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hmf_forms • Show schema
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{'deg': 4, 'dimension': 7, 'disc': 3981, 'field_bad_primes': [3, 1327], 'field_label': '4.4.3981.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.3981.1-53.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [53], 'level_ideal': '[53, 53, 2*w - 3]', 'level_label': '53.1', 'level_norm': 53, 'parallel_weight': 2, 'short_label': '53.1-b', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[53, 53, 2*w - 3]', 1]], 'hecke_eigenvalues': ['e', '1/4*e^6 - 5/4*e^5 - 3/4*e^4 + 51/4*e^3 - 18*e^2 - 3/4*e + 11/2', '1/2*e^6 - 5/2*e^5 - 5/2*e^4 + 51/2*e^3 - 27*e^2 - 9/2*e + 7', '-3/2*e^6 + 9/2*e^5 + 25/2*e^4 - 95/2*e^3 + 25*e^2 + 25/2*e - 5', '5/4*e^6 - 13/4*e^5 - 47/4*e^4 + 143/4*e^3 - 6*e^2 - 83/4*e + 3/2', '-1/2*e^6 + 5/2*e^5 + 7/2*e^4 - 53/2*e^3 + 17*e^2 + 35/2*e - 3', '2*e^6 - 7*e^5 - 15*e^4 + 73*e^3 - 52*e^2 - 16*e + 14', 'e^6 - 3*e^5 - 9*e^4 + 31*e^3 - 11*e^2 - 6*e + 2', 'e^4 + e^3 - 9*e^2 - 3*e + 4', '11/4*e^6 - 39/4*e^5 - 77/4*e^4 + 405/4*e^3 - 85*e^2 - 73/4*e + 53/2', -1, '-3/2*e^6 + 7/2*e^5 + 25/2*e^4 - 75/2*e^3 + 20*e^2 + 7/2*e + 1', '-1/2*e^6 - 1/2*e^5 + 15/2*e^4 + 5/2*e^3 - 30*e^2 + 19/2*e + 9', '2*e^6 - 7*e^5 - 14*e^4 + 74*e^3 - 61*e^2 - 20*e + 19', '-1/2*e^6 + 3/2*e^5 + 13/2*e^4 - 35/2*e^3 - 14*e^2 + 53/2*e + 5', '3/2*e^6 - 9/2*e^5 - 23/2*e^4 + 97/2*e^3 - 35*e^2 - 41/2*e + 19', '-2*e^6 + 8*e^5 + 14*e^4 - 83*e^3 + 65*e^2 + 24*e - 18', '-3/2*e^6 + 11/2*e^5 + 23/2*e^4 - 117/2*e^3 + 37*e^2 + 49/2*e - 9', '-7/2*e^6 + 19/2*e^5 + 59/2*e^4 - 203/2*e^3 + 51*e^2 + 53/2*e - 13', '7/2*e^6 - 25/2*e^5 - 51/2*e^4 + 261/2*e^3 - 97*e^2 - 67/2*e + 21', '-6*e^6 + 19*e^5 + 46*e^4 - 202*e^3 + 139*e^2 + 60*e - 35', 'e^6 - 5*e^5 - 4*e^4 + 51*e^3 - 64*e^2 - 5*e + 26', '-3/2*e^6 + 11/2*e^5 + 17/2*e^4 - 115/2*e^3 + 65*e^2 + 11/2*e - 19', '-5*e^6 + 16*e^5 + 40*e^4 - 169*e^3 + 102*e^2 + 51*e - 30', '-e^6 + e^5 + 12*e^4 - 13*e^3 - 27*e^2 + 13*e + 20', '4*e^6 - 12*e^5 - 33*e^4 + 127*e^3 - 70*e^2 - 36*e + 23', '-9/2*e^6 + 33/2*e^5 + 61/2*e^4 - 347/2*e^3 + 149*e^2 + 89/2*e - 43', '1/2*e^6 + 1/2*e^5 - 21/2*e^4 - 5/2*e^3 + 60*e^2 - 45/2*e - 27', '9/2*e^6 - 31/2*e^5 - 71/2*e^4 + 325/2*e^3 - 101*e^2 - 97/2*e + 32', '7/4*e^6 - 15/4*e^5 - 65/4*e^4 + 165/4*e^3 - 10*e^2 - 69/4*e + 25/2', '3*e^6 - 10*e^5 - 25*e^4 + 107*e^3 - 53*e^2 - 52*e + 12', '11/4*e^6 - 35/4*e^5 - 93/4*e^4 + 373/4*e^3 - 42*e^2 - 161/4*e + 29/2', '-3/2*e^6 + 11/2*e^5 + 27/2*e^4 - 115/2*e^3 + 18*e^2 + 55/2*e + 8', '-5/2*e^6 + 13/2*e^5 + 49/2*e^4 - 141/2*e^3 + 3*e^2 + 73/2*e - 3', '5/2*e^6 - 15/2*e^5 - 41/2*e^4 + 157/2*e^3 - 46*e^2 - 29/2*e + 21', '-4*e^6 + 14*e^5 + 31*e^4 - 146*e^3 + 96*e^2 + 36*e - 34', '1/2*e^6 - 3/2*e^5 - 5/2*e^4 + 35/2*e^3 - 24*e^2 - 31/2*e + 17', '-3/2*e^6 + 17/2*e^5 + 9/2*e^4 - 171/2*e^3 + 114*e^2 + 13/2*e - 33', '3/2*e^6 - 9/2*e^5 - 25/2*e^4 + 91/2*e^3 - 26*e^2 + 3/2*e + 11', '-7*e^6 + 23*e^5 + 55*e^4 - 242*e^3 + 153*e^2 + 74*e - 41', '5*e^6 - 15*e^5 - 38*e^4 + 158*e^3 - 118*e^2 - 26*e + 45', '-9/2*e^6 + 33/2*e^5 + 65/2*e^4 - 343/2*e^3 + 132*e^2 + 77/2*e - 33', 'e^6 - e^5 - 14*e^4 + 13*e^3 + 41*e^2 - 22*e - 12', '13/4*e^6 - 45/4*e^5 - 95/4*e^4 + 467/4*e^3 - 92*e^2 - 83/4*e + 55/2', '4*e^6 - 13*e^5 - 29*e^4 + 137*e^3 - 109*e^2 - 31*e + 35', '7/4*e^6 - 7/4*e^5 - 73/4*e^4 + 89/4*e^3 + 18*e^2 - 33/4*e - 19/2', '2*e^5 - 6*e^4 - 18*e^3 + 62*e^2 - 21*e - 20', '19/4*e^6 - 67/4*e^5 - 145/4*e^4 + 701/4*e^3 - 118*e^2 - 205/4*e + 69/2', '11/2*e^6 - 37/2*e^5 - 77/2*e^4 + 385/2*e^3 - 167*e^2 - 47/2*e + 56', '7/4*e^6 - 27/4*e^5 - 61/4*e^4 + 289/4*e^3 - 27*e^2 - 193/4*e + 33/2', '2*e^6 - 3*e^5 - 23*e^4 + 37*e^3 + 38*e^2 - 43*e - 6', '-11/2*e^6 + 35/2*e^5 + 81/2*e^4 - 373/2*e^3 + 143*e^2 + 111/2*e - 46', '-2*e^4 + 3*e^3 + 20*e^2 - 33*e - 3', 'e^6 - 7*e^5 + e^4 + 70*e^3 - 118*e^2 - 2*e + 52', '7/4*e^6 - 27/4*e^5 - 49/4*e^4 + 277/4*e^3 - 58*e^2 - 45/4*e + 33/2', '3/4*e^6 - 27/4*e^5 + 11/4*e^4 + 269/4*e^3 - 109*e^2 - 1/4*e + 41/2', '-13/4*e^6 + 37/4*e^5 + 111/4*e^4 - 407/4*e^3 + 42*e^2 + 227/4*e - 3/2', '-1/2*e^6 + 3/2*e^5 + 13/2*e^4 - 37/2*e^3 - 14*e^2 + 69/2*e + 1', 'e^6 - 14*e^4 + 7*e^3 + 48*e^2 - 45*e - 6', '11/2*e^6 - 27/2*e^5 - 95/2*e^4 + 289/2*e^3 - 63*e^2 - 55/2*e + 9', '9/4*e^6 - 5/4*e^5 - 115/4*e^4 + 71/4*e^3 + 78*e^2 - 55/4*e - 85/2', '5/2*e^6 - 15/2*e^5 - 47/2*e^4 + 163/2*e^3 - 15*e^2 - 107/2*e - 5', '4*e^6 - 13*e^5 - 34*e^4 + 140*e^3 - 62*e^2 - 76*e + 26', '9/2*e^6 - 33/2*e^5 - 65/2*e^4 + 341/2*e^3 - 129*e^2 - 67/2*e + 35', '-5*e^6 + 19*e^5 + 34*e^4 - 198*e^3 + 169*e^2 + 51*e - 46', '3*e^6 - 9*e^5 - 26*e^4 + 96*e^3 - 43*e^2 - 46*e + 30', '5*e^6 - 15*e^5 - 42*e^4 + 161*e^3 - 77*e^2 - 63*e + 10', '-3/2*e^6 + 7/2*e^5 + 35/2*e^4 - 77/2*e^3 - 27*e^2 + 69/2*e + 19', '-17/2*e^6 + 49/2*e^5 + 141/2*e^4 - 523/2*e^3 + 138*e^2 + 167/2*e - 34', '-5*e^6 + 18*e^5 + 34*e^4 - 186*e^3 + 166*e^2 + 19*e - 56', 'e^6 - 5*e^5 - 5*e^4 + 50*e^3 - 56*e^2 - 6*e + 26', '-9*e^6 + 30*e^5 + 73*e^4 - 315*e^3 + 177*e^2 + 95*e - 46', '29/4*e^6 - 113/4*e^5 - 191/4*e^4 + 1179/4*e^3 - 262*e^2 - 311/4*e + 151/2', '-5/2*e^6 + 23/2*e^5 + 27/2*e^4 - 239/2*e^3 + 126*e^2 + 69/2*e - 41', '7/2*e^6 - 23/2*e^5 - 49/2*e^4 + 239/2*e^3 - 104*e^2 - 11/2*e + 35', '-8*e^6 + 26*e^5 + 58*e^4 - 273*e^3 + 219*e^2 + 56*e - 72', 'e^6 + e^5 - 16*e^4 - 5*e^3 + 71*e^2 - 20*e - 32', '25/2*e^6 - 75/2*e^5 - 211/2*e^4 + 799/2*e^3 - 192*e^2 - 271/2*e + 41', '-7/2*e^6 + 11/2*e^5 + 75/2*e^4 - 137/2*e^3 - 38*e^2 + 147/2*e + 15', '-4*e^6 + 9*e^5 + 37*e^4 - 96*e^3 + 19*e^2 + 15*e + 1', '-17/2*e^6 + 55/2*e^5 + 141/2*e^4 - 577/2*e^3 + 151*e^2 + 169/2*e - 39', '17/2*e^6 - 57/2*e^5 - 127/2*e^4 + 597/2*e^3 - 219*e^2 - 161/2*e + 62', '-11/2*e^6 + 35/2*e^5 + 87/2*e^4 - 369/2*e^3 + 117*e^2 + 107/2*e - 28', '-25/2*e^6 + 83/2*e^5 + 195/2*e^4 - 879/2*e^3 + 280*e^2 + 289/2*e - 66', '17/2*e^6 - 51/2*e^5 - 135/2*e^4 + 545/2*e^3 - 169*e^2 - 173/2*e + 51', '-7/2*e^6 + 25/2*e^5 + 51/2*e^4 - 265/2*e^3 + 102*e^2 + 111/2*e - 43', '-5*e^6 + 21*e^5 + 33*e^4 - 216*e^3 + 184*e^2 + 50*e - 56', '-9/2*e^6 + 39/2*e^5 + 39/2*e^4 - 401/2*e^3 + 264*e^2 + 15/2*e - 92', '4*e^6 - 7*e^5 - 42*e^4 + 80*e^3 + 34*e^2 - 43*e - 14', '6*e^5 - 13*e^4 - 57*e^3 + 144*e^2 - 11*e - 54', '11/2*e^6 - 23/2*e^5 - 113/2*e^4 + 253/2*e^3 + 27*e^2 - 133/2*e - 21', '-3/2*e^6 + 15/2*e^5 + 7/2*e^4 - 151/2*e^3 + 119*e^2 - 33/2*e - 41', '-17/2*e^6 + 61/2*e^5 + 125/2*e^4 - 631/2*e^3 + 238*e^2 + 119/2*e - 71', '3*e^6 - 10*e^5 - 29*e^4 + 104*e^3 - 13*e^2 - 46*e - 12', '-8*e^6 + 32*e^5 + 47*e^4 - 332*e^3 + 343*e^2 + 64*e - 108', '13/4*e^6 - 33/4*e^5 - 139/4*e^4 + 355/4*e^3 + 25*e^2 - 211/4*e - 61/2', '27/2*e^6 - 85/2*e^5 - 221/2*e^4 + 895/2*e^3 - 246*e^2 - 269/2*e + 49', '2*e^6 - 11*e^5 - 7*e^4 + 112*e^3 - 143*e^2 - 18*e + 43', '3/2*e^6 - 17/2*e^5 - 11/2*e^4 + 179/2*e^3 - 107*e^2 - 95/2*e + 45', '-2*e^6 + 5*e^5 + 22*e^4 - 56*e^3 - 21*e^2 + 61*e + 2', '-9/2*e^6 + 19/2*e^5 + 93/2*e^4 - 209/2*e^3 - 22*e^2 + 101/2*e + 19', '19/4*e^6 - 75/4*e^5 - 117/4*e^4 + 761/4*e^3 - 195*e^2 + 23/4*e + 129/2', '1/2*e^6 - 13/2*e^5 + 21/2*e^4 + 127/2*e^3 - 163*e^2 + 39/2*e + 73', '7/2*e^6 - 23/2*e^5 - 59/2*e^4 + 245/2*e^3 - 58*e^2 - 133/2*e + 23', '-11/2*e^6 + 33/2*e^5 + 91/2*e^4 - 353/2*e^3 + 96*e^2 + 149/2*e - 43', '15*e^6 - 50*e^5 - 120*e^4 + 527*e^3 - 309*e^2 - 178*e + 79', '10*e^6 - 34*e^5 - 71*e^4 + 357*e^3 - 289*e^2 - 86*e + 70', '7/2*e^6 - 25/2*e^5 - 65/2*e^4 + 257/2*e^3 - 36*e^2 - 69/2*e - 7', '-7/2*e^6 + 39/2*e^5 + 21/2*e^4 - 391/2*e^3 + 262*e^2 + 15/2*e - 76', '-9*e^6 + 28*e^5 + 78*e^4 - 300*e^3 + 123*e^2 + 131*e - 42', '-23/2*e^6 + 77/2*e^5 + 181/2*e^4 - 803/2*e^3 + 254*e^2 + 183/2*e - 63', '-2*e^6 + 14*e^5 + e^4 - 142*e^3 + 211*e^2 + 26*e - 90', '2*e^6 - 10*e^5 - 7*e^4 + 102*e^3 - 137*e^2 - 18*e + 44', '-5*e^6 + 19*e^5 + 35*e^4 - 198*e^3 + 160*e^2 + 61*e - 48', 'e^5 - 7*e^4 - 4*e^3 + 71*e^2 - 61*e - 12', '-23/2*e^6 + 73/2*e^5 + 189/2*e^4 - 769/2*e^3 + 207*e^2 + 247/2*e - 53', '-5*e^6 + 16*e^5 + 38*e^4 - 173*e^3 + 116*e^2 + 86*e - 28', '-7/2*e^6 + 17/2*e^5 + 61/2*e^4 - 199/2*e^3 + 37*e^2 + 173/2*e - 23', '-9*e^6 + 34*e^5 + 63*e^4 - 352*e^3 + 285*e^2 + 71*e - 78', '-12*e^6 + 39*e^5 + 98*e^4 - 412*e^3 + 229*e^2 + 145*e - 58', '11/2*e^6 - 39/2*e^5 - 89/2*e^4 + 411/2*e^3 - 116*e^2 - 149/2*e + 47', '-7/2*e^6 + 17/2*e^5 + 55/2*e^4 - 177/2*e^3 + 70*e^2 - 49/2*e - 37', '-15/2*e^6 + 51/2*e^5 + 119/2*e^4 - 543/2*e^3 + 155*e^2 + 231/2*e - 31', '11/2*e^6 - 31/2*e^5 - 87/2*e^4 + 337/2*e^3 - 107*e^2 - 145/2*e + 38', '-1/2*e^6 + 7/2*e^5 + 9/2*e^4 - 61/2*e^3 + 12*e^2 - 37/2*e + 3', '9/2*e^6 - 31/2*e^5 - 65/2*e^4 + 331/2*e^3 - 120*e^2 - 131/2*e + 7', '5*e^6 - 24*e^5 - 28*e^4 + 247*e^3 - 244*e^2 - 63*e + 86', '-2*e^6 + 12*e^5 + 8*e^4 - 119*e^3 + 134*e^2 + 7*e - 46', '-1/2*e^6 - 3/2*e^5 + 21/2*e^4 + 29/2*e^3 - 60*e^2 + 3/2*e', '-2*e^6 + 12*e^5 + 9*e^4 - 118*e^3 + 125*e^2 + 7*e - 34', '19/4*e^6 - 67/4*e^5 - 145/4*e^4 + 701/4*e^3 - 114*e^2 - 181/4*e + 61/2', '3/2*e^6 - 17/2*e^5 - 15/2*e^4 + 179/2*e^3 - 79*e^2 - 93/2*e + 9', '5/2*e^6 - 33/2*e^5 - 13/2*e^4 + 329/2*e^3 - 205*e^2 - 43/2*e + 56', '-43/4*e^6 + 155/4*e^5 + 321/4*e^4 - 1617/4*e^3 + 290*e^2 + 445/4*e - 169/2', '1/2*e^6 - 17/2*e^5 + 19/2*e^4 + 163/2*e^3 - 161*e^2 + 33/2*e + 57', '-9/2*e^6 + 33/2*e^5 + 51/2*e^4 - 347/2*e^3 + 197*e^2 + 67/2*e - 63', '-15/4*e^6 + 71/4*e^5 + 117/4*e^4 - 749/4*e^3 + 101*e^2 + 473/4*e - 53/2', '13/2*e^6 - 39/2*e^5 - 125/2*e^4 + 421/2*e^3 - 28*e^2 - 259/2*e + 15', '-e^6 + 2*e^5 + 12*e^4 - 20*e^3 - 28*e^2 - 7*e + 48', '11*e^6 - 34*e^5 - 95*e^4 + 361*e^3 - 151*e^2 - 122*e + 12', '-4*e^6 + 11*e^5 + 31*e^4 - 119*e^3 + 84*e^2 + 32*e - 17', '-1/2*e^6 + 11/2*e^5 - 7/2*e^4 - 91/2*e^3 + 97*e^2 - 137/2*e - 23', '17/2*e^6 - 35/2*e^5 - 169/2*e^4 + 395/2*e^3 + 18*e^2 - 225/2*e - 18', '-1/2*e^6 + 15/2*e^5 - 29/2*e^4 - 141/2*e^3 + 203*e^2 - 93/2*e - 75', '2*e^5 - 6*e^4 - 18*e^3 + 64*e^2 - 13*e - 32', '9/4*e^6 - 13/4*e^5 - 111/4*e^4 + 159/4*e^3 + 56*e^2 - 195/4*e - 29/2', '15/2*e^6 - 45/2*e^5 - 131/2*e^4 + 485/2*e^3 - 91*e^2 - 237/2*e + 3', '-6*e^5 + 5*e^4 + 61*e^3 - 62*e^2 - 45*e - 14', '-5/4*e^6 + 29/4*e^5 + 7/4*e^4 - 295/4*e^3 + 114*e^2 + 51/4*e - 119/2', '-21/2*e^6 + 63/2*e^5 + 179/2*e^4 - 673/2*e^3 + 158*e^2 + 257/2*e - 51', '7*e^6 - 21*e^5 - 65*e^4 + 222*e^3 - 49*e^2 - 83*e - 9', '-19/2*e^6 + 67/2*e^5 + 149/2*e^4 - 703/2*e^3 + 221*e^2 + 237/2*e - 62', '15/2*e^6 - 43/2*e^5 - 127/2*e^4 + 465/2*e^3 - 105*e^2 - 189/2*e + 12', '-2*e^6 + 10*e^5 + 7*e^4 - 99*e^3 + 139*e^2 - 9*e - 67', '-5*e^6 + 19*e^5 + 31*e^4 - 197*e^3 + 191*e^2 + 33*e - 46', '-39/4*e^6 + 147/4*e^5 + 265/4*e^4 - 1517/4*e^3 + 327*e^2 + 297/4*e - 201/2', '-13/2*e^6 + 35/2*e^5 + 125/2*e^4 - 373/2*e^3 + 19*e^2 + 153/2*e + 13', '15/2*e^6 - 47/2*e^5 - 111/2*e^4 + 483/2*e^3 - 193*e^2 - 7/2*e + 61', '-10*e^6 + 24*e^5 + 93*e^4 - 258*e^3 + 54*e^2 + 85*e - 6', '61/4*e^6 - 197/4*e^5 - 499/4*e^4 + 2079/4*e^3 - 290*e^2 - 687/4*e + 167/2', '-15/2*e^6 + 65/2*e^5 + 97/2*e^4 - 665/2*e^3 + 294*e^2 + 131/2*e - 108', '3*e^6 - 11*e^5 - 15*e^4 + 116*e^3 - 148*e^2 - 15*e + 57', '7/2*e^6 - 21/2*e^5 - 67/2*e^4 + 223/2*e^3 - 12*e^2 - 83/2*e - 31', '-e^6 + 5*e^5 - 6*e^4 - 47*e^3 + 160*e^2 - 66*e - 60', '-11/2*e^6 + 45/2*e^5 + 73/2*e^4 - 471/2*e^3 + 193*e^2 + 155/2*e - 51', '-20*e^6 + 65*e^5 + 154*e^4 - 689*e^3 + 461*e^2 + 221*e - 114', '2*e^6 + 4*e^5 - 32*e^4 - 32*e^3 + 146*e^2 - 13*e - 54', '45/4*e^6 - 149/4*e^5 - 355/4*e^4 + 1559/4*e^3 - 251*e^2 - 387/4*e + 175/2', '-3*e^6 + 7*e^5 + 26*e^4 - 77*e^3 + 28*e^2 + 20*e + 10'], 'hecke_polynomial': 'x^7 - 3*x^6 - 9*x^5 + 33*x^4 - 10*x^3 - 23*x^2 + 4*x + 4', 'label': '4.4.3981.1-53.1-b'}
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hmf_fields • Show schema
Hide schema
