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hmf_forms • Show schema
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{'deg': 4, 'dimension': 6, 'disc': 9909, 'field_bad_primes': [3, 367], 'field_label': '4.4.9909.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.9909.1-13.1-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [13], 'level_ideal': '[13, 13, -w^3 + w^2 + 3*w - 1]', 'level_label': '13.1', 'level_norm': 13, 'parallel_weight': 2, 'short_label': '13.1-c', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[13, 13, -w^3 + w^2 + 3*w - 1]', 1]], 'hecke_eigenvalues': ['e', '-1/2*e^5 + 15/2*e^3 - 45/2*e - 10', '-1/2*e^5 + 15/2*e^3 - 45/2*e - 10', '-3/2*e^5 + e^4 + 45/2*e^3 - 10*e^2 - 133/2*e - 26', -1, '2*e^5 - e^4 - 29*e^3 + 11*e^2 + 80*e + 33', '-3/2*e^5 + e^4 + 43/2*e^3 - 12*e^2 - 113/2*e - 18', '-e^2 - 2*e + 8', '-1/2*e^5 + e^4 + 15/2*e^3 - 10*e^2 - 39/2*e - 4', '-3/2*e^5 + e^4 + 41/2*e^3 - 12*e^2 - 95/2*e - 14', '3/2*e^5 - e^4 - 41/2*e^3 + 12*e^2 + 95/2*e + 14', '1/2*e^5 - 15/2*e^3 + 49/2*e + 18', '1/2*e^5 - e^4 - 15/2*e^3 + 12*e^2 + 37/2*e - 6', '2*e^3 + 2*e^2 - 19*e - 12', '-e^3 + 7*e - 4', '-e^5 + 14*e^3 - 38*e - 22', 'e^5 - 15*e^3 + 45*e + 20', 'e^5 - 16*e^3 - 2*e^2 + 54*e + 32', '2*e^5 - e^4 - 28*e^3 + 12*e^2 + 70*e + 24', '-4*e^5 + 2*e^4 + 56*e^3 - 24*e^2 - 144*e - 50', '2*e^3 + 2*e^2 - 16*e - 14', '-5*e^5 + 2*e^4 + 72*e^3 - 24*e^2 - 196*e - 80', '-2*e - 8', '-e^5 + 15*e^3 - 47*e - 28', '-3/2*e^5 + e^4 + 45/2*e^3 - 12*e^2 - 127/2*e - 14', '2*e^5 - 2*e^4 - 30*e^3 + 20*e^2 + 84*e + 36', 'e^5 - 17*e^3 - 3*e^2 + 67*e + 40', '-9/2*e^5 + 3*e^4 + 131/2*e^3 - 32*e^2 - 361/2*e - 66', '-3*e^5 + 2*e^4 + 43*e^3 - 24*e^2 - 115*e - 44', 'e^5 - 13*e^3 + 25*e + 28', '7/2*e^5 - 3*e^4 - 105/2*e^3 + 32*e^2 + 307/2*e + 52', '11/2*e^5 - 3*e^4 - 165/2*e^3 + 32*e^2 + 487/2*e + 96', '2*e^5 - 30*e^3 + 94*e + 56', '-e^5 + 13*e^3 - 29*e - 20', '11/2*e^5 - 3*e^4 - 161/2*e^3 + 32*e^2 + 451/2*e + 86', '9/2*e^5 - 3*e^4 - 127/2*e^3 + 36*e^2 + 313/2*e + 44', '-1/2*e^5 + e^4 + 19/2*e^3 - 7*e^2 - 77/2*e - 26', '-e^5 + 13*e^3 - 4*e^2 - 25*e - 4', '3/2*e^5 - e^4 - 37/2*e^3 + 14*e^2 + 63/2*e', '-1/2*e^5 + e^4 + 11/2*e^3 - 12*e^2 - 1/2*e + 12', '-6*e^5 + 4*e^4 + 88*e^3 - 43*e^2 - 244*e - 96', '3*e^5 - 43*e^3 + 123*e + 60', '-9/2*e^5 + e^4 + 129/2*e^3 - 14*e^2 - 351/2*e - 66', '1/2*e^5 + e^4 - 19/2*e^3 - 14*e^2 + 81/2*e + 42', '-3/2*e^5 + e^4 + 45/2*e^3 - 8*e^2 - 127/2*e - 30', '2*e^3 + 4*e^2 - 20*e - 22', '4*e^5 - 2*e^4 - 58*e^3 + 22*e^2 + 154*e + 74', '6*e^5 - 5*e^4 - 88*e^3 + 56*e^2 + 240*e + 78', '3*e^5 - e^4 - 45*e^3 + 8*e^2 + 137*e + 68', '-9/2*e^5 + e^4 + 135/2*e^3 - 8*e^2 - 409/2*e - 98', '4*e^5 - 2*e^4 - 56*e^3 + 25*e^2 + 144*e + 48', '2*e^5 - 2*e^4 - 30*e^3 + 22*e^2 + 92*e + 16', '3/2*e^5 - e^4 - 45/2*e^3 + 12*e^2 + 141/2*e + 10', '-6*e^5 + 3*e^4 + 88*e^3 - 36*e^2 - 250*e - 88', '-2*e - 8', '-e^5 + 2*e^4 + 17*e^3 - 18*e^2 - 55*e - 28', '-9/2*e^5 + e^4 + 135/2*e^3 - 8*e^2 - 415/2*e - 98', '-1/2*e^5 + e^4 + 15/2*e^3 - 14*e^2 - 49/2*e + 14', '-7*e^5 + 4*e^4 + 105*e^3 - 39*e^2 - 313*e - 128', '-e^5 + 2*e^4 + 12*e^3 - 28*e^2 - 8*e + 28', '-3*e^5 + 45*e^3 + 2*e^2 - 131*e - 76', '-13/2*e^5 + 5*e^4 + 195/2*e^3 - 50*e^2 - 573/2*e - 116', '-9*e^5 + 4*e^4 + 132*e^3 - 44*e^2 - 380*e - 158', '-5/2*e^5 + 3*e^4 + 71/2*e^3 - 32*e^2 - 169/2*e - 20', '5*e^5 - 2*e^4 - 75*e^3 + 20*e^2 + 225*e + 100', '2*e^5 - 2*e^4 - 26*e^3 + 24*e^2 + 50*e + 8', '-4*e^5 + 2*e^4 + 56*e^3 - 23*e^2 - 140*e - 64', '4*e^5 - 2*e^4 - 62*e^3 + 18*e^2 + 192*e + 98', '-e^5 + 15*e^3 + e^2 - 49*e - 22', '-1/2*e^5 + e^4 + 15/2*e^3 - 14*e^2 - 35/2*e + 10', '-2*e^5 + 2*e^4 + 28*e^3 - 24*e^2 - 68*e - 16', '7*e^5 - 4*e^4 - 101*e^3 + 44*e^2 + 275*e + 116', '1/2*e^5 - e^4 - 15/2*e^3 + 12*e^2 + 47/2*e - 2', 'e^5 - 14*e^3 + 2*e^2 + 36*e + 8', '-2*e^2 + 4*e + 26', '-7*e^5 + 4*e^4 + 107*e^3 - 40*e^2 - 331*e - 130', '-6*e^5 + 4*e^4 + 88*e^3 - 44*e^2 - 242*e - 84', '3/2*e^5 - e^4 - 47/2*e^3 + 8*e^2 + 145/2*e + 46', 'e^5 - 17*e^3 - 4*e^2 + 67*e + 44', '2*e^5 - 2*e^4 - 28*e^3 + 22*e^2 + 72*e + 14', '11/2*e^5 - 3*e^4 - 165/2*e^3 + 30*e^2 + 507/2*e + 102', '6*e^5 - 2*e^4 - 88*e^3 + 24*e^2 + 250*e + 104', '2*e^5 - 32*e^3 - 3*e^2 + 116*e + 64', '-e^5 + 2*e^4 + 15*e^3 - 24*e^2 - 42*e + 24', '-5*e^3 - 6*e^2 + 47*e + 34', '-e^5 - e^4 + 13*e^3 + 10*e^2 - 35*e - 18', '2*e^5 - 30*e^3 - 6*e^2 + 90*e + 70', '11/2*e^5 - e^4 - 161/2*e^3 + 10*e^2 + 463/2*e + 110', '5/2*e^5 - e^4 - 75/2*e^3 + 11*e^2 + 217/2*e + 50', '-2*e^5 + 30*e^3 + 6*e^2 - 90*e - 72', '-e^5 + 13*e^3 + 2*e^2 - 25*e - 36', '-7*e^5 + 4*e^4 + 103*e^3 - 44*e^2 - 289*e - 100', '5*e^5 - 2*e^4 - 75*e^3 + 18*e^2 + 228*e + 112', '-19/2*e^5 + 5*e^4 + 277/2*e^3 - 52*e^2 - 779/2*e - 166', '3*e^5 - 2*e^4 - 47*e^3 + 20*e^2 + 146*e + 64', '-3*e^5 + 2*e^4 + 45*e^3 - 20*e^2 - 129*e - 36', '7*e^5 - 4*e^4 - 105*e^3 + 40*e^2 + 315*e + 140', '-3*e^5 + 45*e^3 + 2*e^2 - 142*e - 88', '5/2*e^5 + e^4 - 71/2*e^3 - 12*e^2 + 205/2*e + 74', 'e^5 - 9*e^3 + 6*e^2 - 9*e - 20', '2*e^5 - 2*e^4 - 30*e^3 + 23*e^2 + 82*e + 24', '5*e^5 - 3*e^4 - 75*e^3 + 32*e^2 + 219*e + 76', '-3/2*e^5 + e^4 + 45/2*e^3 - 10*e^2 - 123/2*e - 38', '6*e^5 - 2*e^4 - 90*e^3 + 22*e^2 + 274*e + 100', '4*e^5 - 4*e^4 - 60*e^3 + 44*e^2 + 178*e + 44', '6*e^5 - 4*e^4 - 90*e^3 + 42*e^2 + 261*e + 82', '2*e^5 - 30*e^3 + 90*e + 40', '-8*e^5 + 4*e^4 + 118*e^3 - 45*e^2 - 340*e - 128', '13/2*e^5 - 3*e^4 - 183/2*e^3 + 30*e^2 + 469/2*e + 122', '5*e^5 - 3*e^4 - 75*e^3 + 30*e^2 + 215*e + 92', '9*e^5 - 6*e^4 - 135*e^3 + 64*e^2 + 397*e + 152', '-3*e^5 + 45*e^3 - 135*e - 62', '-15/2*e^5 + 3*e^4 + 213/2*e^3 - 38*e^2 - 567/2*e - 94', '9*e^5 - 4*e^4 - 129*e^3 + 44*e^2 + 349*e + 148', '8*e^5 - 3*e^4 - 114*e^3 + 34*e^2 + 310*e + 120', '-3*e^5 + 2*e^4 + 43*e^3 - 22*e^2 - 117*e - 52', '15/2*e^5 - 3*e^4 - 217/2*e^3 + 36*e^2 + 595/2*e + 112', '1/2*e^5 - e^4 - 11/2*e^3 + 13*e^2 + 13/2*e', '-3*e^5 + 2*e^4 + 43*e^3 - 24*e^2 - 111*e - 32', '9/2*e^5 - 3*e^4 - 133/2*e^3 + 32*e^2 + 371/2*e + 46', '3*e^5 - 4*e^4 - 46*e^3 + 40*e^2 + 126*e + 56', '25/2*e^5 - 9*e^4 - 369/2*e^3 + 98*e^2 + 1035/2*e + 198', '-2*e^5 + 4*e^4 + 32*e^3 - 42*e^2 - 102*e + 8', '11/2*e^5 - e^4 - 153/2*e^3 + 18*e^2 + 391/2*e + 62', '17/2*e^5 - 3*e^4 - 247/2*e^3 + 36*e^2 + 685/2*e + 138', '23/2*e^5 - 7*e^4 - 341/2*e^3 + 72*e^2 + 987/2*e + 198', '-6*e^5 + 2*e^4 + 88*e^3 - 22*e^2 - 244*e - 112', '-e^5 + 13*e^3 - 2*e^2 - 23*e', '5/2*e^5 + e^4 - 75/2*e^3 - 10*e^2 + 233/2*e + 72', '-6*e^5 + 4*e^4 + 90*e^3 - 42*e^2 - 266*e - 98', '-4*e^5 + 2*e^4 + 62*e^3 - 21*e^2 - 206*e - 64', '-5*e^5 + 4*e^4 + 73*e^3 - 44*e^2 - 189*e - 68', '11*e^5 - 6*e^4 - 161*e^3 + 66*e^2 + 449*e + 166', '2*e^4 + 4*e^3 - 16*e^2 - 34*e - 6', '5*e^5 - 2*e^4 - 75*e^3 + 18*e^2 + 222*e + 110', '3*e^5 - 41*e^3 - 2*e^2 + 101*e + 84', '13/2*e^5 - 2*e^4 - 203/2*e^3 + 16*e^2 + 665/2*e + 162', '4*e^5 - 2*e^4 - 56*e^3 + 24*e^2 + 142*e + 60', '29/2*e^5 - 9*e^4 - 427/2*e^3 + 98*e^2 + 1205/2*e + 250', '-e^5 + 2*e^4 + 16*e^3 - 20*e^2 - 40*e - 32', '8*e^5 - 6*e^4 - 123*e^3 + 62*e^2 + 373*e + 148', '17/2*e^5 - 4*e^4 - 259/2*e^3 + 36*e^2 + 793/2*e + 182', '4*e^5 - 4*e^4 - 60*e^3 + 44*e^2 + 168*e + 36', '19/2*e^5 - 5*e^4 - 281/2*e^3 + 56*e^2 + 815/2*e + 158', '6*e^5 - 4*e^4 - 92*e^3 + 41*e^2 + 272*e + 112', '2*e^5 - 4*e^4 - 30*e^3 + 44*e^2 + 78*e - 8', '5/2*e^5 - e^4 - 75/2*e^3 + 4*e^2 + 237/2*e + 78', '-3*e^5 + 3*e^4 + 41*e^3 - 40*e^2 - 87*e + 4', '-13/2*e^5 + 5*e^4 + 187/2*e^3 - 58*e^2 - 473/2*e - 66', '-12*e^5 + 6*e^4 + 178*e^3 - 64*e^2 - 516*e - 216', '9/2*e^5 - 2*e^4 - 123/2*e^3 + 28*e^2 + 297/2*e + 26', '5*e^5 - 6*e^4 - 73*e^3 + 67*e^2 + 191*e + 44', '5*e^5 - 4*e^4 - 75*e^3 + 42*e^2 + 213*e + 84', '2*e^2 - e - 4', '-2*e^4 + 2*e^3 + 26*e^2 - 34*e - 40', '-1/2*e^5 + e^4 + 15/2*e^3 - 8*e^2 - 57/2*e - 34', '7*e^5 - 2*e^4 - 103*e^3 + 18*e^2 + 291*e + 140', '-3*e^5 - 2*e^4 + 45*e^3 + 25*e^2 - 141*e - 100', '-1/2*e^5 + 3*e^4 + 19/2*e^3 - 34*e^2 - 61/2*e + 36', '-14*e^5 + 8*e^4 + 199*e^3 - 94*e^2 - 521*e - 182', '-2*e^4 - 2*e^3 + 24*e^2 + 6*e - 32', '12*e^5 - 8*e^4 - 174*e^3 + 92*e^2 + 476*e + 168', '3*e^5 + 2*e^4 - 44*e^3 - 22*e^2 + 142*e + 88', '-14*e^5 + 9*e^4 + 206*e^3 - 96*e^2 - 586*e - 232', 'e^5 - 13*e^3 + 25*e + 4', '-4*e^5 + 6*e^4 + 58*e^3 - 66*e^2 - 140*e - 16', '-3/2*e^5 - e^4 + 53/2*e^3 + 18*e^2 - 235/2*e - 102', '-17/2*e^5 + 5*e^4 + 239/2*e^3 - 60*e^2 - 613/2*e - 98'], 'hecke_polynomial': 'x^6 - 15*x^4 - 2*x^3 + 45*x^2 + 38*x + 8', 'label': '4.4.9909.1-13.1-c'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 9909, 'ideals': ['[1, 1, 1]', '[3, 3, w]', '[5, 5, w - 1]', '[7, 7, w^3 - w^2 - 4*w + 1]', '[9, 3, -w^2 + 3]', '[11, 11, -w^2 + w + 2]', '[13, 13, -w^3 + w^2 + 3*w - 1]', '[15, 15, w^3 - w^2 - 5*w]', '[16, 2, 2]', '[17, 17, -w^3 + 5*w + 2]', '[21, 21, -w^2 + 2*w + 3]', '[25, 25, w^3 - 2*w^2 - 4*w + 5]', '[27, 3, -w^3 + 6*w + 3]', '[29, 29, -w^2 + w + 1]', '[33, 33, w^3 - 4*w]', '[35, 35, w^3 - w^2 - 3*w - 2]', '[37, 37, -w^3 + 2*w^2 + 4*w - 4]', '[39, 39, w + 3]', '[41, 41, -w^3 + w^2 + 5*w + 1]', '[41, 41, w^2 - 5]', '[45, 15, -w^3 + w^2 + 3*w - 3]', '[47, 47, w^3 - w^2 - 5*w - 2]', '[47, 47, -w^3 + 2*w^2 + 4*w - 1]', '[48, 6, 2*w]', '[49, 49, -2*w - 1]', '[51, 51, -w^2 - w + 3]', '[53, 53, w^3 - 4*w - 4]', '[53, 53, 2*w^3 - 2*w^2 - 9*w + 1]', '[55, 55, w^3 - w^2 - 4*w + 4]', '[61, 61, -w^3 + w^2 + 6*w - 2]', '[63, 21, w^3 - w^2 - 6*w]', '[65, 65, w^3 - 5*w - 1]', '[71, 71, w^3 - w^2 - 6*w - 2]', '[75, 75, -2*w^3 + 2*w^2 + 8*w - 3]', '[77, 77, -w^3 + 2*w^2 + 2*w - 4]', '[80, 10, 2*w - 2]', '[81, 3, 3]', '[85, 85, w^3 - w^2 - 6*w + 1]', '[87, 87, -w^2 + 2*w + 6]', '[91, 91, 2*w^2 - w - 8]', '[99, 33, -w^3 + 2*w^2 + 3*w - 6]', '[103, 103, 2*w^3 - 2*w^2 - 8*w + 1]', '[103, 103, -3*w^3 + 3*w^2 + 13*w - 5]', '[105, 105, w^3 - 2*w^2 - 5*w + 6]', '[109, 109, 2*w^3 - w^2 - 8*w - 4]', '[109, 109, 