000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 486404420235000 beta4 nu^2 + 19456178269800 beta4 nu + 194561786349 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [666125000000000 beta4^2 nu^2 + 48653770000000000 beta4^2 nu + 972808950000000 beta4^2 - 499730625000000 beta4 nu^3 - 24350207587500000 beta4 nu^2 - 973408626750000 beta4 nu - 9732087345000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [68437500000 beta4^2 nu^3 + 13326606250000 beta4^2 nu^2 + 486804232125000 beta4^2 nu + 9730754547500 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 27375000 beta4 nu + 1332797500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1095000000 beta4^2 nu^2 + 93301300000 beta4^2 nu + 1865588000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 5000 nu^2 - 127550 nu - 2553 > 0 /\ 50 nu - 3649 <= 0 /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 3500 beta4^2 nu + 693570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2007500000 beta4^2 nu^2 + 213240300000 beta4^2 nu + 4866976503000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 500000 beta4^2 nu^2 + 94920000 beta4^2 nu + 4265098200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [226482500000000 beta4^2 nu^2 + 4871771800000000 beta4^2 nu + 97344843000000 beta4^2 - 161024312500000 beta4 nu^3 - 2036346771250000 beta4 nu^2 - 81260641675000 beta4 nu - 811962319500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [187062500000 beta4^2 nu^3 + 19328848750000 beta4^2 nu^2 + 414103491975000 beta4^2 nu + 8274339796500 beta4^2 - 68456250000 beta4 nu^4 - 6668551500000 beta4 nu^3 - 122001067545000 beta4 nu^2 - 4872042630600 beta4 nu - 48693763053 beta4 < 0 \/ [74825000 beta4 nu + 2266321500 beta4 - 27382500 nu^2 - 667402800 nu - 13337103 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [365000000 beta4^2 nu + 90600300000 beta4^2 - 152125000 beta4 nu^2 - 64415810000 beta4 nu - 1288255350 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [1551250000 beta4^2 nu^2 + 386414550000 beta4^2 nu + 19944848920500 beta4^2 - 456375000 beta4 nu^3 - 133288882500 beta4 nu^2 - 7301398132650 beta4 nu - 145974650751 beta4 < 0 \/ 31025000 beta4 nu + 5462845500 beta4 - 9127500 nu^2 - 1999287600 nu - 39982101 = 0 ]]] /\ [365000000 beta4^2 nu^2 + 26659600000 beta4^2 nu + 533046000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [7300000 beta4^2 nu + 533046000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [7300000 beta4^2 nu + 533046000 beta4^2 - 3042500 beta4 nu^2 - 222224200 beta4 nu - 4443267 beta4 < 0 \/ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 146000 beta4 - 60850 nu - 1217 = 0 ]] /\ [365000000 beta4^2 nu^2 + 26659600000 beta4^2 nu + 533046000 beta4^2 - 152125000 beta4 nu^3 - 11114252500 beta4 nu^2 - 444387550 beta4 nu - 4443267 beta4 < 0 \/ [146000 beta4 - 60850 nu - 1217 = 0 /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [620500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [511000000 beta4^2 nu + 101261220000 beta4^2 - 212975000 beta4 nu^2 - 68860294000 beta4 nu - 1377120690 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [87500 beta4^2 nu^2 + 34678500 beta4^2 nu + 2065681035 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 565785 beta4 - 182550 nu - 3651 = 0 ]]] /\ [253127500000000 beta4^2 nu^2 + 6817922600000000 beta4^2 nu + 136257201000000 beta4^2 - 172129437500000 beta4 nu^3 - 2847687203750000 beta4 nu^2 - 113700932825000 beta4 nu - 1136320810500 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [70718750000 beta4^2 nu^3 + 6332430625000 beta4^2 nu^2 + 85350681112500 beta4^2 nu + 1704481215750 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 28287500 beta4 nu + 466853250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 5000 nu^2 - 127550 nu - 2553 > 0 /\ 50 nu - 3649 <= 0 /\ [1916250000 beta4^2 nu^2 + 46705400000 beta4^2 nu + 933341500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [63875000 beta4^2 nu + 1866427500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [63875000 beta4 nu + 1866427500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1916250000 beta4^2 nu^2 + 186591650000 beta4^2 nu + 3731066500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 38325000 beta4 nu + 3731066500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1733750000 beta4^2 nu^2 + 46698100000 beta4^2 nu + 933268500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 34675000 beta4 nu + 933268500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [25550000 beta4^2 nu + 933086000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1916250000 beta4^2 nu^2 + 93334150000 beta4^2 nu + 1865916500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [2500 nu^2 - 364900 nu - 7299 < 0 \/ 50 nu - 3649 /= 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [3500 beta4^2 nu + 511070 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [350000 beta4^2 nu^2 + 25564000 beta4^2 nu + 511140 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 /\ [700000 beta4^2 nu^2 + 38353000 beta4^2 nu + 766780 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [14000 beta4 nu + 766780 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [3500 beta4^2 nu + 766570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [7000 beta4^2 nu + 1277640 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 7000 beta4 nu + 1277640 beta4 - 182550 nu - 3651 = 0 ]]] /\ [3500 beta4^2 nu + 693570 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 693570 beta4 - 182550 nu - 3651 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 359769550000 beta4^2 nu + 19458044770500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 158795000 beta4^2 nu + 12526325700 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [255500 beta4 - 182550 nu - 3651 = 0 \/ 2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ] /\ [255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 4530635550 