{'degree': 4, 'discriminant': 3981, 'ideals': ['[1, 1, 1]', '[3, 3, w + 1]', '[5, 5, w^3 - w^2 - 3*w + 1]', '[9, 3, -w^2 + 2]', '[9, 3, -w^2 + w + 2]', '[13, 13, -w^3 + w^2 + 4*w]', '[15, 15, w^3 - 4*w]', '[16, 2, 2]', '[23, 23, w^2 - 2*w - 2]', '[25, 25, -w^3 + 2*w^2 + 4*w - 3]', '[27, 3, w^3 - 2*w^2 - 2*w + 4]', '[27, 9, -w^3 + 3*w + 2]', '[37, 37, w^3 - 4*w + 1]', '[37, 37, w^3 - w^2 - 5*w + 1]', '[39, 39, -w^2 - w + 3]', '[41, 41, w^3 - 5*w + 1]', '[43, 43, 2*w^3 - w^2 - 7*w]', '[45, 15, w^3 - w^2 - 5*w + 2]', '[45, 15, -w^3 + w^2 + 2*w - 3]', '[48, 6, 2*w + 2]', '[53, 53, 2*w - 3]', '[59, 59, -2*w^3 + w^2 + 9*w - 1]', '[65, 65, w^3 - 3*w - 3]', '[67, 67, -w - 3]', '[67, 67, w^3 + w^2 - 5*w - 4]', '[69, 69, w^3 - 5*w + 2]', '[71, 71, 2*w^3 - 3*w^2 - 7*w + 5]', '[73, 73, w^3 - 6*w]', '[73, 73, -w^3 - w^2 + 5*w + 3]', '[75, 75, -w^2 + 2*w + 3]', '[79, 79, w^3 - 3*w - 4]', '[80, 10, 2*w^3 - 2*w^2 - 6*w + 2]', '[81, 3, 3]', '[81, 9, -w^3 + 2*w^2 + 4*w - 2]', '[81, 9, -2*w^3 + 2*w^2 + 7*w - 1]', '[83, 83, w^3 - 2*w^2 - 3*w + 1]', '[83, 83, -2*w^3 + 2*w^2 + 6*w - 3]', '[89, 89, 2*w^3 - w^2 - 7*w + 3]', '[89, 89, -2*w^3 + w^2 + 8*w - 2]', '[97, 97, 2*w^3 - 8*w - 1]', '[103, 103, -2*w^3 + 3*w^2 + 5*w - 2]', '[103, 103, w^2 + w - 4]', '[111, 111, -2*w^2 + 5]', '[111, 111, -w^3 + w^2 + w + 2]', '[113, 113, 2*w^3 - w^2 - 7*w + 4]', '[115, 115, -2*w^2 + 3]', '[117, 39, -2*w^3 + 9*w + 1]', '[117, 39, -2*w^3 + 7*w]', '[123, 123, 2*w^3 - w^2 - 6*w]', '[125, 5, -2*w^3 + w^2 + 6*w - 1]', '[125, 125, w^3 - w^2 - 6*w]', '[129, 129, -w^3 + w^2 + 3*w - 5]', '[131, 131, -2*w^3 + 2*w^2 + 5*w - 3]', '[131, 131, -4*w^3 + 5*w^2 + 13*w - 9]', '[135, 15, w^3 - 2*w^2 - 5*w + 1]', '[135, 45, 2*w^3 - 2*w^2 - 7*w]', '[137, 137, w^3 - 2*w^2 - 4*w + 1]', '[137, 137, 2*w^2 - 2*w - 3]', '[137, 137, 3*w^3 - 2*w^2 - 10*w - 1]', '[137, 137, w - 4]', '[139, 139, w^2 - 2*w - 4]', '[144, 6, -2*w^2 + 4]', '[144, 6, -2*w^2 + 2*w + 4]', '[149, 149, 2*w^3 - 7*w - 4]', '[151, 151, -2*w^3 + 4*w^2 + 7*w - 9]', '[157, 157, -w^3 + 3*w^2 + 2*w - 7]', '[159, 159, 2*w^2 - w - 3]', '[169, 169, -2*w^3 + w^2 + 8*w - 3]', '[173, 173, w^2 + w - 5]', '[173, 173, -w^3 + 3*w^2 + 3*w - 5]', '[177, 177, -3*w^3 + 2*w^2 + 12*w + 1]', '[179, 179, -w^3 + w^2 + 6*w - 3]', '[181, 181, 3*w^3 - 4*w^2 - 11*w + 7]', '[185, 185, -2*w^2 + w + 5]', '[185, 185, w^3 - 2*w^2 - w + 4]', '[191, 191, -2*w^3 + 2*w^2 + 9*w - 3]', '[191, 191, 2*w^3 + w^2 - 9*w - 4]', '[193, 193, -2*w^3 + 3*w^2 + 9*w - 6]', '[195, 195, 2*w^3 - 3*w^2 - 7*w + 4]', '[197, 197, -w^3 + w^2 + 6*w - 1]', '[199, 199, 2*w^2 - w - 4]', '[201, 201, -w^2 - 4*w - 3]', '[201, 201, 3*w^3 - 11*w - 5]', '[205, 205, -w^3 + 2*w^2 + 6*w - 4]', '[207, 69, w^3 - 2*w - 3]', '[207, 69, w^3 - 3*w^2 - 3*w + 7]', '[208, 26, -2*w^3 + 2*w^2 + 8*w]', '[211, 211, w^3 - 5*w - 5]', '[213, 213, w^3 - 2*w^2 - 6*w + 3]', '[215, 215, -w^3 + 4*w + 5]', '[219, 219, -3*w^3 + 10*w + 4]', '[219, 219, 2*w^3 - 2*w^2 - 8*w - 1]', '[223, 223, w^3 + 2*w^2 - 4*w - 7]', '[223, 223, 2*w^3 - w^2 - 8*w - 4]', '[225, 75, -2*w^3 + w^2 + 8*w - 4]', '[225, 75, w^3 - 3*w^2 - 2*w + 6]', '[227, 227, -3*w^3 + 4*w^2 + 8*w - 6]', '[229, 229, w^3 - 3*w - 6]', '[229, 229, 2*w^3 - 2*w^2 - 9*w - 1]', '[233, 233, 2*w^3 - w^2 - 10*w + 6]', '[233, 233, -w^3 + 7*w - 2]', '[237, 237, 2*w^3 + w^2 - 9*w - 5]', '[240, 30, 2*w^3 - 8*w]', '[243, 9, w^3 - 2*w^2 - 5*w + 7]', '[243, 9, 3*w + 3]', '[243, 27, -w^3 - w^2 + 7*w + 4]', '[249, 249, -w^2 - 4*w]', '[249, 249, -2*w^3 + 7*w - 1]', '[256, 4, 4]', '[257, 257, 3*w^3 - 2*w^2 - 10*w + 3]', '[257, 257, 3*w^3 - 2*w^2 - 10*w]', '[263, 263, 3*w + 4]', '[265, 265, -2*w^3 - w^2 + 6*w]', '[267, 267, -3*w^3 + w^2 + 10*w]', '[267, 267, 3*w^3 - 8*w + 1]', '[269, 269, w^3 + w^2 - 3*w - 5]', '[281, 281, 2*w^3 - 9*w]', '[281, 281, -2*w^3 + w^2 + 9*w - 5]', '[283, 283, 3*w^3 - 3*w^2 - 9*w + 2]', '[283, 283, 3*w^3 - w^2 - 10*w - 1]', '[291, 291, 4*w^3 - 13*w - 3]', '[295, 295, 3*w^2 - 3*w - 8]', '[299, 299, 3*w - 5]', '[309, 309, -w^3 + 7*w]', '[309, 309, w^3 + 2*w^2 - 3*w - 4]', '[311, 311, -w^3 + 7*w - 1]', '[317, 317, -w^3 + w^2 + 4*w - 6]', '[317, 317, -w^3 - w^2 + 6*w - 1]', '[325, 325, -3*w^3 + 3*w^2 + 10*w - 1]', '[333, 111, w^3 - w^2 - 2*w - 4]', '[333, 111, 2*w^3 - 3*w^2 - 6*w + 2]', '[333, 111, 3*w^3 - 2*w^2 - 10*w + 1]', '[333, 111, 2*w^3 - 7*w - 6]', '[335, 335, -3*w^3 + w^2 + 14*w]', '[335, 335, -3*w^3 + 2*w^2 + 10*w - 2]', '[339, 339, 3*w^3 - 7*w + 2]', '[345, 345, w^3 + 2*w^2 - 6*w - 7]', '[349, 349, 3*w^3 - w^2 - 13*w + 1]', '[351, 39, -2*w^3 + w^2 + 10*w - 2]', '[351, 117, w^3 - 2*w^2 - w + 5]', '[353, 353, w^3 + w^2 - 2*w - 4]', '[355, 355, 2*w^3 - 3*w^2 - 9*w + 10]', '[359, 359, 3*w^2 - 10]', '[365, 365, 2*w^3 - 11*w - 1]', '[365, 365, -3*w^2 + 4*w + 5]', '[368, 46, 2*w^2 - 4*w - 4]', '[369, 123, 2*w^3 - 3*w^2 - 7*w + 3]', '[369, 123, -w^3 + 3*w - 4]', '[373, 373, -w^3 + 2*w^2 + 7*w - 1]', '[375, 15, -3*w^3 - w^2 + 9*w + 1]', '[375, 375, 2*w^3 - 10*w + 1]', '[379, 379, -3*w^3 + 3*w^2 + 9*w - 5]', '[387, 129, 2*w^3 - 2*w^2 - 10*w + 1]', '[387, 129, 3*w^3 - w^2 - 14*w - 1]', '[393, 393, -2*w^3 - w^2 + 6*w - 1]', '[393, 393, -3*w^3 + 2*w^2 + 12*w - 5]', '[395, 395, -4*w^3 + 4*w^2 + 13*w - 2]', '[397, 397, -2*w^3 + w^2 + 10*w - 1]', '[400, 50, -2*w^3 + 4*w^2 + 8*w - 6]', '[405, 15, 3*w^3 - 3*w^2 - 9*w + 3]', '[405, 45, w^2 + 2*w - 5]', '[405, 45, 3*w^3 - 2*w^2 - 9*w + 4]', '[409, 409, 4*w^3 - 5*w^2 - 12*w + 5]', '[411, 411, w^2 - 3*w - 4]', '[411, 411, -2*w^2 - 5*w]', '[411, 411, 2*w^3 - 5*w - 3]', '[411, 411, 4*w^3 - 17*w - 4]', '[415, 415, -w^3 + w^2 + 3]', '[415, 415, -w^3 + w^2 + 5*w - 7]', '[417, 417, w^3 - w^2 - 6*w - 4]', '[419, 419, 2*w^3 - 5*w^2 - 3*w + 8]', '[419, 419, w^2 - w - 7]', '[421, 421, -2*w^3 + 8*w - 1]', '[431, 431, w^3 - 2*w - 5]', '[431, 431, w^3 + 2*w^2 - 4*w - 6]', '[432, 6, 2*w^3 - 4*w^2 - 4*w + 8]', '[432, 18, -2*w^3 + 6*w + 4]', '[433, 433, -3*w^3 + 3*w^2 + 8*w - 8]', '[433, 433, -3*w^3 + 4*w^2 + 11*w - 6]', '[439, 439, -3*w^3 + 3*w^2 + 9*w - 4]', '[439, 439, -3*w^3 + 3*w^2 + 11*w - 2]', '[445, 445, 2*w^3 - 3*w^2 - 5*w + 8]', '[445, 445, -w^3 + 3*w^2 + w - 8]', '[447, 447, 4*w^3 + w^2 - 15*w - 6]', '[449, 449, 2*w^2 - 3*w - 6]', '[449, 449, -w^2 + w - 3]', '[453, 453, -w^3 - 2*w^2 + 6*w + 4]', '[463, 463, -w^3 - w^2 + 9*w + 2]', '[471, 471, w^3 + w^2 - 3*w - 6]', '[477, 159, 2*w^3 + w^2 - 4*w - 3]', '[477, 159, -2*w^3 + 3*w^2 + 4*w - 6]', '[481, 481, w^3 + 2*w^2 - 4*w - 4]', '[481, 481, 4*w^3 - 4*w^2 - 13*w + 8]', '[485, 485, -w^3 - w^2 + 7*w + 5]', '[491, 491, -3*w^2 + 3*w + 10]', '[491, 491, 5*w^3 - 