2*w^3 - w^2 - 9*w - 1]', '[111, 111, 2*w^3 - 2*w^2 - 7*w + 3]', '[112, 14, 2*w^3 - 2*w^2 - 8*w + 2]', '[113, 113, -2*w^3 + w^2 + 11*w - 1]', '[113, 113, 2*w^3 - w^2 - 10*w - 4]', '[117, 39, -2*w^3 + w^2 + 9*w + 3]', '[119, 119, -w^3 + 2*w^2 + 3*w - 7]', '[121, 121, w^3 - 2*w^2 - 4*w + 8]', '[123, 123, w^3 - w^2 - 2*w + 3]', '[123, 123, w^3 - 5*w]', '[125, 5, 2*w^3 - 3*w^2 - 10*w + 4]', '[125, 125, -w^3 + 2*w^2 + 5*w - 1]', '[131, 131, -2*w^3 + w^2 + 9*w - 1]', '[135, 15, w^3 - 6*w]', '[139, 139, 2*w^3 - 4*w^2 - 7*w + 5]', '[139, 139, 3*w^3 - w^2 - 16*w - 5]', '[141, 141, 2*w^3 - 2*w^2 - 4*w + 3]', '[141, 141, -w^3 + w^2 + w - 3]', '[143, 143, w^3 - 2*w^2 - 6*w + 1]', '[144, 6, -2*w^2 + 6]', '[145, 145, 2*w^3 - w^2 - 9*w - 2]', '[147, 147, -w^3 + 3*w^2 + 2*w - 6]', '[149, 149, w^2 + w - 4]', '[149, 149, 3*w^3 - 3*w^2 - 13*w + 1]', '[151, 151, w^2 - 2*w - 8]', '[153, 51, -2*w^3 + 2*w^2 + 9*w]', '[157, 157, w^3 - w^2 - 7*w - 2]', '[157, 157, -2*w^2 + w + 7]', '[159, 159, 2*w^2 - w - 3]', '[159, 159, -2*w^3 + 3*w^2 + 7*w - 6]', '[165, 165, 2*w^2 - w - 6]', '[167, 167, 2*w^3 - 2*w^2 - 7*w + 5]', '[169, 169, -2*w^2 + 5]', '[173, 173, -w^3 + 6*w - 2]', '[173, 173, -w^3 + 2*w^2 + 5*w - 7]', '[175, 175, w + 4]', '[176, 22, -2*w^2 + 2*w + 4]', '[181, 181, -3*w^3 + 2*w^2 + 14*w + 1]', '[183, 183, w^3 - 5*w + 3]', '[185, 185, 3*w^3 - 4*w^2 - 11*w + 7]', '[187, 187, 2*w^3 - w^2 - 11*w - 1]', '[189, 21, -w^3 + 3*w^2 + 3*w - 9]', '[191, 191, -w^3 + 2*w^2 + 2*w - 5]', '[191, 191, -w^3 + 2*w^2 + 6*w - 5]', '[193, 193, -w^3 + 3*w^2 + 4*w - 4]', '[193, 193, 2*w^3 + 3*w^2 - 13*w - 20]', '[195, 195, w^2 + 2*w - 3]', '[197, 197, w^3 - 2*w - 2]', '[199, 199, 2*w^3 - w^2 - 11*w - 2]', '[203, 203, -2*w^3 + 3*w^2 + 6*w - 5]', '[205, 205, w^3 - w^2 - 5*w + 5]', '[205, 205, 2*w^3 - 2*w^2 - 7*w + 2]', '[208, 26, -2*w^3 + 2*w^2 + 6*w - 2]', '[211, 211, -2*w^3 + 9*w + 5]', '[213, 213, w^3 + w^2 - 5*w - 9]', '[221, 221, w^3 - w^2 - 2*w + 4]', '[223, 223, -w^3 + w^2 + 4*w - 5]', '[223, 223, w^2 - 3*w - 2]', '[225, 75, w^2 - 3*w - 3]', '[229, 229, 2*w^3 - 2*w^2 - 7*w + 1]', '[231, 231, 2*w^3 + w^2 - 11*w - 9]', '[235, 235, -2*w^3 + 2*w^2 + 6*w - 1]', '[235, 235, 3*w^3 - 4*w^2 - 8*w + 4]', '[240, 30, 2*w^3 - 2*w^2 - 10*w]', '[241, 241, 3*w^2 - 2*w - 13]', '[241, 241, -w^3 + w^2 + 5*w + 4]', '[243, 9, 3*w]', '[245, 245, -2*w^3 + w^2 + 11*w + 5]', '[255, 255, -2*w^3 + w^2 + 8*w + 3]', '[256, 4, 4]', '[257, 257, -3*w^3 + w^2 + 15*w + 8]', '[259, 259, -2*w^3 + 2*w^2 + 11*w - 4]', '[261, 87, -w^3 + 2*w^2 + 6*w]', '[263, 263, -3*w^3 + 5*w^2 + 9*w - 7]', '[263, 263, 2*w^3 - w^2 - 9*w + 2]', '[263, 263, -w^3 + 4*w^2 + 2*w - 16]', '[263, 263, w^3 - w^2 - 2*w - 2]', '[265, 265, -4*w^3 + 5*w^2 + 16*w - 7]', '[265, 265, -w^3 + 2*w^2 + 3*w + 1]', '[271, 271, -3*w - 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10]', '[1479, 1479, -4*w^3 + 3*w^2 + 17*w + 3]', '[1481, 1481, -3*w^3 + 4*w^2 + 16*w - 11]', '[1481, 1481, w^3 + w^2 - 4*w - 11]', '[1483, 1483, 3*w^3 - 2*w^2 - 11*w + 2]', '[1485, 165, 2*w^3 - 3*w^2 - 6*w - 3]', '[1491, 1491, -4*w^3 + 3*w^2 + 19*w + 3]', '[1493, 1493, 3*w^3 - 3*w^2 - 16*w - 1]', '[1493, 1493, 2*w^3 - 7*w - 7]', '[1499, 1499, -w^3 + 2*w^2 + 7*w - 7]', '[1499, 1499, 2*w^2 + 2*w - 7]', '[1503, 501, w^3 - 5*w^2 - 9*w + 9]', '[1509, 1509, 2*w^3 - 2*w^2 - 5*w - 3]', '[1511, 1511, 4*w^3 - 4*w^2 - 19*w + 2]', '[1517, 1517, -2*w^3 + 10*w + 1]', '[1517, 1517, -2*w^3 + 2*w^2 + 12*w + 5]', '[1521, 507, -w^3 + 2*w^2 + 3*w + 3]', '[1523, 1523, w^3 + 2*w^2 - 5*w - 4]', '[1523, 1523, -w^3 - w^2 + 7*w - 1]', '[1525, 1525, -8*w^3 + 9*w^2 + 35*w - 16]', '[1527, 1527, 5*w^3 - 7*w^2 - 14*w + 9]', '[1529, 1529, -5*w^3 + 10*w^2 + 15*w - 8]', '[1529, 1529, -5*w^3 + 6*w^2 + 23*w - 8]', '[1531, 1531, -w^2 - w - 4]', '[1531, 1531, -w^3 + 4*w^2 + 3*w - 8]', '[1531, 1531, 5*w^3 - 5*w^2 - 25*w + 7]', '[1531, 1531, -2*w^3 + 6*w^2 + 7*w - 20]', '[1535, 1535, -4*w^3 + 6*w^2 + 14*w - 11]', '[1535, 1535, -3*w^3 + 3*w^2 + 14*w + 1]', '[1537, 1537, -3*w^3 + 6*w^2 + 10*w - 11]', '[1537, 1537, -w^3 + 3*w^2 - 2*w - 7]', '[1545, 1545, w^3 - 3*w^2 - 5*w + 12]', '[1545, 1545, -6*w^3 + 9*w^2 + 28*w - 21]', '[1547, 1547, 2*w^3 - 9*w + 1]', '[1549, 1549, -2*w^3 + 5*w^2 + 6*w - 11]', '[1551, 1551, 5*w^2 + 4*w - 6]', '[1551, 1551, -w^3 - 4*w^2 + 2*w + 9]', '[1553, 1553, -w^3 + 3*w^2 + w - 11]', '[1553, 1553, w^2 + 3*w - 5]', '[1555, 1555, 5*w^3 - 8*w^2 - 20*w + 13]', '[1557, 519, -3*w^3 + 5*w^2 + 15*w - 6]', '[1557, 519, -2*w^3 + 4*w^2 + 6*w - 15]', '[1561, 1561, -3*w^3 + 6*w^2 + 10*w - 10]', '[1561, 1561, -5*w^3 + 5*w^2 + 21*w - 8]', '[1563, 1563, 2*w^3 - 3*w^2 - 11*w]', '[1565, 1565, w^3 + w^2 - 8*w + 1]', '[1569, 1569, 4*w^3 - 4*w^2 - 13*w + 6]', '[1569, 1569, -w^3 + w^2 + 5*w + 6]', '[1571, 1571, 4*w^3 - 4*w^2 - 18*w + 1]', '[1573, 1573, -4*w^3 + 4*w^2 + 16*w - 5]', '[1575, 525, 2*w^3 - 5*w^2 - 6*w + 9]', '[1583, 1583, -2*w^3 + 3*w^2 + 6*w - 10]', '[1584, 66, -2*w^3 + 4*w^2 + 6*w - 12]', '[1595, 1595, 3*w^2 - 5*w - 13]', '[1597, 1597, 4*w^3 - 5*w^2 - 11*w + 4]', '[1599, 1599, -3*w^3 + 3*w^2 + 8*w - 6]', '[1599, 1599, -2*w^3 + 2*w^2 + 13*w + 6]', '[1601, 1601, 3*w^3 - 4*w^2 - 12*w - 1]', '[1603, 1603, w^2 - 2*w + 4]', '[1607, 1607, -4*w^3 + w^2 + 21*w + 13]', '[1607, 1607, 4*w^3 - 4*w^2 - 17*w - 1]', '[1607, 1607, w^2 + 2*w - 7]', '[1607, 1607, -3*w^3 + 5*w^2 + 10*w - 11]', '[1617, 1617, -3*w^2 + 4*w + 15]', '[1623, 1623, -2*w^3 + 5*w^2 + 10*w - 9]', '[1625, 65, -w^3 + 4*w^2 + 10*w - 7]', '[1625, 1625, 3*w^3 - 6*w^2 - 7*w + 10]', '[1627, 1627, -4*w^3 + 7*w^2 + 19*w - 14]', '[1627, 1627, -3*w^3 + 7*w^2 + 10*w - 8]', '[1629, 543, -5*w^3 + 2*w^2 + 27*w + 9]', '[1635, 1635, -3*w^3 - w^2 + 14*w + 15]', '[1635, 1635, w^3 - 5*w^2 - 4*w + 18]', '[1637, 1637, w^3 - w^2 - w - 5]', '[1637, 1637, 3*w^3 + 3*w^2 - 17*w - 26]', '[1639, 1639, w^2 - 5*w - 5]', '[1639, 1639, -2*w^3 + 7*w^2 + 2*w - 16]', '[1645, 1645, -5*w^3 + 4*w^2 + 19*w + 7]', '[1645, 1645, 6*w^3 - 9*w^2 - 17*w + 5]', '[1647, 183, 2*w^3 - 3*w^2 - 9*w + 12]', '[1648, 206, 4*w^3 - 4*w^2 - 16*w + 2]', '[1648, 206, -6*w^3 + 6*w^2 + 26*w - 10]', '[1657, 1657, -2*w^3 + 13*w + 7]', '[1657, 1657, -2*w^3 + 5*w^2 + 6*w - 10]', '[1661, 1661, 3*w^3 + 2*w^2 - 15*w - 13]', '[1665, 555, 2*w^3 - 4*w^2 - 12*w + 9]', '[1667, 1667, 3*w^2 - 4*w - 5]', '[1667, 1667, 4*w^3 - 5*w^2 - 15*w - 2]', '[1680, 210, 2*w^3 - 4*w^2 - 10*w + 12]', '[1681, 41, 4*w^3 - w^2 - 19*w - 8]', '[1681, 41, 4*w^3 - 23*w - 14]', '[1681, 1681, -w^3 + 7*w + 10]', '[1681, 1681, 4*w^2 - 7*w - 11]', '[1683, 561, w^3 - 5*w^2 + 12]', '[1685, 1685, -3*w^3 + w^2 + 16*w + 1]', '[1685, 1685, -4*w^3 + 5*w^2 + 10*w - 1]', '[1687, 1687, -5*w^3 + 3*w^2 + 26*w + 2]', '[1687, 1687, 3*w^3 - 2*w^2 - 11*w - 2]', '[1689, 1689, 3*w^3 - 4*w^2 - 14*w + 3]', '[1689, 1689, 3*w^2 - 2*w - 3]', '[1693, 1693, -w^3 - w^2 + 9*w + 7]', '[1695, 1695, -5*w^3 + 9*w^2 + 20*w - 24]', '[1695, 1695, 3*w^3 - 6*w^2 - 11*w + 9]', '[1699, 1699, -w^3 - w^2 + 9*w + 4]', '[1701, 63, -3*w^2 + 6*w + 9]', '[1703, 1703, 3*w^3 - 2*w^2 - 9*w + 7]', '[1707, 1707, 4*w^3 - 3*w^2 - 10*w + 6]', '[1707, 1707, 3*w^3 - w^2 - 14*w]', '[1713, 1713, 2*w^2 - 4*w + 3]', '[1715, 35, -3*w^3 + 5*w^2 + 12*w - 4]', '[1715, 1715, 3*w^2 - 13]', '[1719, 573, w^3 + 2*w^2 - 3*w - 9]', '[1719, 573, -3*w^3 + 2*w^2 + 9*w - 9]', '[1723, 1723, -w^3 + 4*w^2 + 4*w - 8]', '[1723, 1723, 4*w^3 - w^2 - 16*w - 10]', '[1727, 1727, 2*w^3 + 2*w^2 - 7*w - 10]', '[1727, 1727, 2*w^2 + 4*w - 5]', '[1731, 1731, -2*w^3 + 2*w^2 + 10*w - 9]', '[1733, 1733, w^3 + 2*w^2 - 5*w - 14]', '[1735, 1735, 2*w^3 - 13*w - 4]', '[1735, 1735, 3*w^3 - w^2 - 12*w - 5]', '[1737, 579, -w^3 - 2*w^2 - 3]', '[1737, 579, -w^3 + 4*w^2 + 3*w - 9]', '[1739, 1739, -w^3 - 2*w^2 + 6*w + 5]', '[1739, 1739, -5*w^3 + 6*w^2 + 19*w - 1]', '[1741, 1741, w^3 + 2*w^2 - 10*w - 11]', '[1741, 1741, w^3 + 4*w^2 - 7*w - 19]', '[1744, 218, 4*w^3 - 2*w^2 - 16*w - 8]', '[1744, 218, 4*w^3 - 2*w^2 - 18*w - 2]', '[1745, 1745, 4*w^3 - 5*w^2 - 15*w + 11]', '[1745, 1745, -3*w^3 + 5*w^2 + 13*w - 5]', '[1747, 1747, 4*w^3 - 3*w^2 - 21*w + 1]', '[1747, 1747, -w^3 + 5*w - 5]', '[1747, 1747, -w^3 + 4*w - 5]', '[1747, 1747, -2*w^3 + 5*w^2 + 7*w - 8]', '[1749, 1749, 3*w^3 - 6*w^2 - 13*w + 15]', '[1749, 1749, -w^3 + w^2 + 10*w + 6]', '[1751, 1751, 5*w^3 - 7*w^2 - 20*w + 20]', '[1751, 1751, -w^3 + 4*w^2 + w - 16]', '[1753, 1753, 2*w^3 - w^2 - 13*w - 5]', '[1753, 1753, -w^3 + 4*w^2 + 4*w - 10]', '[1755, 195, w^3 + 3*w^2 - 6*w - 18]', '[1759, 1759, w^2 - 10]', '[1761, 1761, -5*w^3 + 6*w^2 + 19*w - 12]', '[1761, 1761, w^3 + 2*w^2 - w - 6]', '[1765, 1765, 2*w^2 - 6*w - 1]', '[1769, 1769, -5*w + 4]', '[1773, 591, -w^3 - w^2 - 3*w - 6]', '[1775, 1775, -2*w^3 + w^2 + 6*w + 5]', '[1776, 222, 4*w^3 - 4*w^2 - 14*w + 6]', '[1777, 1777, -w^3 + 4*w^2 + 3*w - 10]', '[1783, 1783, 3*w^3 - w^2 - 12*w - 2]', '[1783, 1783, w^3 - 4*w^2 - 2*w + 19]', '[1785, 1785, w^3 - w^2 - 4*w - 6]', '[1787, 1787, -w^3 + 2*w^2 - 8]', '[1787, 1787, w^3 + 2*w^2 - 4*w - 11]', '[1791, 597, 5*w^3 - w^2 - 24*w - 9]', '[1792, 28, 4*w^3 - 4*w^2 - 16*w + 4]', '[1795, 1795, 2*w^3 - 3*w^2 - 5*w - 4]', '[1797, 1797, w^3 + w^2 - 2*w - 6]', '[1799, 1799, w^3 + 2*w^2 - 5*w - 16]', '[1801, 1801, -w^3 + 2*w^2 + 3*w - 11]', '[1807, 1807, 4*w^3 - 6*w^2 - 5*w + 4]', '[1807, 1807, -2*w^3 + 5*w^2 + 7*w - 13]', '[1808, 226, -4*w^3 + 2*w^2 + 22*w - 2]', '[1808, 226, 4*w^3 - 2*w^2 - 20*w - 8]', '[1813, 1813, -3*w^3 + 2*w^2 + 10*w - 2]', '[1815, 1815, 2*w^3 - 5*w^2 - 4*w + 12]', '[1821, 1821, -4*w^3 + 4*w^2 + 16*w - 3]', '[1827, 609, 2*w^2 + 3*w - 6]', '[1833, 1833, -w^3 + 4*w^2 + 8*w]', '[1833, 1833, 2*w^3 - 2*w^2 - 14*w - 9]', '[1835, 1835, 2*w^3 - 3*w^2 - 3*w - 1]', '[1835, 1835, 4*w^3 - 6*w^2 - 13*w + 10]', '[1835, 1835, -7*w^3 + 13*w^2 + 22*w - 13]', '[1837, 1837, -3*w^3 + 2*w^2 + 9*w - 2]', '[1839, 1839, 3*w^3 - w^2 - 11*w]', '[1839, 1839, -w^3 + 4*w^2 + 4*w - 9]', '[1841, 1841, -3*w^2 + 7*w - 1]', '[1841, 1841, -8*w^3 + 6*w^2 + 39*w - 4]', '[1841, 1841, -4*w^3 + 6*w^2 + 15*w - 5]', '[1841, 1841, 5*w^3 - 6*w^2 - 20*w + 14]', '[1845, 615, 2*w^3 - 5*w^2 - 9*w + 12]', '[1845, 615, w^3 - 2*w^2 - 9*w]', '[1847, 1847, 3*w^3 - 3*w^2 - 9*w + 7]', '[1853, 1853, 3*w^3 + 3*w^2 - 21*w - 26]', '[1853, 1853, 4*w^2 - 5*w - 23]', '[1855, 1855, -6*w^3 + 6*w^2 + 24*w + 1]', '[1855, 1855, -5*w^3 + 4*w^2 + 20*w + 11]', '[1857, 1857, 2*w^3 - 5*w^2 - 8*w]', '[1859, 1859, -2*w^3 + 4*w^2 + 5*w - 10]', '[1865, 1865, -w^3 + 2*w^2 - 3*w + 2]', '[1865, 1865, 4*w^3 - 3*w^2 - 19*w + 8]', '[1867, 1867, 4*w^3 - 7*w^2 - 17*w + 17]', '[1872, 78, -4*w^3 + 2*w^2 + 18*w + 6]', '[1875, 15, 5*w^3 - 5*w^2 - 20*w + 15]', '[1875, 1875, -w^3 + 2*w - 6]', '[1885, 1885, -w^2 - 4]', '[1887, 1887, -3*w^3 + 3*w^2 + 10*w - 9]', '[1889, 1889, 2*w^3 - 3*w^2 - 12*w - 1]', '[1893, 1893, -2*w^3 + 13*w + 6]', '[1895, 1895, -w^3 + w^2 - 2*w + 2]', '[1895, 1895, 6*w^3 - 9*w^2 - 21*w + 14]', '[1897, 1897, 2*w^3 - 5*w^2 - 8*w + 8]', '[1899, 633, -3*w^3 + w^2 + 21*w + 15]', '[1901, 1901, -4*w^3 + w^2 + 21*w + 14]', '[1901, 1901, -3*w^3 - w^2 + 14*w + 8]', '[1903, 1903, w^3 + w^2 - 9*w - 5]', '[1903, 1903, -2*w^3 + 5*w^2 + 4*w - 1]', '[1904, 238, -2*w^3 + 4*w^2 + 6*w - 14]', '[1907, 1907, w^3 - w - 4]', '[1907, 1907, 3*w^3 - 3*w^2 - 15*w - 1]', '[1911, 1911, 2*w^3 - 2*w^2 - 8*w + 9]', '[1913, 1913, -2*w^3 + 3*w^2 + 4*w - 7]', '[1917, 213, w^3 - 3]', '[1921, 1921, 2*w^3 - 6*w^2 - 7*w + 25]', '[1921, 1921, -w^2 + w - 4]', '[1925, 1925, w^2 + 2*w - 8]', '[1927, 1927, 3*w^3 - 2*w^2 - 11*w - 1]', '[1927, 1927, 2*w^3 - 13*w - 5]', '[1927, 1927, -4*w^3 + 19*w + 13]', '[1927, 1927, w^3 - 9*w + 1]', '[1933, 1933, 4*w^3 - 19*w - 11]', '[1936, 242, 2*w^3 - 4*w^2 - 8*w + 16]', '[1937, 1937, w^3 - 2*w^2 + w - 4]', '[1937, 1937, 2*w^3 - 5*w^2 - 10*w + 4]', '[1941, 1941, -2*w^3 + w^2 + 4*w - 6]', '[1945, 1945, -w^3 + w^2 + 3*w - 8]', '[1949, 1949, 5*w^3 - w^2 - 26*w - 16]', '[1949, 1949, 4*w^3 - 5*w^2 - 17*w + 4]', '[1959, 1959, -5*w^3 + 10*w^2 + 16*w - 9]', '[1961, 1961, w^3 + w^2 - 3*w - 8]', '[1961, 1961, -w^3 + 3*w^2 - 10]', '[1963, 1963, 3*w^3 - 10*w - 1]', '[1965, 1965, -3*w^3 + 7*w^2 + 14*w - 18]', '[1967, 1967, 2*w^3 - 2*w^2 - 13*w + 10]', '[1967, 1967, -4*w + 5]', '[1968, 246, 2*w^3 - 2*w^2 - 4*w + 6]', '[1968, 246, 2*w^3 - 10*w]', '[1973, 1973, 4*w^3 + 3*w^2 - 22*w - 28]', '[1981, 1981, -4*w^3 + 3*w^2 + 17*w + 2]', '[1985, 1985, 6*w^3 - 9*w^2 - 20*w + 13]', '[1987, 1987, w^3 + 5*w^2 - 9*w - 25]', '[1987, 1987, -2*w^3 + 5*w^2 + 8*w - 13]', '[1989, 663, -w^3 + w^2 + 3]', '[1991, 1991, -4*w^2 + 5*w + 17]', '[1993, 1993, -3*w^3 + w^2 + 12*w + 4]', '[1993, 1993, 3*w^3 - 4*w^2 - 17*w + 7]', '[1997, 1997, -2*w^3 + 3*w^2 + 5*w - 8]', '[1997, 1997, -5*w^3 + 8*w^2 + 21*w - 11]', '[1999, 1999, 6*w^3 - 3*w^2 - 29*w - 7]', '[2000, 10, 4*w^3 - 6*w^2 - 20*w + 8]', '[2000, 250, -2*w^3 + 4*w^2 + 10*w - 2]', '[2005, 2005, -5*w^3 + 6*w^2 + 19*w - 5]', '[2005, 2005, 7*w^3 - 7*w^2 - 29*w + 14]', '[2005, 2005, 2*w^3 - w^2 - 13*w + 2]', '[2005, 2005, -4*w^3 + 7*w^2 + 15*w - 13]', '[2007, 669, -w^3 + 5*w^2 + 6*w - 12]', '[2007, 669, -3*w^3 + w^2 + 12*w + 3]', '[2009, 2009, -w^3 + w^2 - w - 7]', '[2009, 2009, -2*w^3 - w^2 + 10*w + 5]', '[2013, 2013, -3*w^3 + 6*w^2 + 17*w - 12]', '[2017, 2017, 3*w^3 - 18*w - 8]', '[2023, 2023, -4*w^2 + 3*w + 13]', '[2025, 75, 3*w^3 - 6*w^2 - 12*w + 15]', '[2027, 2027, -3*w^3 + 3*w^2 + 14*w + 2]', '[2029, 2029, w^2 - 5*w - 4]', '[2029, 2029, 4*w^3 - 3*w^2 - 17*w + 2]', '[2031, 2031, 4*w^3 - 7*w^2 - 14*w + 6]', '[2035, 2035, -5*w^3 + 8*w^2 + 23*w - 16]', '[2041, 2041, 5*w^2 + 4*w - 7]', '[2041, 2041, 5*w + 2]', '[2049, 2049, 3*w^3 - 2*w^2 - 8*w + 6]', '[2049, 2049, w^3 - 2*w - 6]', '[2049, 2049, 3*w^3 - 6*w^2 - 11*w + 3]', '[2049, 2049, 3*w^3 - w^2 - 14*w + 6]', '[2051, 2051, -5*w^3 + 7*w^2 + 20*w - 16]', '[2053, 2053, -w^3 + 2*w^2 + 4*w - 11]', '[2053, 2053, 4*w^3 - 4*w^2 - 21*w + 7]', '[2057, 2057, 2*w^3 - 8*w - 11]', '[2059, 2059, 4*w^2 + w - 8]', '[2061, 687, w^3 - w^2 - 9*w - 3]', '[2067, 2067, 3*w^3 + 2*w^2 - 13*w - 15]', '[2067, 2067, 4*w^3 - 3*w^2 - 20*w - 3]', '[2069, 2069, w^3 + 2*w^2 - 10*w - 16]', '[2069, 2069, -3*w^3 + 4*w^2 + 9*w - 8]', '[2073, 2073, w^3 - 4*w^2 - w]', '[2079, 231, 4*w^3 - 3*w^2 - 18*w - 6]', '[2081, 2081, -4*w^3 - 3*w^2 + 23*w + 23]', '[2083, 2083, -w^3 + 5*w^2 + 4*w - 7]', '[2085, 2085, 2*w^3 - 10*w + 3]', '[2085, 2085, 3*w^3 - 4*w^2 - 16*w + 12]', '[2089, 2089, 5*w^3 - 8*w^2 - 20*w + 14]', '[2089, 2089, w - 7]', '[2091, 2091, -w^3 + 2*w^2 + 2*w - 12]', '[2091, 2091, -3*w^3 + 11*w + 3]', '[2096, 262, -4*w^3 + 2*w^2 + 18*w - 2]', '[2101, 2101, -5*w - 1]', '[2101, 2101, 4*w^3 - 4*w^2 - 13*w - 1]', '[2105, 2105, 4*w^3 - 5*w^2 - 22*w + 13]', '[2105, 2105, 2*w^3 - 11*w + 