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 2500 beta4 nu + 620550 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 38328500 beta4^2 nu + 3731066535 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 9328624375000 beta4^2 nu^2 + 340762962487500 beta4^2 nu + 6811528183250 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1231875000 beta4^2 nu^2 + 78318962500 beta4^2 nu + 1217244011500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 500000 beta4^2 nu^2 + 42907500 beta4^2 nu + 900126700 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 /= 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 608738641500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [6387500 beta4^2 nu + 233271500 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [255500 beta4 - 182550 nu - 3651 /= 0 \/ 2500 nu^2 + 182600 nu + 3651 < 0 ] /\ [1788500000 beta4^2 nu + 130596270000 beta4^2 - 1277850000 beta4 nu^2 - 139975689000 beta4 nu - 2799002640 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[7000 beta4 nu + 511140 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 12778500 beta4^2 nu + 349971160 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 < 0 \/ 3500 beta4 nu + 383320 beta4 - 182550 nu - 3651 = 0 ]]] /\ [489601875000000 beta4^2 nu^2 + 11933229700000000 beta4^2 nu + 238468753250000 beta4^2 - 466415250000000 beta4 nu^3 - 8540063227500000 beta4 nu^2 - 341042830800000 beta4 nu - 3408562647000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[38325000 beta4 nu + 933341500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [31937500000 beta4^2 nu^3 + 1750494375000 beta4^2 nu^2 + 21344348637500 beta4^2 nu + 426187030500 beta4^2 - 11409375000 beta4 nu^4 - 417354937500 beta4 nu^3 - 25013913750 beta4 nu^2 - 500095725 beta4 nu - 3333363 beta4 < 0 \/ 25550000 beta4 nu + 466798500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1095000000 beta4^2 nu^2 + 93301300000 beta4^2 nu + 1865588000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1250 nu^2 - 63825 nu - 1277 >= 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 38332000 beta4^2 nu + 766570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 949000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [159870000000000 beta4^2 nu^2 + 9731819800000000 beta4^2 nu + 194572448000000 beta4^2 - 133261500000000 beta4 nu^3 - 4061366315000000 beta4 nu^2 - 162294738800000 beta4 nu - 1622414342000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[21900000 beta4 nu + 1332688000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [1095000000 beta4^2 nu^2 + 113285050000 beta4^2 nu + 2265263000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 \/ [21900000 beta4 nu + 2265263000 beta4 - 9127500 nu^2 - 666672600 nu - 13329801 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [117238000000 beta4^2 - 75514850000 beta4 nu - 1510297000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[803000 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [529250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 529250 beta4 - 182550 nu - 3651 = 0 ]]] /\ [7300000 beta4^2 nu + 146000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [146000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [146000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 146000 beta4 - 60850 nu - 1217 = 0 ]] /\ [7300000 beta4^2 nu + 146000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 146000 beta4 - 60850 nu - 1217 = 0 ]] /\ [138554000000 beta4^2 - 84398950000 beta4 nu - 1687979000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[949000 beta4 - 182550 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [693500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 693500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [159870000000000 beta4^2 nu^2 + 13621989800000000 beta4^2 nu + 272375848000000 beta4^2 - 133261500000000 beta4 nu^3 - 5682714565000000 beta4 nu^2 - 227148668800000 beta4 nu - 2270953642000 beta4 + 27770418750000 nu^4 + 2221633500000 nu^3 + 66649005000 nu^2 + 888653400 nu + 4443267 > 0 \/ [[21900000 beta4 nu + 1865588000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 146000 beta4 - 60850 nu - 1217 = 0 ] /\ [1095000000 beta4^2 nu^2 + 46672550000 beta4^2 nu + 933013000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 21900000 beta4 nu + 933013000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 1250 nu^2 - 63825 nu - 1277 > 0 /\ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 3731066500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 3731066500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [12775000 beta4^2 nu + 2797980500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 279798050000 beta4^2 nu + 5595705500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 5595705500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1095000000 beta4^2 nu^2 + 93301300000 beta4^2 nu + 1865588000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 21900000 beta4 nu + 1865588000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ [175000 beta4^2 nu^2 + 38332000 beta4^2 nu + 766570 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 63889000 beta4^2 nu + 1277640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 1277640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [1022000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [1788500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1788500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [949000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 949000 beta4 - 182550 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [63875000 beta4^2 nu + 1277500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 60850 nu - 1217 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [319375000 beta4^2 nu^2 + 11669962500 beta4^2 nu + 233271500 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 /\ 50 nu - 3649 = 0 ]] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [261121000000 beta4^2 - 233207625000 beta4 nu - 4664152500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1022000 beta4 - 182550 nu - 3651 = 0 /\ [638750 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 638750 beta4 - 182550 nu - 3651 = 0 ]]] /\ [163200625000000 beta4^2 nu^2 + 35747464900000000 beta4^2 nu + 714884017750000 beta4^2 - 233207625000000 beta4 nu^3 - 25550227395000000 beta4 nu^2 - 1021729246650000 beta4 nu - 10216359636000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [12775000 beta4 nu + 2797980500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 69968675000 beta4^2 nu + 1399118000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 1399118000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 < 0 /\ 250000 beta4^2 nu^2 + 85785000 beta4^2 nu + 7195865600 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 - 93231950000 beta4^2 nu - 27233054894500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 19458843682350 beta4 nu + 389150228649 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 14599 = 0 ]]] /\ [1095000000 beta4^2 nu^2 + 226526300000 beta4^2 nu + 9729955088000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 21900000 beta4 nu + 1332688000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 13615594744500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 9728088952350 beta4 nu + 194561786349 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 680779711675000 beta4^2 nu - 13615594744500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 486404420235000 beta4 nu^2 + 19456178269800 beta4 nu + 194561786349 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [894250000 beta4^2 nu + 195858635000 beta4^2 - 638925000 beta4 nu^2 - 186591657000 beta4 nu - 3731577570 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 766570 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 38328500 beta4^2 nu + 3731066535 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 < 0 \/ 1750 beta4 nu + 511035 beta4 - 182550 nu - 3651 = 0 ]]] /\ [326401250000000 beta4^2 nu^2 + 23840347300000000 beta4^2 nu + 476676385500000 beta4^2 - 349811437500000 beta4 nu^3 - 17045145311250000 beta4 nu^2 - 681386038725000 beta4 nu - 6812461141500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 9328624375000 beta4^2 nu^2 + 340762962487500 beta4^2 nu + 6811528183250 beta4^2 - 22818750000 beta4 nu^4 - 3333363000000 beta4 nu^3 - 199947015000 beta4 nu^2 - 3998575200 beta4 nu - 26655951 beta4 < 0 \/ 19162500 beta4 nu + 932958250 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 nu^2 - 127550 nu - 2553 > 0 /\ 50 nu - 3649 <= 0 /\ [1551250000 beta4^2 nu^2 + 46690800000 beta4^2 nu + 933195500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 170194899175000 beta4^2 nu - 3403898494500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 3403898494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 - 93231950000 beta4^2 nu - 10213561144500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 7298731807350 beta4 nu + 145947991149 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 10949 = 0 ]]] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 25553500 beta4^2 nu + 1399373535 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 4665749375000 beta4^2 nu^2 + 85284041237500 beta4^2 nu + 1703814908250 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [2463750000 beta4^2 nu^2 + 66711050000 beta4^2 nu + 1333235500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 2007500000 beta4^2 nu^2 + 66692800000 beta4^2 nu + 1333053000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 31025000 beta4^2 nu + 2665120500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 <= 0 /\ [31025000 beta4^2 nu + 1332870500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 985600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ 25 nu - 1277 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 620500 beta4 - 182550 nu - 3651 /= 0 /\ [203834250000 beta4^2 - 97725100000 beta4 nu - 1954502000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [181186000000 beta4^2 - 91062025000 beta4 nu - 1821240500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [962550625000000 beta4^2 nu^2 + 41371558275000000 beta4^2 nu + 827046145250000 beta4^2 - 566361375000000 beta4 nu^3 - 12194093557500000 beta4 nu^2 - 487084108650000 beta4 nu - 4868575641000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [962550625000000 beta4^2 nu^2 + 28971641400000000 beta4^2 nu + 579047807750000 beta4^2 - 566361375000000 beta4 nu^3 - 8546059995000000 beta4 nu^2 - 341162766150000 beta4 nu - 3409362216000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [511000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [1612022500000000 beta4^2 nu^2 + 26809399650000000 beta4^2 nu + 535543184000000 beta4^2 - 732938250000000 beta4 nu^3 - 6124032232500000 beta4 nu^2 - 244081763400000 beta4 nu - 2437885881000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[40150000 beta4 nu + 666928000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [1003750000 beta4^2 nu^2 + 45003587500 beta4^2 nu + 899670250 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [20075000 beta4 nu + 899670250 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [263785500000 beta4^2 - 108830225000 beta4 nu - 2176604500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[803000 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2591500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 2591500 beta4 - 547650 nu - 10953 = 0 ]]] /\ [40150000 beta4^2 nu + 803000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 803000 beta4 - 182550 nu - 3651 = 0 ]] /\ [40150000 beta4^2 nu + 803000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 803000 beta4 - 182550 nu - 3651 = 0 ]] /\ [937904000000 beta4^2 - 359806050000 beta4 nu - 7196121000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1168000 