7*w^2 - 16*w + 12]', '[499, 499, -2*w^3 + 9*w - 1]', '[503, 503, -w^3 + 2*w^2 - 4]', '[503, 503, -4*w^3 + 7*w^2 + 12*w - 15]', '[507, 507, -3*w^3 + w^2 + 9*w - 1]', '[509, 509, 4*w^3 - w^2 - 14*w + 1]', '[515, 515, -3*w^3 + 4*w^2 + 10*w - 5]', '[515, 515, -4*w - 3]', '[519, 519, w^3 + 2*w^2 - 4]', '[519, 519, w^3 + 2*w^2 - 4*w - 5]', '[529, 529, -w^3 + 2*w^2 + w - 6]', '[531, 177, -4*w^3 + 3*w^2 + 14*w - 3]', '[531, 177, -5*w^3 + 4*w^2 + 17*w - 1]', '[533, 533, w^3 + 2*w^2 - 6*w - 5]', '[537, 537, -w^3 + 3*w^2 + 5*w - 2]', '[541, 541, 3*w^3 - 2*w^2 - 9*w]', '[543, 543, 2*w^3 - 3*w^2 - 10*w + 4]', '[555, 555, 3*w^3 - 3*w^2 - 13*w + 5]', '[555, 555, -3*w^3 + 4*w^2 + 13*w - 9]', '[557, 557, 2*w^3 - 3*w^2 - 7*w + 2]', '[559, 559, w^2 + 3]', '[563, 563, 4*w^3 - 2*w^2 - 17*w + 3]', '[565, 565, 3*w^3 - 4*w^2 - 8*w + 9]', '[569, 569, 2*w^3 - w^2 - 9*w - 5]', '[573, 573, 5*w^3 - 17*w - 6]', '[573, 573, -2*w^3 + 3*w^2 + 10*w - 1]', '[575, 575, w^3 - w^2 - 7*w + 3]', '[577, 577, -3*w^3 + 3*w^2 + 7*w]', '[577, 577, 3*w^3 - 2*w^2 - 9*w + 3]', '[579, 579, -w^3 + 4*w^2 + 7*w - 4]', '[585, 195, w^2 - 3*w - 5]', '[585, 195, w^3 - 2*w^2 - 7*w + 2]', '[591, 591, -w^3 + 3*w^2 + 7*w]', '[592, 74, 2*w^3 - 8*w + 2]', '[592, 74, 2*w^3 - 2*w^2 - 10*w + 2]', '[597, 597, 2*w^3 + w^2 - 5*w - 4]', '[601, 601, -3*w^3 + 3*w^2 + 13*w - 1]', '[603, 201, w^3 + 3*w^2 - 2*w - 6]', '[603, 201, w^3 + 2*w^2 - 5*w - 6]', '[603, 201, 3*w^3 - w^2 - 11*w - 7]', '[603, 201, w^3 - 5*w - 6]', '[607, 607, w^2 + 2*w - 6]', '[613, 613, -2*w^3 - 2*w^2 + 9*w + 4]', '[613, 613, -3*w^3 + 4*w^2 + 13*w - 8]', '[615, 615, -w^3 + w^2 + 3*w + 4]', '[619, 619, 4*w^3 - 4*w^2 - 13*w + 5]', '[619, 619, -2*w^3 + 2*w^2 + 10*w - 5]', '[621, 69, 2*w^3 - 4*w^2 - 7*w + 5]', '[621, 207, -w^3 - 2*w^2 + 2*w + 6]', '[624, 78, -2*w^2 - 2*w + 6]', '[625, 5, 5]', '[625, 625, -w^3 - 2*w^2 + 5*w + 5]', '[631, 631, -w^3 + w^2 + 7*w - 2]', '[633, 633, 2*w^3 - w^2 - 12*w - 6]', '[639, 213, 4*w^3 - 3*w^2 - 14*w + 9]', '[639, 213, 3*w^3 - 2*w^2 - 13*w + 7]', '[641, 641, -w - 5]', '[641, 641, -3*w^3 + 2*w^2 + 14*w - 5]', '[645, 645, -4*w^3 + 4*w^2 + 13*w - 7]', '[655, 655, 3*w^2 - 7]', '[655, 655, -w^3 + 6*w - 6]', '[656, 82, 2*w^3 - 10*w + 2]', '[657, 219, 3*w^3 - 2*w^2 - 9*w + 1]', '[657, 219, 4*w^3 - 4*w^2 - 11*w]', '[657, 219, -3*w^3 + 2*w^2 + 10*w + 5]', '[657, 219, -w^3 + w^2 + 5*w + 4]', '[659, 659, -w^3 + 2*w^2 + w - 7]', '[661, 661, 3*w^2 - 5]', '[669, 669, 4*w^3 + 2*w^2 - 13*w - 8]', '[669, 669, 3*w^3 - w^2 - 16*w - 6]', '[673, 673, -w^3 + 4*w^2 + 4*w - 8]', '[673, 673, -4*w^3 + w^2 + 15*w]', '[675, 75, -w^3 - w^2 + 2*w + 5]', '[675, 225, -3*w^3 + w^2 + 8*w - 2]', '[677, 677, -w^3 + 4*w^2 + 3*w - 6]', '[681, 681, -2*w^3 + 8*w - 3]', '[683, 683, -w^3 + 4*w^2 - 7]', '[685, 685, -3*w^3 + 2*w^2 + 9*w + 6]', '[685, 685, -4*w^3 + 5*w^2 + 11*w - 5]', '[685, 685, -w^3 + w + 4]', '[685, 685, -w^3 - w^2 + 9*w - 1]', '[687, 687, 2*w^3 + w^2 - 11*w - 7]', '[687, 687, 2*w^3 - 3*w^2 - 14*w - 3]', '[688, 86, 4*w^3 - 2*w^2 - 14*w]', '[689, 689, 3*w^3 - 3*w^2 - 8*w + 2]', '[695, 695, -3*w^3 + w^2 + 13*w - 2]', '[699, 699, 3*w^3 - 3*w^2 - 8*w + 4]', '[699, 699, -2*w^3 + 3*w^2 + 7*w - 1]', '[701, 701, -4*w^3 + 4*w^2 + 13*w - 6]', '[701, 701, 2*w^3 - 2*w^2 - 8*w + 9]', '[701, 701, -w^3 + 2*w^2 + 7*w - 3]', '[701, 701, -3*w^3 + 4*w^2 + 9*w - 3]', '[709, 709, -w^2 + 2*w - 4]', '[709, 709, -4*w^3 + 5*w^2 + 15*w - 8]', '[711, 237, w^3 + 3*w^2 - 9*w - 8]', '[711, 237, 2*w^2 - 3*w - 7]', '[720, 30, 2*w^3 - 2*w^2 - 10*w + 4]', '[720, 30, -2*w^3 + 2*w^2 + 4*w - 6]', '[727, 727, -2*w^3 + 3*w^2 + 10*w - 5]', '[727, 727, -w^3 + 2*w^2 + 6*w - 8]', '[727, 727, -4*w^3 + 3*w^2 + 17*w - 4]', '[727, 727, -3*w^3 + 14*w + 1]', '[729, 9, -3*w^2 + 6]', '[729, 9, -3*w^2 + 3*w + 6]', '[729, 27, -2*w^3 + 9*w - 2]', '[729, 27, -3*w^3 + w^2 + 12*w - 2]', '[733, 733, 2*w^2 - 4*w - 5]', '[739, 739, 3*w^2 - 3*w - 5]', '[739, 739, -w^3 + 4*w^2 + w - 5]', '[739, 739, 2*w^3 - 6*w - 5]', '[739, 739, -2*w^3 + 5*w^2 - 5]', '[743, 743, w^3 - 3*w - 7]', '[743, 743, w^3 + w^2 - 3*w - 8]', '[745, 745, -4*w^3 + 3*w^2 + 15*w + 1]', '[747, 249, 2*w^3 + w^2 - 7*w + 1]', '[747, 249, w^3 + 2*w^2 - 8*w]', '[747, 249, -2*w^3 + 3*w^2 + 10*w - 6]', '[747, 249, -2*w^3 + w^2 + 11*w - 4]', '[751, 751, -w^3 + w^2 + 2*w - 7]', '[751, 751, w^2 + 2*w - 7]', '[755, 755, 3*w^3 + w^2 - 11*w - 2]', '[757, 757, -3*w^3 + 3*w^2 + 8*w - 3]', '[767, 767, -3*w^3 - w^2 + 15*w + 9]', '[768, 12, 4*w + 4]', '[769, 769, 3*w^3 - 5*w^2 - 11*w + 8]', '[771, 771, 4*w^3 - 16*w - 3]', '[771, 771, 4*w^3 - 13*w]', '[785, 785, -4*w^3 + w^2 + 13*w]', '[787, 787, -2*w^3 + 4*w^2 + 3*w - 7]', '[787, 787, -3*w^3 + w^2 + 11*w - 3]', '[789, 789, 4*w^3 - w^2 - 21*w - 7]', '[795, 795, -w^3 + 8*w - 2]', '[797, 797, -3*w^3 + 2*w^2 + 10*w - 9]', '[801, 267, 3*w^3 - 4*w^2 - 11*w + 5]', '[801, 267, 2*w^3 - 5*w^2 - 10*w + 7]', '[801, 267, -3*w^3 + 4*w^2 + 12*w - 5]', '[801, 267, -4*w^3 + 4*w^2 + 14*w - 3]', '[807, 807, 3*w^3 + 2*w^2 - 10*w - 6]', '[809, 809, 2*w^2 - 2*w - 11]', '[809, 809, 3*w^2 - w - 8]', '[809, 809, -3*w^3 + 3*w^2 + 7*w - 4]', '[809, 809, -2*w^3 + 4*w^2 + 8*w - 5]', '[821, 821, 3*w^3 - 11*w]', '[821, 821, -w^3 + 4*w^2 + 3*w - 10]', '[823, 823, -4*w^3 + 4*w^2 + 15*w - 4]', '[829, 829, 2*w^3 + w^2 - 8*w]', '[843, 843, 4*w^3 - w^2 - 13*w - 2]', '[843, 843, -3*w^3 + 2*w^2 + 8*w - 3]', '[845, 845, -2*w^3 + 4*w^2 + 4*w - 9]', '[848, 106, 4*w - 6]', '[849, 849, 3*w^3 - 13*w - 1]', '[849, 849, 5*w^3 + w^2 - 17*w - 4]', '[851, 851, -3*w^3 + 3*w^2 + 7*w - 1]', '[851, 851, -3*w^3 + 3*w^2 + 11*w]', '[853, 853, -w^3 + 2*w^2 - 5]', '[857, 857, 6*w^3 - 6*w^2 - 25*w + 16]', '[857, 857, 3*w^2 - w - 5]', '[859, 859, 4*w + 5]', '[859, 859, w^3 - w^2 - 2*w - 5]', '[865, 865, -2*w^3 + 2*w^2 + 11*w - 7]', '[865, 865, -4*w^3 + 5*w^2 + 13*w - 6]', '[871, 871, 6*w^3 - w^2 - 25*w - 5]', '[871, 871, 3*w^3 - 3*w^2 - 14*w - 1]', '[873, 291, 4*w^3 - 3*w^2 - 15*w - 2]', '[873, 291, 2*w^3 - 3*w^2 - 10*w]', '[877, 877, 2*w^3 - 3*w^2 - 9*w + 1]', '[877, 877, -w^3 + 3*w^2 + w - 10]', '[883, 883, w^3 + 2*w^2 - 3*w - 