4]', '[2111, 2111, -4*w^3 + w^2 + 20*w + 5]', '[2113, 2113, w^2 - 3*w + 5]', '[2113, 2113, -5*w^3 + 4*w^2 + 22*w - 4]', '[2115, 705, w^2 + 6*w + 3]', '[2115, 705, -w^3 - w^2 - 3*w]', '[2123, 2123, 3*w^3 - 7*w^2 - 11*w + 4]', '[2123, 2123, -2*w^2 - w + 10]', '[2125, 85, -3*w^3 + 7*w^2 + 15*w - 16]', '[2125, 2125, 4*w^3 - 8*w^2 - 12*w + 11]', '[2127, 2127, -2*w^3 + 5*w^2 + 7*w - 9]', '[2127, 2127, -2*w^3 + 3*w^2 + w - 3]', '[2129, 2129, 2*w^3 + 3*w^2 - 15*w - 23]', '[2131, 2131, -w - 7]', '[2135, 2135, 3*w^2 - 6*w - 2]', '[2137, 2137, w^2 - 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11*w - 3]', '[5200, 650, -2*w^3 + 2*w^2 + 14*w - 4]', '[5205, 5205, -w^2 + 2*w - 6]', '[5205, 5205, -w^3 + 6*w^2 + 4*w - 9]', '[5211, 579, 4*w^3 - 3*w^2 - 15*w]', '[5211, 579, 5*w^3 - 30*w - 21]', '[5213, 5213, -w^3 - 2*w^2 + 8*w + 2]', '[5213, 5213, 2*w^3 - 2*w^2 - 4*w - 5]', '[5213, 5213, 3*w^3 - 5*w^2 - 8*w + 11]', '[5213, 5213, 2*w^3 - 6*w^2 - 15*w + 11]', '[5215, 5215, -2*w^3 + 2*w^2 + 7*w + 8]', '[5215, 5215, -10*w^3 + 11*w^2 + 38*w + 1]', '[5217, 5217, -2*w^3 + 2*w + 3]', '[5217, 5217, 6*w^3 - 11*w^2 - 16*w + 15]', '[5219, 5219, -6*w^3 + 3*w^2 + 31*w + 10]', '[5219, 5219, w^3 + w^2 - w - 7]', '[5223, 5223, 2*w^3 - 4*w^2 - 8*w - 3]', '[5223, 5223, 4*w^3 - w^2 - 16*w - 3]', '[5227, 5227, -w^3 + 6*w - 7]', '[5231, 5231, 4*w^3 - 3*w^2 - 14*w - 10]', '[5232, 654, -2*w^3 + 8*w^2 + 4*w - 12]', '[5232, 654, -2*w^3 + 6*w^2 + 10*w - 12]', '[5233, 5233, -5*w^3 + 3*w^2 + 22*w + 1]', '[5235, 5235, -6*w^3 + 3*w^2 + 28*w]', '[5235, 5235, -4*w^2 - w + 15]', '[5237, 5237, -2*w^3 + 5*w^2 + 10*w - 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4]', '[5295, 5295, -w^3 + 6*w^2 + w - 21]', '[5299, 5299, -2*w^2 + 3*w + 16]', '[5303, 5303, -3*w^3 + 4*w^2 + 9*w - 11]', '[5307, 5307, -4*w^3 + 5*w^2 + 20*w - 3]', '[5309, 5309, -3*w^3 + w^2 + 17*w - 4]', '[5311, 5311, 5*w^3 - 5*w^2 - 27*w + 11]', '[5311, 5311, 2*w^3 - 2*w^2 - 9*w - 8]', '[5311, 5311, 4*w^3 - 2*w^2 - 15*w + 1]', '[5311, 5311, 5*w^2 - w - 17]', '[5319, 591, 2*w^3 + 3*w^2 - 12*w - 12]', '[5321, 5321, -w^3 - 4*w^2 + 6*w + 22]', '[5325, 5325, w^3 - 6*w^2 - w + 6]', '[5327, 5327, 7*w^3 - 8*w^2 - 33*w + 10]', '[5328, 222, -2*w^3 + 2*w^2 + 6*w - 12]', '[5329, 73, -2*w^3 + 6*w^2 + 9*w - 10]', '[5329, 73, -w^3 + 6*w^2 - 19]', '[5331, 5331, 4*w^3 - 3*w^2 - 13*w + 3]', '[5341, 5341, -7*w^2 + 4*w + 16]', '[5341, 5341, -5*w^2 - w + 13]', '[5347, 5347, -4*w^3 + w^2 + 15*w + 1]', '[5349, 5349, -4*w^3 + 4*w^2 + 22*w - 3]', '[5349, 5349, -w^3 + 6*w^2 + 7*w - 9]', '[5351, 5351, 5*w^3 - 5*w^2 - 23*w + 1]', '[5351, 5351, -7*w^3 + 11*w^2 + 26*w - 13]', '[5355, 1785, -w^3 + 2*w^2 - 3*w - 3]', '[5357, 5357, 5*w^3 - 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4*w - 15]', '[5677, 5677, 6*w^3 - 3*w^2 - 32*w - 4]', '[5677, 5677, 4*w^3 - 8*w^2 - 19*w + 14]', '[5679, 1893, w^2 + 6]', '[5680, 710, -4*w^3 + 2*w^2 + 14*w - 2]', '[5685, 5685, -5*w^3 + 3*w^2 + 25*w - 3]', '[5685, 5685, -3*w^3 + 5*w^2 + 16*w - 3]', '[5687, 5687, -4*w^3 + 5*w^2 + 18*w - 2]', '[5687, 5687, 5*w^3 - 2*w^2 - 26*w - 13]', '[5689, 5689, 6*w^3 - 7*w^2 - 23*w + 8]', '[5691, 5691, 3*w^3 - 5*w^2 - 11*w - 3]', '[5697, 633, -5*w^3 - 6*w^2 + 30*w + 42]', '[5699, 5699, 5*w^3 - 2*w^2 - 27*w - 13]', '[5699, 5699, -2*w^3 + 4*w^2 + 3*w - 11]', '[5699, 5699, 5*w - 7]', '[5699, 5699, -5*w^3 + 7*w^2 + 17*w - 13]', '[5701, 5701, w^3 + 2*w^2 - 11*w - 10]', '[5701, 5701, 4*w^3 - 9*w^2 - 14*w + 11]', '[5701, 5701, 6*w^3 - 7*w^2 - 23*w + 7]', '[5701, 5701, 3*w^3 - 7*w^2 - 13*w + 11]', '[5703, 5703, w^3 - 3*w^2 + 2*w + 12]', '[5703, 5703, -w^3 - 5*w^2 + 11*w + 27]', '[5707, 5707, -w^2 - 7*w + 1]', '[5709, 5709, -5*w^3 + 3*w^2 + 20*w - 12]', '[5709, 5709, -6*w^3 + 7*w^2 + 31*w - 9]', '[5711, 5711, w^3 + 2*w^2 - 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w^2 - 19*w]', '[9807, 9807, 7*w^3 - 2*w^2 - 35*w - 24]', '[9808, 1226, 6*w^3 - 2*w^2 - 28*w - 10]', '[9808, 1226, 6*w^2 - 2*w - 22]', '[9809, 9809, -2*w^3 + 9*w^2 + 6*w - 37]', '[9815, 9815, -7*w^3 + 33*w + 14]', '[9825, 9825, 10*w^3 - 11*w^2 - 41*w + 27]', '[9831, 9831, 9*w^3 - 14*w^2 - 35*w + 24]', '[9831, 9831, -9*w^3 + 5*w^2 + 43*w + 9]', '[9835, 9835, -9*w^3 + 13*w^2 + 28*w - 7]', '[9835, 9835, -11*w^3 + 16*w^2 + 36*w - 11]', '[9839, 9839, -2*w^3 + 5*w^2 + 4*w - 20]', '[9839, 9839, w^3 + 2*w^2 - 3*w - 14]', '[9840, 1230, -2*w^3 + 2*w^2 + 16*w - 6]', '[9840, 1230, 2*w^2 - 4*w - 18]', '[9841, 9841, -2*w^2 - 4*w - 7]', '[9843, 9843, -4*w^3 + 7*w - 6]', '[9843, 9843, 4*w^3 + 6*w^2 - 28*w - 45]', '[9851, 9851, -2*w^3 + 5*w^2 + 4*w - 19]', '[9851, 9851, -4*w^3 + 6*w^2 + 12*w - 13]', '[9857, 9857, w^3 + 3*w^2 - 8*w - 5]', '[9863, 9863, -9*w^3 + 7*w^2 + 44*w - 8]', '[9865, 9865, -w^3 - w^2 + 6*w + 16]', '[9869, 9869, -w^3 + 3*w^2 + 8*w - 11]', '[9869, 9869, 6*w^3 - 6*w^2 - 26*w - 1]', '[9881, 9881, 4*w^3 + 2*w^2 - 19*w - 23]', '[9881, 