beta4 - 182550 nu - 3651 = 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [849975500000 beta4^2 - 339816825000 beta4 nu - 6796336500 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[1058500 beta4 - 182550 nu - 3651 = 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [310250 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 310250 beta4 - 60850 nu - 1217 = 0 ]]] /\ [1612022500000000 beta4^2 nu^2 + 53554318400000000 beta4^2 nu + 1070441559000000 beta4^2 - 732938250000000 beta4 nu^3 - 12204088170000000 beta4 nu^2 - 487284000900000 beta4 nu - 4869908256000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[40150000 beta4 nu + 1333053000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [2007500000 beta4^2 nu^2 + 33386550000 beta4^2 nu + 666928000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 40150000 beta4 nu + 666928000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1612022500000000 beta4^2 nu^2 + 37507367150000000 beta4^2 nu + 749502534000000 beta4^2 - 732938250000000 beta4 nu^3 - 8556054607500000 beta4 nu^2 - 341362658400000 beta4 nu - 3410694831000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[40150000 beta4 nu + 933378000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ] /\ [2007500000 beta4^2 nu^2 + 23394675000 beta4^2 nu + 467090500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 40150000 beta4 nu + 467090500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ [2463750000 beta4^2 nu^2 + 66711050000 beta4^2 nu + 1333235500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [67525000 beta4^2 nu + 2665850500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [67525000 beta4 nu + 2665850500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [31025000 beta4^2 nu + 2665120500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [31025000 beta4 nu + 2665120500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1551250000 beta4^2 nu^2 + 266512050000 beta4^2 nu + 5329620500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 31025000 beta4 nu + 5329620500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2007500000 beta4^2 nu^2 + 66692800000 beta4^2 nu + 1333053000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 40150000 beta4 nu + 1333053000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [31025000 beta4^2 nu + 1332870500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1551250000 beta4^2 nu^2 + 133287050000 beta4^2 nu + 2665120500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [350 nu - 36493 < 0 \/ [17500 nu^2 - 3649300 nu - 72993 < 0 /\ 350 nu - 36493 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 /\ [250000 beta4^2 nu^2 + 49285000 beta4^2 nu + 985600 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 67545000 beta4^2 nu + 1350700 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1350700 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [1350500 beta4 - 182550 nu - 3651 = 0 /\ [693500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 693500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [1168000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1168000 beta4 - 182550 nu - 3651 = 0 ] /\ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 \/ [67525000 beta4^2 nu + 1350500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4 - 60850 nu - 1217 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [1250 nu^2 - 63825 nu - 1277 > 0 \/ [5000 nu^2 - 127550 nu - 2553 > 0 /\ 25 nu - 1277 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 693500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 620500 beta4 - 182550 nu - 3651 /= 0 /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [837985250000 beta4^2 - 359806050000 beta4 nu - 7196121000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1350500 beta4 - 182550 nu - 3651 = 0 /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ]]] /\ [702095750000 beta4^2 - 319827600000 beta4 nu - 6396552000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [1131500 beta4 - 182550 nu - 3651 = 0 /\ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [962550625000000 beta4^2 nu^2 + 82704614525000000 beta4^2 nu + 1653707270250000 beta4^2 - 566361375000000 beta4 nu^3 - 24354205432500000 beta4 nu^2 - 973488583650000 beta4 nu - 9732620391000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [31025000 beta4 nu + 2665120500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [962550625000000 beta4^2 nu^2 + 57904780775000000 beta4^2 nu + 1157710595250000 beta4^2 - 566361375000000 beta4 nu^3 - 17058138307500000 beta4 nu^2 - 681645898650000 beta4 nu - 6814193541000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [31025000 beta4 nu + 1865770500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1551250000 beta4^2 nu^2 + 46690800000 beta4^2 nu + 933195500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 113303300000 beta4^2 nu + 2265445500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 104045000 beta4^2 nu + 4931405700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [620500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[620500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [1551250000 beta4^2 nu^2 - 226420450000 beta4^2 nu - 24804362779500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 7298731807350 beta4 nu + 145947991149 beta4 > 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 10949 = 0 ]]] /\ [2007500000 beta4^2 nu^2 + 179934050000 beta4^2 nu + 2434954128000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 40150000 beta4 nu + 666928000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [31025000 beta4^2 nu + 2265445500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 62050000 beta4^2 nu - 8266610629500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 /= 0 ] /\ [77562500000 beta4^2 nu^3 + 4653750000 beta4^2 nu^2 - 413330469425000 beta4^2 nu - 