8]', '[883, 883, -3*w^3 + 4*w^2 + 10*w - 4]', '[885, 885, 3*w^3 - 11*w - 8]', '[895, 895, -2*w^3 + 5*w^2 + 4*w - 8]', '[897, 897, 3*w^2 - 2*w - 5]', '[905, 905, 3*w^3 - 5*w^2 - 12*w + 15]', '[907, 907, -5*w^3 + 8*w^2 + 15*w - 18]', '[911, 911, -w^3 + 3*w - 5]', '[923, 923, -w^3 + w^2 + 3*w - 7]', '[925, 925, 2*w^3 - 11*w + 4]', '[925, 925, 3*w^3 - 2*w^2 - 14*w + 4]', '[927, 309, -2*w^3 + 3*w^2 + 9*w + 1]', '[927, 309, -2*w^3 + 10*w - 3]', '[927, 309, -2*w^3 + 2*w^2 + 4*w - 7]', '[927, 309, -w^3 + 3*w^2 - 7]', '[933, 933, -2*w^3 + 3*w^2 + 8*w]', '[937, 937, -3*w^3 + w^2 + 16*w - 5]', '[937, 937, -2*w^3 + 9*w - 4]', '[941, 941, -4*w^3 + 5*w^2 + 10*w - 3]', '[943, 943, 4*w^3 - 3*w^2 - 15*w + 8]', '[944, 118, -4*w^3 + 2*w^2 + 18*w - 2]', '[947, 947, -w^3 + 4*w^2 + 3*w - 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8]', '[1579, 1579, -w^3 + 9*w - 3]', '[1585, 1585, -2*w^3 + 5*w^2 - 6]', '[1585, 1585, -5*w^3 + 6*w^2 + 15*w - 9]', '[1587, 1587, -w^2 - 3*w - 5]', '[1591, 1591, -w^2 + 4*w + 6]', '[1591, 1591, -2*w^3 + 2*w^2 + 3*w - 6]', '[1593, 177, -7*w^3 + 8*w^2 + 23*w - 10]', '[1593, 531, -6*w^3 + w^2 + 26*w + 4]', '[1597, 1597, -5*w^3 + 6*w^2 + 17*w - 8]', '[1599, 1599, 2*w^3 - 2*w^2 - 11*w + 5]', '[1601, 1601, 2*w^3 - w^2 - 4*w - 5]', '[1607, 1607, -3*w^3 + w^2 + 16*w - 8]', '[1607, 1607, -5*w^3 + 2*w^2 + 19*w - 2]', '[1611, 537, -4*w^3 + 5*w^2 + 10*w - 5]', '[1611, 537, -4*w^3 + 3*w^2 + 11*w - 6]', '[1613, 1613, -w^3 + 2*w^2 - 7]', '[1613, 1613, -4*w^3 + 5*w^2 + 10*w - 6]', '[1619, 1619, w^3 + 3*w^2 - 6*w - 10]', '[1619, 1619, 5*w^3 - 3*w^2 - 17*w - 1]', '[1619, 1619, 5*w^3 - 3*w^2 - 17*w + 4]', '[1619, 1619, -5*w^3 + 6*w^2 + 18*w - 9]', '[1623, 1623, 4*w^3 + w^2 - 15*w - 3]', '[1625, 65, -3*w^3 - w^2 + 9*w + 6]', '[1625, 1625, 4*w^3 - 3*w^2 - 12*w + 5]', '[1627, 1627, -w^3 + 2*w^2 + 7*w - 9]', '[1627, 1627, -w^3 + 2*w^2 + 8*w - 3]', '[1629, 543, 6*w^3 - 5*w^2 - 21*w + 13]', '[1629, 543, 5*w^3 - 4*w^2 - 20*w + 10]', '[1633, 1633, -2*w^3 + w^2 + 12*w - 5]', '[1648, 206, -4*w^3 + 6*w^2 + 10*w - 4]', '[1648, 206, 2*w^2 + 2*w - 8]', '[1663, 1663, -3*w^3 + 3*w^2 + 14*w - 6]', '[1665, 555, w^3 - w^2 - 2*w + 8]', '[1665, 555, -w^3 + 3*w + 8]', '[1665, 555, -2*w^2 - 3*w + 7]', '[1665, 555, -w^3 + w^2 - w + 6]', '[1667, 1667, -4*w^3 + 5*w^2 + 14*w - 6]', '[1671, 1671, w^3 - 2*w^2 - 9*w]', '[1675, 1675, 4*w^3 - 2*w^2 - 15*w + 5]', '[1675, 1675, 2*w^3 - 6*w^2 - 11*w + 8]', '[1677, 1677, 3*w^3 - 4*w^2 - 13*w + 3]', '[1679, 1679, 5*w^3 - 3*w^2 - 15*w - 6]', '[1679, 1679, -5*w^3 + 6*w^2 + 13*w + 1]', '[1681, 1681, -2*w^3 + 5*w^2 + 8*w - 6]', '[1689, 1689, 6*w^3 - 3*w^2 - 22*w - 1]', '[1695, 1695, 2*w^3 - 5*w + 6]', '[1697, 1697, 2*w^3 - 3*w^2 - 11*w + 4]', '[1697, 1697, 3*w^3 - 4*w^2 - 10*w + 2]', '[1699, 1699, 3*w^3 - 5*w^2 - 10*w + 6]', '[1703, 1703, w^3 - 3*w^2 - 5*w + 13]', '[1703, 1703, -w^3 - w^2 + 5]', '[1707, 1707, 3*w^3 - 2*w^2 - 18*w - 7]', '[1719, 573, -5*w^3 + 4*w^2 + 17*w - 4]', '[1719, 573, -5*w^3 + 3*w^2 + 16*w - 6]', '[1719, 573, 5*w^3 - 3*w^2 - 18*w - 7]', '[1719, 573, 2*w^3 - 2*w^2 - 10*w - 5]', '[1721, 1721, 2*w^2 - 4*w - 7]', '[1723, 1723, 3*w^3 - 2*w^2 - 15*w + 6]', '[1725, 1725, 2*w^3 - 3*w^2 - 4*w + 10]', '[1731, 1731, -3*w^3 - 2*w^2 + 13*w + 3]', '[1731, 1731, 4*w^3 + w^2 - 12*w]', '[1733, 1733, -2*w^3 + 2*w^2 + 11*w - 3]', '[1737, 579, -5*w^3 + 5*w^2 + 16*w - 9]', '[1737, 579, -6*w^3 + 4*w^2 + 18*w - 11]', '[1745, 1745, -4*w^2 + 5*w + 11]', '[1747, 1747, 5*w^3 - 4*w^2 - 17*w + 5]', '[1747, 1747, 5*w^2 - w - 16]', '[1753, 1753, -2*w^3 + 2*w^2 + 11*w - 4]', '[1755, 195, 4*w^3 - 2*w^2 - 14*w + 7]', '[1755, 585, 3*w^3 - w^2 - 14*w + 5]', '[1763, 1763, -w^3 - 2*w^2 + 8*w + 8]', '[1765, 1765, -3*w^3 + 4*w^2 + 11*w - 3]', '[1773, 591, -4*w^3 + w^2 + 11*w - 2]', '[1773, 591, -4*w^3 + 3*w^2 + 12*w - 1]', '[1775, 1775, -7*w^3 + 7*w^2 + 24*w - 21]', '[1776, 222, -4*w^2 + 10]', '[1776, 222, -2*w^3 + 2*w^2 + 2*w + 4]', '[1777, 1777, 2*w^3 + w^2 - 6*w - 7]', '[1781, 1781, w^3 - 2*w^2 - 6*w - 4]', '[1781, 1781, 4*w^3 - 4*w^2 - 14*w + 1]', '[1781, 1781, 3*w^3 + w^2 - 14*w - 2]', '[1781, 1781, 7*w^3 - 2*w^2 - 26*w - 10]', '[1783, 1783, 5*w^3 - 23*w - 4]', '[1789, 1789, 2*w^3 - 4*w^2 - 8*w + 3]', '[1791, 597, -w^3 + 2*w - 6]', '[1791, 597, w^3 - w^2 - 2*w - 6]', '[1795, 1795, -7*w^3 + 7*w^2 + 27*w - 10]', '[1803, 1803, -3*w^3 + 4*w^2 + 18*w + 2]', '[1807, 1807, 4*w^3 - 2*w^2 - 19*w - 2]', '[1808, 226, 4*w^3 - 2*w^2 - 14*w + 8]', '[1809, 201, -2*w^3 + 4*w^2 + 4*w - 11]', '[1809, 201, w^3 + w^2 - 2*w - 11]', '[1809, 603, 4*w^3 + w^2 - 13*w - 7]', '[1809, 603, 5*w^3 - 24*w - 10]', '[1817, 1817, -2*w^3 - 4*w^2 + 15*w + 9]', '[1821, 1821, w^3 + 3*w^2 - 4*w - 6]', '[1823, 1823, -w^3 + 9*w - 2]', '[1825, 1825, -2*w^3 + 3*w^2 + 3*w - 7]', '[1825, 1825, -3*w^3 + 11*w - 2]', '[1839, 1839, -6*w^3 - w^2 + 17*w + 6]', '[1839, 1839, -2*w^3 + 5*w^2 + 11*w - 5]', '[1840, 230, -4*w^2 + 6]', '[1845, 615, -4*w^3 + 4*w^2 + 11*w - 6]', '[1845, 615, -w^2 - 3*w + 8]', '[1847, 1847, -4*w^3 + 6*w^2 + 7*w - 4]', '[1849, 1849, w^3 + w^2 - w - 6]', '[1857, 1857, 4*w^3 - w^2 - 16*w + 1]', '[1857, 1857, -2*w^3 + 4*w^2 + 9*w - 3]', '[1861, 1861, -w^3 + 3*w - 6]', '[1861, 1861, -6*w^3 + 8*w^2 + 17*w - 8]', '[1863, 69, 3*w^2 - 6*w - 6]', '[1863, 207, w^3 - 9*w + 1]', '[1863, 207, -w^3 + w^2 - w - 5]', '[1865, 1865, w^3 + 3*w^2 - 4*w - 7]', '[1867, 1867, -3*w^3 + 2*w^2 + 15*w]', '[1867, 1867, -w^3 + 2*w^2 - 8]', '[1867, 1867, w^3 + w^2 - 10*w + 1]', '[1867, 1867, -3*w^3 + 5*w^2 + 7*w - 11]', '[1872, 78, -4*w^3 + 18*w + 2]', '[1872, 78, -4*w^3 + 14*w]', '[1873, 1873, 5*w^3 - 5*w^2 - 17*w + 3]', '[1875, 15, -5*w - 5]', '[1875, 1875, -2*w^3 + 3*w^2 + 11*w - 6]', '[1877, 1877, 4*w^3 - 2*w^2 - 17*w + 5]', '[1877, 1877, w - 7]', '[1879, 1879, 6*w^3 - 6*w^2 - 25*w + 15]', '[1893, 1893, -w^3 + 4*w^2 + 7*w - 1]', '[1895, 1895, -2*w^3 + 2*w^2 + 9*w - 11]', '[1899, 633, 2*w^3 + 3*w^2 - 7*w - 9]', '[1899, 633, 3*w^3 + 2*w^2 - 14*w - 10]', '[1901, 1901, 2*w^3 - 3*w^2 - 11*w + 5]', '[1901, 1901, w^3 + 3*w^2 - 7*w - 7]', '[1907, 1907, w^2 + w - 10]', '[1909, 1909, 2*w^3 + w^2 - 12*w + 2]', '[1909, 1909, -3*w^2 + 9*w + 1]', '[1913, 1913, 2*w^3 - w^2 - 4*w - 6]', '[1917, 213, 7*w^3 - 8*w^2 - 29*w + 22]', '[1917, 639, 4*w^3 - 3*w^2 - 12*w + 4]', '[1923, 1923, -w^2 - 6*w - 5]', '[1923, 1923, -4*w^3 + 4*w^2 + 15*w - 2]', '[1931, 1931, -5*w^3 + 5*w^2 + 15*w - 3]', '[1931, 1931, 3*w^2 + 2*w - 9]', '[1933, 1933, 5*w^3 - 17*w - 1]', '[1933, 1933, -4*w^3 + 3*w^2 + 18*w - 6]', '[1935, 645, -w^3 - 3*w^2 + 5*w + 9]', '[1935, 645, -4*w^3 + w^2 + 14*w - 3]', '[1937, 1937, 8*w^3 - 2*w^2 - 30*w - 7]', '[1949, 1949, -3*w^3 + 4*w^2 + 12*w - 3]', '[1961, 1961, -3*w^3 + w^2 + 13*w - 5]', '[1961, 1961, -3*w^3 + w^2 + 7*w + 4]', '[1963, 1963, -5*w^3 + 4*w^2 + 15*w + 1]', '[1965, 1965, -2*w^3 + 2*w^2 + 2*w - 5]', '[1965, 1965, -3*w^3 + 6*w^2 + 7*w - 14]', '[1968, 246, 4*w^3 - 2*w^2 - 12*w]', '[1971, 219, 5*w^3 - 7*w^2 - 13*w + 5]', '[1971, 219, -2*w^3 + w^2 + 4*w + 7]', '[1971, 657, -4*w^3 + 21*w + 8]', '[1971, 657, 4*w^3 + w^2 - 19*w - 4]', '[1975, 1975, 5*w^3 - 5*w^2 - 16*w + 8]', '[1977, 1977, -w^2 - 4*w - 6]', '[1983, 1983, 3*w^3 + 3*w^2 - 5*w - 5]', '[1985, 1985, 4*w^2 - 4*w - 9]', '[1987, 1987, 3*w^3 - 4*w^2 - 10*w + 1]', '[1997, 1997, w^2 - w - 9]', '[1997, 1997, 4*w^3 - 3*w^2 - 12*w + 2]', '[1999, 1999, 4*w^3 - 7*w^2 - 9*w + 6]', '[2000, 10, -4*w^3 + 2*w^2 + 12*w - 2]', '[2000, 250, 2*w^3 - 2*w^2 - 12*w]', '[2007, 669, 2*w^3 + w^2 - 10*w - 12]', '[2007, 669, -w^3 + w^2 - w - 11]', '[2007, 669, 3*w^3 + 2*w^2 - 12*w - 7]', '[2007, 669, 4*w^3 + 2*w^2 - 20*w - 9]', '[2011, 2011, -4*w^3 + 5*w^2 + 16*w - 6]', '[2011, 2011, w^3 + 3*w^2 - 6*w - 9]', '[2019, 2019, -7*w^3 + 23*w + 4]', '[2019, 2019, 2*w^3 + 4*w^2 - 2*w - 7]', '[2025, 75, -3*w^3 + 6*w^2 + 12*w - 9]', '[2025, 225, -4*w^3 + 6*w^2 + 12*w - 7]', '[2025, 225, 2*w^3 - 2*w^2 - 7*w + 10]', '[2027, 2027, 5*w^2 - 2*w - 17]', '[2031, 2031, 2*w^3 + 3*w^2 - w - 5]', '[2039, 2039, w^2 + 3*w - 9]', '[2039, 2039, -w^2 + w - 5]', '[2041, 2041, 5*w^3 - 2*w^2 - 21*w + 2]', '[2043, 681, -3*w^3 + 4*w^2 + 15*w - 11]', '[2043, 681, -2*w^3 + 15*w - 8]', '[2045, 2045, -6*w + 13]', '[2047, 2047, 5*w^3 - 4*w^2 - 16*w + 1]', '[2047, 2047, -4*w^3 + 3*w^2 + 12*w - 3]', '[2049, 2049, 2*w^3 - 5*w - 6]', '[2055, 2055, -3*w^3 + 4*w^2 + 10*w]', '[2055, 2055, -4*w^3 - w^2 + 21*w + 9]', '[2055, 2055, -3*w^3 + 14*w - 1]', '[2055, 2055, -2*w^3 - 3*w^2 + 7*w + 5]', '[2061, 687, w^3 + 5*w^2 - 11*w - 12]', '[2061, 687, 4*w^2 - 3*w - 11]', '[2061, 687, 5*w^3 + w^2 - 16*w - 2]', '[2061, 687, 5*w^3 - 21*w - 4]', '[2063, 2063, w^3 + 2*w^2 - 2*w - 8]', '[2064, 258, -2*w^3 + 2*w^2 + 6*w - 10]', '[2067, 2067, 3*w^3 + w^2 - 12*w - 1]', '[2075, 2075, 3*w^3 - 6*w^2 - 14*w + 15]', '[2075, 2075, -2*w^3 - w^2 + 6*w - 5]', '[2083, 2083, 3*w^3 + 3*w^2 - 12*w - 13]', '[2083, 2083, 2*w^3 + w^2 - 5*w - 6]', '[2083, 2083, 4*w^3 - 4*w^2 - 15*w - 3]', '[2083, 2083, -5*w^3 + 4*w^2 + 13*w - 9]', '[2085, 2085, -5*w^3 + 2*w^2 + 17*w + 1]', '[2087, 2087, -2*w^3 + w^2 + 12*w - 4]', '[2087, 2087, -5*w^3 + 7*w^2 + 19*w - 12]', '[2095, 2095, -3*w^3 + 20*w - 9]', '[2095, 2095, -6*w^3 + 5*w^2 + 21*w - 6]', '[2096, 262, -4*w^3 + 4*w^2 + 10*w - 6]', '[2096, 262, -8*w^3 + 10*w^2 + 26*w - 18]', '[2097, 699, 5*w^3 - 8*w^2 - 16*w + 13]', '[2097, 699, 3*w^3 + w^2 - 10*w + 1]', '[2097, 699, -4*w^3 + 4*w^2 + 11*w - 5]', '[2097, 699, -5*w^3 + 7*w^2 + 11*w - 4]', '[2099, 2099, -5*w^3 + 5*w^2 + 19*w - 5]', '[2099, 2099, w^3 - 2*w^2 - 7*w + 13]', '[2103, 2103, 2*w^3 - 2*w^2 - 3*w + 7]', '[2103, 2103, -4*w^3 + w^2 + 15*w - 2]', '[2103, 2103, 5*w^2 + 6*w - 2]', '[2103, 2103, -2*w^3 + w^2 + 12*w]', '[2105, 2105, -w^3 + 3*w^2 - w - 7]', '[2113, 2113, -3*w^3 + 13*w - 1]', '[2113, 2113, w^3 - 5*w^2 - 3*w + 13]', '[2127, 2127, -w^3 + w^2 - 2*w - 4]', '[2127, 2127, -3*w^3 + 4*w^2 + 15*w - 4]', '[2129, 2129, -w^3 - w^2 + 8*w + 10]', '[2131, 2131, w^2 + 4*w - 7]', '[2133, 237, -2*w^3 + 7*w^2 + w - 14]', '[2133, 711, 5*w^3 - 2*w^2 - 19*w - 9]', '[2137, 2137, 4*w^3 - 4*w^2 - 11*w + 4]', '[2137, 2137, 6*w^3 - 5*w^2 - 22*w + 12]', '[2155, 2155, -4*w^3 + 3*w^2 + 18*w - 3]', '[2155, 2155, -5*w^3 + 6*w^2 + 15*w - 4]', '[2160, 30, 2*w^3 - 4*w^2 - 10*w + 2]', '[2160, 90, 4*w^3 - 4*w^2 - 14*w]', '[2161, 2161, 2*w^3 + 3*w^2 - 8*w - 14]', '[2161, 2161, -5*w^3 + 3*w^2 + 17*w - 11]', '[2165, 2165, -5*w^3 + 4*w^2 + 19*w - 13]', '[2165, 2165, -2*w^3 + 4*w^2 + 9*w - 14]', '[2173, 2173, -4*w^3 + 9*w]', '[2181, 2181, -w^3 + 5*w^2 + 9*w - 3]', '[2181, 2181, -5*w^3 + 4*w^2 + 21*w]', '[2181, 2181, 4*w^2 - 7]', '[2181, 2181, -6*w^3 + 2*w^2 + 21*w + 4]', '[2183, 2183, 2*w^3 + w^2 - 9*w - 12]', '[2183, 2183, w^3 + w^2 - 2*w - 9]', '[2187, 9, 3*w^3 - 6*w^2 - 6*w + 12]', '[2187, 27, 4*w^3 - 5*w^2 - 11*w + 13]', '[2187, 27, -3*w^3 + 9*w + 6]', '[2187, 81, 4*w^2 - w - 11]', '[2192, 274, 2*w^3 - 4*w^2 - 8*w + 2]', '[2192, 274, 4*w^2 - 4*w - 6]', '[2192, 274, 6*w^3 - 4*w^2 - 20*w - 2]', '[2192, 274, 2*w - 8]', '[2195, 2195, w^3 + w^2 - 2*w - 10]', '[2195, 2195, -w^3 + w^2 + 6*w - 10]', '[2197, 13, 4*w^3 - 6*w^2 - 13*w + 8]', '[2197, 2197, -w^3 - 3*w^2 + 5*w + 8]', '[2199, 2199, 2*w^3 - 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11]', '[5113, 5113, -3*w^3 + 6*w^2 + 16*w - 12]', '[5113, 5113, -6*w^3 + w^2 + 25*w + 2]', '[5121, 1707, 5*w^3 + 2*w^2 - 23*w - 11]', '[5121, 1707, 4*w^3 + 3*w^2 - 14*w - 9]', '[5125, 205, -w^3 + 3*w^2 - 2*w - 8]', '[5125, 5125, -3*w^3 + 8*w + 7]', '[5129, 5129, -5*w^3 - w^2 + 19*w + 13]', '[5129, 5129, -5*w^3 - 2*w^2 + 28*w + 11]', '[5135, 5135, -6*w^3 + 2*w^2 + 22*w + 13]', '[5141, 5141, -w^3 + 3*w^2 + 4*w - 16]', '[5143, 5143, -5*w^3 + 5*w^2 + 21*w - 2]', '[5143, 5143, -5*w^3 + 3*w^2 + 15*w - 3]', '[5147, 5147, w^3 + w^2 - 8]', '[5153, 5153, 6*w^3 - 3*w^2 - 20*w - 1]', '[5155, 5155, -5*w^3 + 8*w^2 + 14*w - 9]', '[5155, 5155, -2*w^3 + 3*w^2 + 12*w + 6]', '[5157, 573, -8*w^3 + 10*w^2 + 28*w - 17]', '[5157, 573, 4*w^3 - 2*w^2 - 11*w - 8]', '[5157, 1719, 7*w^3 - w^2 - 35*w - 12]', '[5157, 1719, -6*w^3 + w^2 + 23*w + 1]', '[5161, 5161, -3*w^3 - w^2 + 17*w + 10]', '[5163, 5163, 2*w^3 - 2*w^2 - 11*w - 7]', '[5165, 5165, w^3 - 6*w^2 - w + 25]', '[5169, 