9881, -w^3 + 7*w^2 + 7*w - 20]', '[9881, 9881, -2*w^3 + 6*w^2 + 3*w - 19]', '[9881, 9881, 5*w^3 - 8*w^2 - 20*w + 7]', '[9887, 9887, 6*w^3 - 9*w^2 - 22*w + 19]', '[9887, 9887, 2*w^3 + 2*w^2 - 9*w - 22]', '[9891, 3297, 2*w^3 - w^2 + 18]', '[9891, 3297, 7*w^3 - 8*w^2 - 27*w + 6]', '[9893, 9893, -4*w^3 + 7*w^2 + 20*w - 7]', '[9897, 9897, 4*w^3 - 10*w^2 - 25*w + 12]', '[9903, 9903, -w^2 - 8*w - 3]', '[9903, 9903, 5*w^3 - 3*w^2 - 19*w + 3]', '[9904, 1238, 4*w^2 - 10*w - 16]', '[9905, 9905, -7*w^3 + 4*w^2 + 28*w + 20]', '[9907, 9907, -3*w^3 - 7*w^2 + 21*w + 40]', '[9907, 9907, -2*w^3 + w^2 + 15*w - 2]', '[9909, 1101, -4*w^3 + 9*w^2 + 12*w - 15]', '[9909, 1101, -4*w^3 - 3*w^2 + 27*w + 24]', '[9909, 1101, 7*w^3 - 3*w^2 - 33*w - 12]', '[9911, 9911, -5*w^3 - 3*w^2 + 30*w + 25]', '[9911, 9911, 7*w^3 - 14*w^2 - 26*w + 41]', '[9917, 9917, 3*w^3 - 16*w - 1]', '[9917, 9917, 6*w^3 - 11*w^2 - 21*w + 10]', '[9919, 9919, -7*w^3 - 4*w^2 + 44*w + 44]', '[9919, 9919, -9*w^3 + 3*w^2 + 49*w + 20]', '[9921, 9921, w^3 - 6*w^2 - 4*w + 12]', '[9923, 9923, 6*w^3 - 9*w^2 - 17*w + 13]', '[9923, 9923, -4*w^3 + w^2 + 20*w + 1]', '[9925, 9925, -5*w^3 + 6*w^2 + 24*w - 20]', '[9929, 9929, 3*w^3 - w^2 - 10*w - 10]', '[9931, 9931, 6*w^3 - 2*w^2 - 23*w - 13]', '[9931, 9931, -3*w^3 + 8*w^2 + 8*w - 16]', '[9935, 9935, 4*w^3 - 8*w^2 - 13*w + 22]', '[9935, 9935, 7*w^3 - 9*w^2 - 27*w + 19]', '[9945, 3315, -2*w^3 + 7*w^2 + 6*w - 21]', '[9947, 203, -3*w^3 + 5*w^2 + 5*w - 11]', '[9947, 9947, -5*w^3 - 2*w^2 + 26*w + 19]', '[9949, 9949, 2*w^3 + w^2 - 16*w - 4]', '[9949, 9949, -4*w^3 + 4*w^2 + 14*w - 17]', '[9955, 9955, -12*w^3 + 11*w^2 + 55*w - 14]', '[9957, 9957, -w^3 + 6*w^2 + 2*w - 18]', '[9961, 9961, -8*w^3 + 8*w^2 + 40*w - 11]', '[9963, 369, 3*w^3 - 3*w^2 - 6*w + 9]', '[9963, 369, 3*w^3 - 15*w]', '[9965, 9965, 4*w^3 - 7*w^2 - 17*w + 5]', '[9965, 9965, -7*w^3 + 5*w^2 + 33*w - 16]', '[9969, 9969, -7*w^3 + 9*w^2 + 29*w - 9]', '[9973, 9973, -6*w^3 + 11*w^2 + 24*w - 28]', '[9979, 9979, -6*w^3 + 11*w^2 + 26*w - 28]', '[9979, 9979, 4*w^3 + 3*w^2 - 28*w - 38]', '[9984, 156, 4*w + 12]', '[9985, 9985, 13*w^3 - 17*w^2 - 47*w + 26]', '[9985, 9985, 5*w^3 - 10*w^2 - 19*w + 14]', '[9993, 9993, 5*w^3 - 10*w^2 - 22*w + 15]', '[9995, 9995, -9*w^3 + 10*w^2 + 40*w - 11]', '[10000, 10, 10]', '[10000, 1250, 4*w^3 - 2*w^2 - 24*w - 8]'], 'label': '4.4.9909.1', 'narrow_class_no': 2, 'primes': ['[3, 3, w]', '[5, 5, w - 1]', '[7, 7, w^3 - w^2 - 4*w + 1]', '[11, 11, -w^2 + w + 2]', '[13, 13, -w^3 + w^2 + 3*w - 1]', '[16, 2, 2]', '[17, 17, -w^3 + 5*w + 2]', '[29, 29, -w^2 + w + 1]', '[37, 37, -w^3 + 2*w^2 + 4*w - 4]', '[41, 41, -w^3 + w^2 + 5*w + 1]', '[41, 41, w^2 - 5]', '[47, 47, w^3 - w^2 - 5*w - 2]', '[47, 47, -w^3 + 2*w^2 + 4*w - 1]', '[53, 53, w^3 - 4*w - 4]', '[53, 53, 2*w^3 - 2*w^2 - 9*w + 1]', '[61, 61, -w^3 + w^2 + 6*w - 2]', '[71, 71, w^3 - w^2 - 6*w - 2]', '[103, 103, 2*w^3 - 2*w^2 - 8*w + 1]', '[103, 103, -3*w^3 + 3*w^2 + 13*w - 5]', '[109, 109, 2*w^3 - w^2 - 8*w - 4]', '[109, 109, 2*w^3 - w^2 - 9*w - 1]', '[113, 113, -2*w^3 + w^2 + 11*w - 1]', '[113, 113, 2*w^3 - w^2 - 10*w - 4]', '[125, 5, 2*w^3 - 3*w^2 - 10*w + 4]', '[131, 131, -2*w^3 + w^2 + 9*w - 1]', '[139, 139, 2*w^3 - 4*w^2 - 7*w + 5]', '[139, 139, 3*w^3 - w^2 - 16*w - 5]', '[149, 149, w^2 + w - 4]', '[149, 149, 3*w^3 - 3*w^2 - 13*w + 1]', '[151, 151, w^2 - 2*w - 8]', '[157, 157, w^3 - w^2 - 7*w - 2]', '[157, 157, -2*w^2 + w + 7]', '[167, 167, 2*w^3 - 2*w^2 - 7*w + 5]', '[173, 173, -w^3 + 6*w - 2]', '[173, 173, -w^3 + 2*w^2 + 5*w - 7]', '[181, 181, -3*w^3 + 2*w^2 + 14*w + 1]', '[191, 191, -w^3 + 2*w^2 + 2*w - 5]', '[191, 191, -w^3 + 2*w^2 + 6*w - 5]', '[193, 193, -w^3 + 3*w^2 + 4*w - 4]', '[193, 193, 2*w^3 + 3*w^2 - 13*w - 20]', '[197, 197, w^3 - 2*w - 2]', '[199, 199, 2*w^3 - w^2 - 11*w - 2]', '[211, 211, -2*w^3 + 9*w + 5]', '[223, 223, -w^3 + w^2 + 4*w - 5]', '[223, 223, w^2 - 3*w - 2]', '[229, 229, 2*w^3 - 2*w^2 - 7*w + 1]', '[241, 241, 3*w^2 - 2*w - 13]', '[241, 241, -w^3 + w^2 + 5*w + 4]', '[257, 257, -3*w^3 + w^2 + 15*w + 8]', '[263, 263, -3*w^3 + 5*w^2 + 9*w - 7]', '[263, 263, 2*w^3 - w^2 - 9*w + 2]', '[263, 263, -w^3 + 4*w^2 + 2*w - 16]', '[263, 263, w^3 - w^2 - 2*w - 2]', '[271, 271, -3*w - 1]', '[281, 281, 2*w^3 - 3*w^2 - 8*w + 2]', '[281, 281, 3*w^3 - 4*w^2 - 12*w + 4]', '[283, 283, w^3 - 5*w - 7]', '[293, 293, -2*w^3 + w^2 + 10*w - 1]', '[307, 307, w^3 - 3*w^2 - 3*w + 8]', '[307, 307, 3*w^3 - 15*w - 10]', '[311, 311, 2*w^3 - 3*w^2 - 7*w + 7]', '[313, 313, -w^3 + 7*w + 2]', '[337, 337, 3*w^3 - 17*w - 10]', '[337, 337, 2*w^3 - 2*w^2 - 9*w - 5]', '[343, 7, -2*w^3 + w^2 + 8*w + 2]', '[347, 347, -3*w^3 + 17*w + 14]', '[347, 347, -3*w^3 - w^2 + 17*w + 13]', '[349, 349, 2*w^3 - w^2 - 8*w - 1]', '[349, 349, -w^3 + 3*w^2 + 4*w - 8]', '[353, 353, -w^3 - w^2 + 7*w + 4]', '[359, 359, -2*w^3 + 9*w + 10]', '[367, 367, 3*w^3 - 4*w^2 - 9*w + 4]', '[367, 367, -w^3 + w^2 + 