8266610629500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 /= 0 ] /\ [3102500000 beta4^2 nu + 611564800000 beta4^2 - 912750000 beta4 nu^2 - 293211810000 beta4 nu - 5863871100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 985600 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 49280000 beta4^2 nu + 2931935550 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 803050 beta4 - 182550 nu - 3651 = 0 ]]] /\ [2171750000 beta4^2 nu + 543601435000 beta4^2 - 638925000 beta4 nu^2 - 273211632000 beta4 nu - 5463977070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 876070 beta4 - 182550 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 43803500 beta4^2 nu + 2731988535 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 748285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1528756875000000 beta4^2 nu^2 + 41394206525000000 beta4^2 nu + 827272627750000 beta4^2 - 732938250000000 beta4 nu^3 - 12204088170000000 beta4 nu^2 - 487284000900000 beta4 nu - 4869908256000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[49275000 beta4 nu + 1333235500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [100375000000 beta4^2 nu^3 + 8998710000000 beta4^2 nu^2 + 121927640450000 beta4^2 nu + 2434954128000 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 40150000 beta4 nu + 666928000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1358895000000000 beta4^2 nu^2 + 28987495175000000 beta4^2 nu + 579206345500000 beta4^2 - 682965187500000 beta4 nu^3 - 8553056223750000 beta4 nu^2 - 341302690725000 beta4 nu - 3410295046500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[43800000 beta4 nu + 933451000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [93531250000 beta4^2 nu^3 + 7999111875000 beta4^2 nu^2 + 85417320987500 beta4^2 nu + 1705147523250 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 37412500 beta4 nu + 467035750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 >= 0 /\ 500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 >= 0 /\ 500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [10000 beta4^2 nu + 1095200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 100 nu - 2553 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 2920400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 2920400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 3405764155500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 46690800000 beta4^2 nu + 933195500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [25550000 beta4^2 nu + 1865661000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 1865661000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1277500000 beta4^2 nu^2 + 93308600000 beta4^2 nu + 1865661000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [5000 nu^2 - 127550 nu - 2553 > 0 \/ 100 nu - 2553 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1277500000 beta4^2 nu^2 + 186566100000 beta4^2 nu + 3730811000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 25550000 beta4 nu + 3730811000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [51100000 beta4^2 nu + 1866172000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [51100000 beta4 nu + 1866172000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1217010740000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 /\ 500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 666855200 beta4^2 - 4563750 beta4 nu^2 - 166759425 beta4 nu - 3333363 beta4 > 0 /\ 1250 beta4 nu^2 + 45675 beta4 nu + 913 beta4 > 0 /\ 25 beta4 nu + 913 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 851907518000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [10000 beta4^2 nu + 985700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 2920400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 2920400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]]] \/ [1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [36500000 beta4^2 nu + 2665230000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 2665230000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [1825000000 beta4^2 nu^2 + 133298000000 beta4^2 nu + 2665230000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1250 nu^2 - 45575 nu - 912 > 0 \/ 25 nu - 912 = 0 ] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [1825000000 beta4^2 nu^2 + 266523000000 beta4^2 nu + 5329730000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 36500000 beta4 nu + 5329730000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [73000000 beta4^2 nu + 2665960000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4 nu + 2665960000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 /\ 175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 >= 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 60850 beta4 nu - 1217 beta4 >= 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [50 beta4 nu + beta4 > 0 /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 73010000 beta4^2 nu + 5330460100 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 13619325555500 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4^2 - 60850 beta4 nu - 1217 beta4 < 0 \/ 730000 beta4 - 60850 nu - 1217 = 0 ]]] /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 1460200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 365100 nu + 7301 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 46690800000 beta4^2 nu + 933195500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 5000 nu^2 - 127550 nu - 2553 > 0 /\ 50 nu - 3649 <= 0 /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 /\ 638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 <= 0 /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ 3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ 255500 beta4 - 60850 nu - 1217 = 0 ] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [16425000 beta4^2 nu + 328500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [203834250000 beta4^2 - 97725100000 