5169, 4*w^3 - 5*w^2 - 15*w + 3]', '[5171, 5171, -4*w^3 + w^2 + 19*w - 5]', '[5171, 5171, -w^3 + w^2 - 2*w - 8]', '[5175, 1725, 5*w^3 - 6*w^2 - 12*w + 5]', '[5175, 1725, 5*w^3 - 3*w^2 - 13*w + 6]', '[5179, 5179, -w^3 + 4*w^2 + 6*w - 13]', '[5183, 5183, 3*w^3 - 6*w^2 - 5*w + 12]', '[5183, 5183, -4*w^3 + w^2 + 17*w - 4]', '[5189, 5189, 7*w^3 - 6*w^2 - 31*w + 17]', '[5189, 5189, -7*w^3 + 6*w^2 + 24*w - 8]', '[5193, 1731, -w^3 - 5*w^2 + 17*w + 3]', '[5193, 1731, -w^3 + 11*w]', '[5193, 1731, 3*w^3 - 2*w^2 - 16*w + 4]', '[5193, 1731, 2*w^3 - 5*w^2 - 13*w + 7]', '[5199, 5199, -2*w^3 + 5*w^2 + 12*w - 1]', '[5200, 650, -6*w^3 + 6*w^2 + 20*w - 2]', '[5211, 579, -10*w^3 + 14*w^2 + 35*w - 28]', '[5211, 1737, -5*w^3 + w^2 + 17*w - 4]', '[5221, 5221, w^3 + 4*w^2 - 15*w + 5]', '[5233, 5233, 6*w^3 - 4*w^2 - 19*w - 1]', '[5233, 5233, -6*w^3 + 4*w^2 + 25*w - 10]', '[5233, 5233, -w^3 - w^2 + 9*w + 10]', '[5233, 5233, 2*w^3 + 2*w^2 - 5*w - 9]', '[5235, 5235, -4*w^3 + w^2 + 16*w + 11]', '[5237, 5237, -7*w^3 + 6*w^2 + 21*w - 14]', '[5237, 5237, -3*w^3 + 16*w - 6]', '[5241, 5241, -6*w^3 + w^2 + 22*w]', '[5241, 5241, 5*w^3 + 4*w^2 - 17*w - 16]', '[5245, 5245, -w^2 - 5*w + 9]', '[5251, 5251, 5*w^3 - 23*w - 2]', '[5251, 5251, -4*w^3 + 16*w - 1]', '[5255, 5255, -4*w^3 + 7*w^2 + 10*w - 5]', '[5255, 5255, -4*w^3 + 2*w^2 + 21*w - 8]', '[5259, 5259, -2*w^3 + 5*w^2 + 11*w - 2]', '[5261, 5261, -6*w^3 + 3*w^2 + 24*w - 5]', '[5265, 195, 3*w^3 - 9*w - 9]', '[5265, 585, 5*w^3 - 3*w^2 - 15*w + 2]', '[5265, 585, 2*w^3 + 3*w^2 - 4*w - 9]', '[5267, 5267, -2*w^3 - 6*w^2 + 19*w + 13]', '[5267, 5267, -5*w^3 + w^2 + 26*w + 6]', '[5273, 5273, -5*w^3 + 3*w^2 + 19*w - 11]', '[5275, 5275, 4*w^3 - 7*w^2 - 18*w + 9]', '[5279, 5279, -w^3 + 6*w^2 + 4*w - 13]', '[5289, 5289, -5*w^3 + 3*w^2 + 20*w - 9]', '[5293, 5293, -w^3 + 6*w - 9]', '[5293, 5293, -5*w^3 + 4*w^2 + 23*w - 2]', '[5295, 5295, -2*w^3 + 3*w^2 + 14*w]', '[5303, 5303, 6*w^3 - 3*w^2 - 20*w + 2]', '[5303, 5303, 5*w^3 - 2*w^2 - 22*w + 5]', '[5305, 5305, -7*w^3 + 5*w^2 + 20*w + 4]', '[5309, 5309, -3*w^3 + 4*w^2 + 16*w - 4]', '[5309, 5309, 9*w^3 - 5*w^2 - 38*w + 7]', '[5315, 5315, -5*w^3 + 2*w^2 + 19*w - 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3*w^2 - 37*w - 9]', '[5359, 5359, 6*w^3 - 10*w^2 - 11*w + 3]', '[5359, 5359, w^3 - 3*w^2 - 10*w + 11]', '[5360, 670, -6*w^3 + 2*w^2 + 28*w]', '[5360, 670, -6*w^3 + 4*w^2 + 20*w - 4]', '[5367, 5367, -4*w^2 - 9*w + 1]', '[5371, 5371, w^3 + 3*w^2 - w - 10]', '[5371, 5371, -4*w^3 + 7*w^2 + 6*w - 10]', '[5373, 597, -w^3 + 2*w^2 + 8*w - 13]', '[5373, 1791, w^3 + w^2 - 10*w - 7]', '[5375, 215, 2*w^3 - w^2 - 11*w - 9]', '[5375, 5375, -5*w^3 + 7*w^2 + 19*w - 10]', '[5381, 5381, w^3 - 3*w - 10]', '[5385, 5385, -7*w^3 + 6*w^2 + 31*w - 3]', '[5387, 5387, -w^3 + 5*w^2 - 2*w - 13]', '[5387, 5387, 5*w^3 - 3*w^2 - 14*w + 5]', '[5393, 5393, -w^3 + 4*w^2 + 5*w - 16]', '[5395, 5395, 5*w^3 - 6*w^2 - 17*w + 5]', '[5395, 5395, -5*w^3 + 4*w^2 + 13*w]', '[5399, 5399, -3*w^3 - w^2 + 12*w - 3]', '[5407, 5407, -5*w^3 + 6*w^2 + 15*w - 1]', '[5409, 1803, -7*w^3 + w^2 + 23*w - 2]', '[5409, 1803, -7*w^3 + 2*w^2 + 28*w + 1]', '[5413, 5413, 7*w^3 - 5*w^2 - 23*w - 1]', '[5413, 5413, -3*w^3 + 4*w^2 + 5*w - 9]', '[5419, 5419, -6*w^3 + 11*w^2 + 21*w - 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11]', '[5589, 207, 3*w^3 - 15*w + 6]', '[5589, 621, -2*w^2 + 5*w + 10]', '[5591, 5591, 5*w^2 - 5*w - 8]', '[5595, 5595, 5*w^3 + 3*w^2 - 13*w - 8]', '[5601, 5601, -w^3 + 2*w - 8]', '[5601, 5601, 3*w^3 - 5*w^2 - 11*w]', '[5601, 5601, -4*w^3 + 5*w^2 + 21*w + 3]', '[5601, 5601, -2*w^2 - 6*w - 7]', '[5603, 5603, 7*w^3 - 4*w^2 - 24*w - 2]', '[5603, 5603, -4*w^3 + 5*w^2 + 13*w - 18]', '[5609, 5609, -w^3 + 6*w^2 - 2*w - 8]', '[5615, 5615, w^3 + 3*w^2 - 9*w - 12]', '[5616, 78, -4*w^3 + 2*w^2 + 20*w - 4]', '[5616, 234, 2*w^3 - 4*w^2 - 2*w + 10]', '[5617, 5617, -5*w^3 + 8*w^2 + 11*w - 3]', '[5617, 5617, -5*w^2 + 4*w + 7]', '[5617, 5617, -3*w^3 - w^2 + 19*w - 5]', '[5617, 5617, -2*w^3 - 5*w^2 + 18*w + 11]', '[5619, 5619, 5*w^3 - 2*w^2 - 24*w - 2]', '[5625, 15, 5*w^2 - 10]', '[5625, 15, 5*w^3 - 15*w + 5]', '[5625, 1875, w^2 + 3*w + 7]', '[5625, 1875, -3*w^3 + 2*w^2 + 10*w + 8]', '[5629, 5629, -w^2 + 2*w + 11]', '[5629, 5629, 2*w^3 - 5*w^2 - 13*w + 8]', '[5631, 5631, w^2 - 6*w - 7]', '[5631, 5631, 6*w^3 - 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3*w^2 - 12*w - 7]', '[9731, 9731, -8*w^3 + 2*w^2 + 39*w + 10]', '[9731, 9731, -5*w^3 - 3*w^2 + 24*w + 6]', '[9733, 9733, -4*w^3 + 5*w^2 + 20*w - 6]', '[9739, 9739, -4*w^3 - 3*w^2 + 17*w + 11]', '[9743, 9743, 6*w^3 - 6*w^2 - 21*w + 1]', '[9745, 9745, w^3 + 2*w^2 - w - 12]', '[9753, 9753, 3*w^3 - 5*w^2 - 17*w + 6]', '[9761, 9761, -2*w^3 + 2*w^2 + 9*w - 14]', '[9763, 9763, 5*w^3 - 6*w^2 - 23*w + 2]', '[9763, 9763, 7*w^3 - 5*w^2 - 23*w + 2]', '[9767, 9767, -5*w^3 + 3*w^2 + 24*w - 1]', '[9771, 9771, 6*w^3 - 2*w^2 - 17*w + 3]', '[9771, 9771, 3*w^3 - w^2 - 3*w - 5]', '[9771, 9771, 4*w^3 + 3*w^2 - 13*w]', '[9771, 9771, w^3 + 7*w^2 - 9]', '[9777, 9777, -8*w^3 + 3*w^2 + 28*w + 2]', '[9777, 9777, -w^3 + 7*w^2 - 20]', '[9781, 9781, 8*w^3 - 3*w^2 - 29*w + 4]', '[9791, 9791, 8*w^3 - 6*w^2 - 27*w + 10]', '[9791, 9791, -w^3 + 7*w - 11]', '[9803, 9803, 3*w^3 - 3*w^2 - 11*w - 7]', '[9803, 9803, -6*w^3 + 26*w + 3]', '[9805, 9805, -4*w^3 + 9*w^2 + 7*w - 4]', '[9805, 9805, 5*w^3 - 7*w^2 - 14*w]', '[9808, 1226, -4*w^3 - 4*w^2 + 18*w + 8]', '[9808, 1226, -6*w^3 + 8*w^2 + 26*w - 16]', '[9811, 9811, 3*w^3 + 5*w^2 - 11*w - 20]', '[9815, 9815, 3*w^3 - 6*w^2 - 12*w + 4]', '[9817, 9817, -3*w^3 + 2*w^2 + 11*w - 13]', '[9817, 9817, 5*w^3 - 5*w^2 - 19*w - 7]', '[9819, 3273, -2*w^3 + 5*w^2 + w - 12]', '[9819, 3273, -4*w^3 + 3*w^2 + 8*w - 12]', '[9819, 3273, -5*w^3 + 11*w^2 + 25*w - 22]', '[9819, 3273, -5*w^3 + 6*w^2 + 24*w - 17]', '[9825, 9825, -3*w^3 - w^2 + 15*w - 5]', '[9825, 9825, 7*w^3 - 13*w^2 - 25*w + 28]', '[9829, 9829, -6*w^3 + 6*w^2 + 16*w - 3]', '[9833, 9833, w^3 + 5*w^2 - 4*w - 9]', '[9833, 9833, -5*w^3 + w^2 + 19*w - 4]', '[9837, 3279, -3*w^3 + 5*w^2 + 6*w - 16]', '[9837, 