4*w + 4]', '[367, 367, -w^3 + 3*w^2 + 3*w - 7]', '[373, 373, -w^2 + w - 2]', '[373, 373, -2*w^3 + 2*w^2 + 11*w - 2]', '[379, 379, -2*w^3 + 4*w^2 + 7*w - 8]', '[379, 379, -w^2 - 2]', '[389, 389, -w^3 - 2*w^2 + 5*w + 11]', '[397, 397, -2*w^3 + 4*w^2 + 7*w - 7]', '[401, 401, w^3 - 3*w^2 - 2*w + 10]', '[401, 401, -2*w^3 + 11*w + 4]', '[401, 401, 3*w^3 - 2*w^2 - 14*w - 4]', '[401, 401, -3*w^3 + 4*w^2 + 15*w - 5]', '[421, 421, -w^3 + w^2 + 7*w - 1]', '[421, 421, -2*w^3 + 2*w^2 + 9*w - 7]', '[433, 433, w^2 - w - 8]', '[439, 439, -w^3 + 3*w^2 + 4*w - 7]', '[443, 443, -2*w^3 + w^2 + 10*w - 2]', '[449, 449, w^2 + 2*w - 4]', '[449, 449, 2*w^3 - 2*w^2 - 10*w - 1]', '[461, 461, 2*w^3 - 2*w^2 - 6*w + 5]', '[461, 461, -2*w^3 + 4*w^2 + 7*w - 13]', '[463, 463, -3*w^3 + 3*w^2 + 12*w - 4]', '[463, 463, w - 5]', '[467, 467, -3*w^3 + w^2 + 16*w + 8]', '[467, 467, 2*w^2 - 3*w - 10]', '[479, 479, 2*w^2 - 4*w - 1]', '[479, 479, -w^3 + 2*w^2 + 2*w - 7]', '[487, 487, -3*w^3 + 5*w^2 + 12*w - 10]', '[503, 503, w^3 + 2*w^2 - 8*w - 8]', '[509, 509, -3*w^3 + 5*w^2 + 11*w - 5]', '[521, 521, 2*w^2 - 3*w - 11]', '[523, 523, -2*w^3 - w^2 + 13*w + 11]', '[523, 523, -2*w^3 + 4*w^2 + 8*w - 7]', '[541, 541, 3*w^3 - 2*w^2 - 13*w + 1]', '[563, 563, w^3 - 3*w - 5]', '[563, 563, -w^3 + 3*w^2 + 2*w - 11]', '[569, 569, -2*w^3 + 4*w^2 + 9*w - 4]', '[569, 569, 3*w^2 - w - 14]', '[571, 571, -w^3 + 8*w - 1]', '[577, 577, 3*w^3 - 2*w^2 - 16*w + 1]', '[587, 587, -4*w^3 + 5*w^2 + 18*w - 7]', '[587, 587, 2*w^3 + w^2 - 10*w - 7]', '[599, 599, 2*w^3 + w^2 - 11*w - 8]', '[607, 607, w^3 - 3*w + 4]', '[613, 613, 3*w^3 - w^2 - 14*w - 5]', '[613, 613, 3*w^2 - w - 11]', '[619, 619, 2*w^2 - 5*w - 8]', '[631, 631, -2*w^3 - 2*w^2 + 12*w + 19]', '[647, 647, 2*w^3 - 2*w^2 - 11*w - 2]', '[653, 653, 3*w^3 - 5*w^2 - 8*w + 7]', '[677, 677, -2*w^3 + 4*w^2 + 5*w - 8]', '[683, 683, 2*w^3 + w^2 - 12*w - 8]', '[683, 683, -w^3 + 3*w^2 - 8]', '[683, 683, -2*w^3 + 3*w^2 + 11*w - 8]', '[683, 683, -2*w^3 + 3*w^2 + 10*w - 2]', '[691, 691, w^2 - 4*w - 1]', '[709, 709, 3*w^3 - 2*w^2 - 13*w - 2]', '[709, 709, w^3 - 2*w^2 - 3*w - 2]', '[727, 727, -w^3 + 4*w^2 + 2*w - 7]', '[727, 727, -w^3 + 8*w + 5]', '[733, 733, 3*w^2 - 2*w - 10]', '[733, 733, -w^3 + 5*w + 8]', '[757, 757, 3*w^3 - 14*w - 8]', '[761, 761, -w^3 + 3*w^2 + 5*w - 10]', '[773, 773, -2*w^3 + 3*w^2 + 9*w - 1]', '[787, 787, -w^3 + 4*w - 4]', '[797, 797, w^2 + 2*w - 5]', '[797, 797, w^3 + w^2 - 5*w - 1]', '[809, 809, w^3 + 3*w^2 - 9*w - 17]', '[811, 811, -4*w^2 + 3*w + 17]', '[811, 811, w^3 - 2*w^2 - 8*w + 2]', '[823, 823, -4*w^3 + 4*w^2 + 17*w - 4]', '[857, 857, 3*w^2 - w - 16]', '[881, 881, -2*w^3 + 9*w + 1]', '[883, 883, w^3 - w^2 - 4*w - 5]', '[887, 887, 3*w^2 + w - 10]', '[911, 911, w^3 - 3*w - 7]', '[919, 919, -w^3 + w^2 + 3*w - 7]', '[919, 919, 3*w^3 - 2*w^2 - 12*w + 2]', '[929, 929, 3*w^3 - w^2 - 16*w - 2]', '[929, 929, w^3 + w^2 - 6*w - 2]', '[941, 941, -3*w^3 + 5*w^2 + 14*w - 14]', '[941, 941, -w^3 + 2*w^2 + 6*w - 8]', '[947, 947, 3*w^3 - 3*w^2 - 13*w - 5]', '[947, 947, 3*w^3 - 4*w^2 - 12*w + 2]', '[953, 953, -3*w^3 + 5*w^2 + 10*w - 10]', '[961, 31, -w^3 + 4*w^2 + 3*w - 13]', '[961, 31, -4*w^3 + 3*w^2 + 17*w - 4]', '[967, 967, -w^3 - 4*w^2 + 9*w + 19]', '[967, 967, w^3 + 5*w^2 - 9*w - 26]', '[971, 971, -3*w^3 + 6*w^2 + 13*w - 7]', '[971, 971, w^3 + 2*w^2 - 7*w - 7]', '[977, 977, 2*w^3 - 3*w^2 - 4*w - 2]', '[983, 983, 3*w^3 - 5*w^2 - 7*w + 7]', '[991, 991, 2*w^2 - w - 13]', '[991, 991, w^3 - 8*w - 4]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [3, -3, -6, 0, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 9909, 'disc_rad': 1101, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [0]], [5, [[3, 1], [1, 1]]], [7, [[3, 1], [1, 1]]], [11, [[3, 1], [1, 1]]], [13, [[3, 1], [1, 1]]], [17, [[3, 1], [1, 1]]], [19, [[4, 1]]], [23, [[4, 1]]], [29, [[3, 1], [1, 1]]], [31, [[2, 2]]], [37, [[3, 1], [1, 1]]], [41, [[2, 1], [1, 2]]], [43, [[4, 1]]], [47, [[2, 1], [1, 2]]], [53, [[2, 1], [1, 2]]], [59, [[4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [18, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 43.66907302809774, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.9909.1', 'local_algs': ['3.4.3.1', 'm367.1.1.0', 'm367.1.1.0', 'm367.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [3, 367], 'rd': 9.97717195092, 'regulator': {'__RealLiteral__': 0, 'data': '5.73611443522', 'prec': 44}, 'res': {'gal': ['81,0,-3645,0,49950,0,-273213,0,671166,0,-874143,0,658941,0,-299247,0,82369,0,-13406,0,1218,0,-56,0,1'], 'sib': ['-96,-84,135,27,-25,-1,1', '1,-42,-275,-73,765,93,-554,-54,163,13,-21,-1,1', '145,-164,-763,70,418,68,-34,-4,1', '3,-9,1,13,-6,-2,1', '64,272,-428,-1138,863,1319,-773,-479,242,61,-29,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)', '\\( a^{3} - a^{2} - 4 a + 2 \\)', '\\( a^{3} - a^{2} - 5 a + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}