beta4 nu - 1954502000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [2226500 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 2226500 beta4 - 547650 nu - 10953 = 0 ]]] /\ [181186000000 beta4^2 - 91062025000 beta4 nu - 1821240500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [748250 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 748250 beta4 - 182550 nu - 3651 = 0 ]]] /\ [962550625000000 beta4^2 nu^2 + 41371558275000000 beta4^2 nu + 827046145250000 beta4^2 - 566361375000000 beta4 nu^3 - 12194093557500000 beta4 nu^2 - 487084108650000 beta4 nu - 4868575641000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [775625000 beta4^2 nu^2 + 44994462500 beta4^2 nu + 899579000 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [15512500 beta4 nu + 899579000 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [962550625000000 beta4^2 nu^2 + 28971641400000000 beta4^2 nu + 579047807750000 beta4^2 - 566361375000000 beta4 nu^3 - 8546059995000000 beta4 nu^2 - 341162766150000 beta4 nu - 3409362216000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 23376425000 beta4^2 nu + 466908000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 31025000 beta4 nu + 466908000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 5000 nu^2 - 127550 nu - 2553 > 0 /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [638750000 beta4^2 nu^2 + 93283050000 beta4^2 nu + 1865405500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [1551250000 beta4^2 nu^2 + 46690800000 beta4^2 nu + 933195500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 1865405500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 186540550000 beta4^2 nu + 3730555500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 12775000 beta4 nu + 3730555500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [1277500000 beta4^2 nu^2 + 46679850000 beta4^2 nu + 933086000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [38325000 beta4^2 nu + 1865916500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [38325000 beta4 nu + 1865916500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 85795000 beta4^2 nu + 3598790700 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [31937500000 beta4^2 nu^3 + 1916250000 beta4^2 nu^2 - 170194899175000 beta4^2 nu - 3403898494500 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [638750000 beta4^2 nu^2 + 25550000 beta4^2 nu - 3403898494500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 /= 0 ] /\ [1551250000 beta4^2 nu^2 + 179915800000 beta4^2 nu + 4866310195500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [12775000 beta4^2 nu + 932830500 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [[255500 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [638750000 beta4^2 nu^2 - 93231950000 beta4^2 nu - 10213561144500 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 7298731807350 beta4 nu + 145947991149 beta4 > 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 10949 = 0 ]]] /\ [894250000 beta4^2 nu + 130578385000 beta4^2 - 638925000 beta4 nu^2 - 139950132000 beta4 nu - 2798747070 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [87500 beta4^2 nu^2 + 25553500 beta4^2 nu + 1399373535 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 1750 beta4 nu + 383285 beta4 - 182550 nu - 3651 = 0 ]]] /\ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [255500 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [326401250000000 beta4^2 nu^2 + 11926701675000000 beta4^2 nu + 238403473000000 beta4^2 - 349811437500000 beta4 nu^3 - 8533066998750000 beta4 nu^2 - 340902906225000 beta4 nu - 3407629816500 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[25550000 beta4 nu + 933086000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 255500 beta4 - 182550 nu - 3651 = 0 ] /\ [47906250000 beta4^2 nu^3 + 4665749375000 beta4^2 nu^2 + 85284041237500 beta4^2 nu + 1703814908250 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 19162500 beta4 nu + 466670750 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [25550000 beta4^2 nu + 511000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [12775000 beta4^2 nu + 255500 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 511000 beta4 - 182550 nu - 3651 = 0 ]] /\ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [255500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [1277500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1277500 beta4 - 182550 nu - 3651 = 0 ]]] /\ [175000 beta4^2 nu^2 + 25557000 beta4^2 nu + 511070 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [3500 beta4 nu + 511070 beta4 - 182550 nu - 3651 = 0 /\ [350000 beta4^2 nu^2 + 38339000 beta4^2 nu + 766640 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [7000 beta4 nu + 766640 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [12775000 beta4^2 nu + 255500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1715500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 255500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 255500 beta4 - 182550 nu - 3651 /= 0 /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [65280250000 beta4^2 - 62188700000 beta4 nu - 1243774000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [255500 beta4 - 60850 nu - 1217 = 0 /\ [511000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 511000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [163200625000000 beta4^2 nu^2 + 23833819275000000 beta4^2 nu + 476611105250000 beta4^2 - 233207625000000 beta4 nu^3 - 17038149082500000 beta4 nu^2 - 681246114150000 beta4 nu - 6811528311000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [12775000 beta4 nu + 1865405500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [638750000 beta4^2 nu^2 + 46654300000 beta4^2 nu + 932830500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 12775000 beta4 nu + 932830500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 >= 0 /\ 500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [10000 beta4^2 nu + 985700 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 25 nu - 912 <= 0 /\ [1000000 beta4^2 nu^2 + 36540000 beta4^2 nu + 730400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 730400 beta4 - 182550 nu - 3651 = 0 /\ [2000000 beta4^2 nu^2 + 73080000 beta4^2 nu + 1460800 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [40000 beta4 nu + 1460800 beta4 - 182550 nu - 3651 = 0 /\ 1250 nu^2 + 45675 nu + 913 > 0 ]]]] /\ [10000 beta4^2 nu + 1460200 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 /\ [20000 beta4^2 nu + 2920400 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 20000 beta4 nu + 2920400 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 < 0 ]]]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4^2 nu + 1460400 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] /\ [10000 beta4^2 nu + 730200 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ]] \/ [2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 \/ 10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [175000 beta4^2 nu^2 + 51107000 beta4^2 nu + 3731322070 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 /\ 2500 beta4 nu^2 + 365100 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + 7301 beta4 > 0 /\ 50 beta4 nu + beta4 < 0 /\ 2500 nu^2 - 182400 nu - 3649 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 19456179365000 beta4^2 - 456375000 beta4 nu^3 - 66658132500 beta4 nu^2 - 2665777650 beta4 nu - 26655951 beta4 > 0 \/ 18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [500000 beta4^2 nu^2 + 146020000 beta4^2 nu + 10660920200 beta4^2 - 9127500 beta4 nu^2 - 1332980100 beta4 nu - 26655951 beta4 > 0 \/ 10000 beta4 nu + 1460200 beta4 - 182550 nu - 3651 = 0 ]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 >= 0 /\ 50 beta4 nu + beta4 > 0 /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 /\ 18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 <= 0 /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1350500 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ [962550625000000 beta4^2 nu^2 + 28971641400000000 beta4^2 nu + 579047807750000 beta4^2 - 566361375000000 beta4 nu^3 - 8546059995000000 beta4 nu^2 - 341162766150000 beta4 nu - 3409362216000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [775625000 beta4^2 nu^2 + 39998525000 beta4^2 nu + 799660250 beta4^2 - 228187500 beta4 nu^3 - 8342535000 beta4 nu^2 - 333427575 beta4 nu - 3333363 beta4 < 0 \/ [15512500 beta4 nu + 799660250 beta4 - 4563750 nu^2 - 166759425 nu - 3333363 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [181186000000 beta4^2 - 91062025000 beta4 nu - 1821240500 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [2117000 beta4^2 - 547650 beta4 nu - 10953 beta4 < 0 \/ 2117000 beta4 - 547650 nu - 10953 = 0 ]]] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [31025000 beta4^2 nu + 620500 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [14600000 beta4^2 nu + 292000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [620500 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 620500 beta4 - 182550 nu - 3651 = 0 ]] /\ [203834250000 beta4^2 - 97725100000 beta4 nu - 1954502000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [[620500 beta4 - 182550 nu - 3651 = 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [803000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 803000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [962550625000000 beta4^2 nu^2 + 41371558275000000 beta4^2 nu + 827046145250000 beta4^2 - 566361375000000 beta4 nu^3 - 12194093557500000 beta4 nu^2 - 487084108650000 beta4 nu - 4868575641000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 620500 beta4 - 182550 nu - 3651 = 0 ] /\ [1551250000 beta4^2 nu^2 + 33368300000 beta4^2 nu + 666745500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 31025000 beta4 nu + 666745500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 1250 nu^2 - 45575 nu - 912 > 0 /\ [1825000000 beta4^2 nu^2 + 66685500000 beta4^2 nu + 1332980000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ [36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [54750000 beta4^2 nu + 2665595000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [54750000 beta4 nu + 2665595000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [18250000 beta4^2 nu + 2664865000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 266486500000 beta4^2 nu + 5329365000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 18250000 beta4 nu + 5329365000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [1551250000 beta4^2 nu^2 + 66674550000 beta4^2 nu + 1332870500 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 > 0 \/ 31025000 beta4 nu + 1332870500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 2664865000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 /\ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]] /\ [50 nu - 3649 < 0 \/ [2500 nu^2 - 364900 nu - 7299 < 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ [250000 beta4^2 nu^2 + 36510000 beta4^2 nu + 730100 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 /\ [500000 beta4^2 nu^2 + 54770000 beta4^2 nu + 1095200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 1095200 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]] /\ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 1825000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [328500 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 328500 beta4 - 60850 nu - 1217 = 0 ] /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [18250000 beta4^2 nu + 365000 beta4^2 - 3042500 beta4 nu^2 - 121700 beta4 nu - 1217 beta4 < 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ [1250 nu^2 - 45575 nu - 912 > 0 /\ 50 nu - 3649 = 0 ]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 1825000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [292000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 \/ 292000 beta4 - 60850 nu - 1217 = 0 ] /\ [133225000000 beta4^2 - 88841000000 beta4 nu - 1776820000 beta4 + 11108167500 nu^2 + 444326700 nu + 4443267 > 0 \/ [365000 beta4 - 60850 nu - 1217 = 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [333062500000000 beta4^2 nu^2 + 48640447500000000 beta4^2 nu + 972675725000000 beta4^2 - 333153750000000 beta4 nu^3 - 24340212975000000 beta4 nu^2 - 973208734500000 beta4 nu - 9730754730000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [18250000 beta4 nu + 2664865000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 /\ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 - 547650 beta4 nu - 3651 beta4 < 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [912500000 beta4^2 nu^2 + 66649000000 beta4^2 nu + 1332615000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 < 0 /\ 500000 beta4^2 nu^2 + 91270000 beta4^2 nu + 3998575200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [365000 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]] /\ [[365000 beta4 - 182550 nu - 3651 /= 0 /\ 50 nu - 3649 < 0 ] \/ [[365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 3649 = 0 ] /\ [912500000 beta4^2 nu^2 - 133188500000 beta4^2 nu - 14590801635000 beta4^2 - 456375000 beta4 nu^3 + 66603367500 beta4 nu^2 + 7298731807350 beta4 nu + 145947991149 beta4 > 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 \/ 50 nu - 10949 = 0 ]]] /\ [1551250000 beta4^2 nu^2 + 159932050000 beta4^2 nu + 3407096770500 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 31025000 beta4 nu + 933195500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [18250000 beta4^2 nu + 1332615000 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [45625000000 beta4^2 nu^3 + 2737500000 beta4^2 nu^2 - 243135570250000 beta4^2 nu - 4862712135000 beta4^2 - 22818750000 beta4 nu^4 - 1825500000 beta4 nu^3 + 121601063985000 beta4 nu^2 + 4864044019800 beta4 nu + 48640443849 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [912500000 beta4^2 nu^2 + 36500000 beta4^2 nu - 4862712135000 beta4^2 - 456375000 beta4 nu^3 - 27382500 beta4 nu^2 + 2432021827350 beta4 nu + 48640443849 beta4 < 0 \/ 365000 beta4 - 182550 nu - 3651 /= 0 ] /\ [1825000000 beta4^2 nu + 266486500000 beta4^2 - 912750000 beta4 nu^2 - 199928760000 beta4 nu - 3998210100 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ [[5000 beta4 nu + 730100 beta4 - 182550 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [125000 beta4^2 nu^2 + 36505000 beta4^2 nu + 1999105050 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 < 0 \/ 2500 beta4 nu + 547550 beta4 - 182550 nu - 3651 = 0 ]]] /\ [666125000000000 beta4^2 nu^2 + 24340207500000000 beta4^2 nu + 486537700000000 beta4^2 - 499730625000000 beta4 nu^3 - 12190095712500000 beta4 nu^2 - 487004151750000 beta4 nu - 4868042595000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ [[36500000 beta4 nu + 1332980000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 \/ 365000 beta4 - 182550 nu - 3651 = 0 ] /\ [68437500000 beta4^2 nu^3 + 6665356250000 beta4^2 nu^2 + 121834344625000 beta4^2 nu + 2434021297500 beta4^2 - 22818750000 beta4 nu^4 - 1667594250000 beta4 nu^3 - 100000890000 beta4 nu^2 - 1999652700 beta4 nu - 13329801 beta4 < 0 \/ 27375000 beta4 nu + 666672500 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ]]] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [500000 beta4^2 nu^2 + 73020000 beta4^2 nu + 2665960200 beta4^2 - 9127500 beta4 nu^2 - 666672600 beta4 nu - 13329801 beta4 > 0 /\ 2500 beta4 nu^2 + 182600 beta4 nu + 3651 beta4 > 0 /\ 50 beta4 nu + 3651 beta4 > 0 /\ 50 nu - 3649 <= 0 /\ [912500000 beta4^2 nu^2 + 133261500000 beta4^2 nu + 4865377365000 beta4^2 - 456375000 beta4 nu^3 - 33342757500 beta4 nu^2 - 1333162650 beta4 nu - 13329801 beta4 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 50 beta4 nu + beta4 > 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [18250000 beta4^2 nu + 365000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ 365000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 /\ 365000 beta4 - 182550 nu - 3651 /= 0 /\ [266450000000 beta4^2 - 199892250000 beta4 nu - 3997845000 beta4 + 33324502500 nu^2 + 1332980100 nu + 13329801 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [333062500000000 beta4^2 nu^2 + 24326885000000000 beta4^2 nu + 486404475000000 beta4^2 - 333153750000000 beta4 nu^3 - 12180101100000000 beta4 nu^2 - 486804259500000 beta4 nu - 4866709980000 beta4 + 83311256250000 nu^4 + 6664900500000 nu^3 + 199947015000 nu^2 + 2665960200 nu + 13329801 > 0 \/ 18250000 beta4 nu + 1332615000 beta4 - 9127500 nu^2 - 365100 nu - 3651 = 0 ] /\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]] \/ [365000 beta4^2 - 60850 beta4 nu - 1217 beta4 > 0 /\ [36500000 beta4^2 nu + 730000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [73000000 beta4^2 nu + 1460000 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 /\ 730000 beta4 - 182550 nu - 3651 = 0 ]] /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [1460000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ [1460000 beta4 - 182550 nu - 3651 = 0 /\ [2920000 beta4^2 - 182550 beta4 nu - 3651 beta4 < 0 \/ 2920000 beta4 - 182550 nu - 3651 = 0 ]]] /\ [500000 beta4^2 nu^2 + 36520000 beta4^2 nu + 730200 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 > 0 \/ [10000 beta4 nu + 730200 beta4 - 182550 nu - 3651 = 0 /\ [1000000 beta4^2 nu^2 + 73040000 beta4^2 nu + 1460400 beta4^2 - 9127500 beta4 nu^2 - 365100 beta4 nu - 3651 beta4 < 0 \/ [20000 beta4 nu + 1460400 beta4 - 182550 nu - 3651 = 0 /\ 2500 nu^2 + 182600 nu + 3651 > 0 ]]]]/\ [2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]]\/ [50 beta4 nu + beta4 > 0 /\ [730000 beta4^2 - 182550 beta4 nu - 3651 beta4 > 0 \/ 730000 beta4 - 182550 nu - 3651 = 0 ] /\ [ 2500 nu^2 - 182400 nu - 3649 > 0 \/ 50 nu - 3649 = 0 ]]] ]];