3279, -w^3 + 6*w^2 - 3*w - 16]', '[9837, 3279, 2*w^3 + 2*w^2 - 14*w - 11]', '[9837, 3279, -w^3 - 4*w - 9]', '[9840, 1230, -2*w^3 + 2*w^2 + 6*w + 8]', '[9841, 9841, 3*w^3 - 7*w - 8]', '[9847, 9847, -13*w^3 + 7*w^2 + 49*w + 4]', '[9847, 9847, -11*w^3 + 41*w + 16]', '[9851, 9851, w^2 + w - 13]', '[9851, 9851, -2*w^3 + 2*w^2 + 14*w - 3]', '[9855, 1095, 7*w^3 + w^2 - 26*w - 5]', '[9855, 1095, -w^3 - w^2 + 11*w + 8]', '[9855, 3285, 8*w^3 + w^2 - 37*w - 9]', '[9855, 3285, -3*w^3 - 4*w^2 + 22*w + 11]', '[9857, 9857, -4*w^3 + 18*w - 3]', '[9869, 9869, 6*w^3 + w^2 - 21*w - 12]', '[9871, 9871, -8*w^3 + 7*w^2 + 27*w - 11]', '[9871, 9871, 5*w^2 - 8*w - 12]', '[9873, 3291, -4*w^3 + 7*w^2 + 17*w - 8]', '[9873, 3291, -6*w^3 + 7*w^2 + 20*w - 5]', '[9875, 395, -7*w^3 + 6*w^2 + 26*w - 1]', '[9875, 9875, -8*w^3 + w^2 + 34*w + 5]', '[9879, 9879, -8*w^3 + 9*w^2 + 32*w - 12]', '[9879, 9879, 2*w^3 - 2*w^2 - 14*w + 5]', '[9879, 9879, -3*w^3 + 19*w - 2]', '[9879, 9879, 6*w^3 - 11*w^2 - 27*w + 17]', '[9885, 9885, -7*w^3 + 3*w^2 + 23*w - 2]', '[9887, 9887, 3*w^3 - 6*w^2 - 11*w + 3]', '[9903, 9903, -9*w^3 + 34*w + 7]', '[9904, 1238, 8*w^3 - 8*w^2 - 26*w + 10]', '[9904, 1238, -4*w^3 + 4*w^2 + 20*w - 10]', '[9907, 9907, -w^3 - w^2 + 5*w - 8]', '[9913, 9913, -w^3 - 7*w^2 + 15*w + 11]', '[9913, 9913, -5*w^3 + 17*w + 11]', '[9915, 9915, -2*w^3 + 6*w^2 + 11*w - 3]', '[9921, 9921, -w^3 - 3*w^2 - w - 5]', '[9921, 9921, -2*w^3 + 3*w^2 + 14*w - 3]', '[9925, 9925, 4*w^3 - 5*w^2 - 9*w + 14]', '[9929, 9929, w^3 + 5*w^2 - 4*w - 12]', '[9931, 9931, 5*w^3 - 4*w^2 - 11*w + 12]', '[9931, 9931, -5*w^3 + 7*w^2 + 15*w - 4]', '[9935, 9935, -3*w^3 + 2*w^2 + 5*w + 8]', '[9936, 138, 4*w^3 - 8*w^2 - 14*w + 10]', '[9936, 414, -2*w^3 - 4*w^2 + 4*w + 12]', '[9939, 9939, -2*w^3 - 2*w^2 - 3*w - 6]', '[9939, 9939, 6*w^3 + 4*w^2 - 17*w - 3]', '[9949, 9949, 7*w^3 - 6*w^2 - 28*w + 2]', '[9949, 9949, -8*w^3 + 7*w^2 + 33*w - 4]', '[9949, 9949, 7*w^3 + w^2 - 33*w - 7]', '[9949, 9949, -7*w^3 + 3*w^2 + 28*w - 4]', '[9953, 9953, -8*w^3 + 2*w^2 + 29*w - 1]', '[9953, 9953, -3*w^3 + 4*w^2 + 17*w - 4]', '[9959, 9959, 2*w^3 - 9*w + 10]', '[9959, 9959, 4*w^3 - 2*w^2 - 21*w + 5]', '[9963, 369, 6*w^3 - 3*w^2 - 18*w]', '[9963, 369, 5*w^3 - w^2 - 16*w - 10]', '[9963, 1107, -7*w^3 + 4*w^2 + 26*w - 9]', '[9971, 9971, -4*w^2 - w + 20]', '[9973, 9973, 7*w^3 - 3*w^2 - 23*w - 2]', '[9973, 9973, 9*w^3 - 8*w^2 - 38*w + 19]', '[9981, 3327, -4*w^3 + 7*w^2 + 20*w - 14]', '[9981, 3327, -4*w^3 + 3*w^2 + 21*w - 10]', '[9981, 3327, -7*w^3 + 7*w^2 + 26*w - 6]', '[9981, 3327, -5*w^3 + 8*w^2 + 22*w - 10]', '[9983, 9983, w^3 + 5*w^2 - 9*w - 9]', '[9983, 9983, 6*w^3 - 7*w^2 - 26*w + 13]', '[9984, 156, -4*w^2 - 4*w + 12]', '[9985, 9985, -w^3 + w^2 + w + 10]', '[9985, 9985, -8*w^3 + 7*w^2 + 27*w - 8]', '[9987, 9987, 7*w^3 - 25*w - 12]', '[9991, 9991, -4*w^3 + 3*w^2 + 21*w]', '[9991, 9991, 10*w^3 - 8*w^2 - 35*w + 5]', '[9995, 9995, -w^3 + 4*w^2 - 10*w + 11]', '[9997, 9997, -2*w^3 + w^2 + 5*w - 11]', '[10000, 10, 10]', '[10000, 1250, -2*w^3 - 4*w^2 + 10*w + 10]'], 'label': '4.4.3981.1', 'narrow_class_no': 1, 'primes': ['[3, 3, w + 1]', '[5, 5, w^3 - w^2 - 3*w + 1]', '[9, 3, -w^2 + 2]', '[13, 13, -w^3 + w^2 + 4*w]', '[16, 2, 2]', '[23, 23, w^2 - 2*w - 2]', '[37, 37, w^3 - 4*w + 1]', '[37, 37, w^3 - w^2 - 5*w + 1]', '[41, 41, w^3 - 5*w + 1]', '[43, 43, 2*w^3 - w^2 - 7*w]', '[53, 53, 2*w - 3]', '[59, 59, -2*w^3 + w^2 + 9*w - 1]', '[67, 67, -w - 3]', '[67, 67, w^3 + w^2 - 5*w - 4]', '[71, 71, 2*w^3 - 3*w^2 - 7*w + 5]', '[73, 73, w^3 - 6*w]', '[73, 73, -w^3 - w^2 + 5*w + 3]', '[79, 79, w^3 - 3*w - 4]', '[83, 83, w^3 - 2*w^2 - 3*w + 1]', '[83, 83, -2*w^3 + 2*w^2 + 6*w - 3]', '[89, 89, 2*w^3 - w^2 - 7*w + 3]', '[89, 89, -2*w^3 + w^2 + 8*w - 2]', '[97, 97, 2*w^3 - 8*w - 1]', '[103, 103, -2*w^3 + 3*w^2 + 5*w - 2]', '[103, 103, w^2 + w - 4]', '[113, 113, 2*w^3 - w^2 - 7*w + 4]', '[125, 5, -2*w^3 + w^2 + 6*w - 1]', '[131, 131, -2*w^3 + 2*w^2 + 5*w - 3]', '[131, 131, -4*w^3 + 5*w^2 + 13*w - 9]', '[137, 137, w^3 - 2*w^2 - 4*w + 1]', '[137, 137, 2*w^2 - 2*w - 3]', '[137, 137, 3*w^3 - 2*w^2 - 10*w - 1]', '[137, 137, w - 4]', '[139, 139, w^2 - 2*w - 4]', '[149, 149, 2*w^3 - 7*w - 4]', '[151, 151, -2*w^3 + 4*w^2 + 7*w - 9]', '[157, 157, -w^3 + 3*w^2 + 2*w - 7]', '[173, 173, w^2 + w - 5]', '[173, 173, -w^3 + 3*w^2 + 3*w - 5]', '[179, 179, -w^3 + w^2 + 6*w - 3]', '[181, 181, 3*w^3 - 4*w^2 - 11*w + 7]', '[191, 191, -2*w^3 + 2*w^2 + 9*w - 3]', '[191, 191, 2*w^3 + w^2 - 9*w - 4]', '[193, 193, -2*w^3 + 3*w^2 + 9*w - 6]', '[197, 197, -w^3 + w^2 + 6*w - 1]', '[199, 199, 2*w^2 - w - 4]', '[211, 211, w^3 - 5*w - 5]', '[223, 223, w^3 + 2*w^2 - 4*w - 7]', '[223, 223, 2*w^3 - w^2 - 8*w - 4]', '[227, 227, -3*w^3 + 4*w^2 + 8*w - 6]', '[229, 229, w^3 - 3*w - 6]', '[229, 229, 2*w^3 - 2*w^2 - 9*w - 1]', '[233, 233, 2*w^3 - w^2 - 10*w + 6]', '[233, 233, -w^3 + 7*w - 2]', '[257, 257, 3*w^3 - 2*w^2 - 10*w + 3]', '[257, 257, 3*w^3 - 2*w^2 - 10*w]', '[263, 263, 3*w + 4]', '[269, 269, w^3 + w^2 - 3*w - 5]', '[281, 281, 2*w^3 - 9*w]', '[281, 281, -2*w^3 + w^2 + 9*w - 5]', '[283, 283, 3*w^3 - 3*w^2 - 9*w + 2]', '[283, 283, 3*w^3 - w^2 - 10*w - 1]', '[311, 311, -w^3 + 7*w - 1]', '[317, 317, -w^3 + w^2 + 4*w - 6]', '[317, 317, -w^3 - w^2 + 6*w - 1]', '[349, 349, 3*w^3 - w^2 - 13*w + 1]', '[353, 353, w^3 + w^2 - 2*w - 4]', '[359, 359, 3*w^2 - 10]', '[373, 373, -w^3 + 2*w^2 + 7*w - 1]', '[379, 379, -3*w^3 + 3*w^2 + 9*w - 5]', '[397, 397, -2*w^3 + w^2 + 10*w - 1]', '[409, 409, 4*w^3 - 5*w^2 - 12*w + 5]', '[419, 419, 2*w^3 - 5*w^2 - 3*w + 8]', '[419, 419, w^2 - w - 7]', '[421, 421, -2*w^3 + 8*w - 1]', '[431, 431, w^3 - 2*w - 5]', '[431, 431, w^3 + 2*w^2 - 4*w - 6]', '[433, 433, -3*w^3 + 3*w^2 + 8*w - 8]', '[433, 433, -3*w^3 + 4*w^2 + 11*w - 6]', '[439, 439, -3*w^3 + 3*w^2 + 9*w - 4]', '[439, 439, -3*w^3 + 3*w^2 + 11*w - 2]', '[449, 449, 2*w^2 - 3*w - 6]', '[449, 449, -w^2 + w - 3]', '[463, 463, -w^3 - w^2 + 9*w + 2]', '[491, 491, -3*w^2 + 3*w + 10]', '[491, 491, 5*w^3 - 7*w^2 - 16*w + 12]', '[499, 499, -2*w^3 + 9*w - 1]', '[503, 503, -w^3 + 2*w^2 - 4]', '[503, 503, -4*w^3 + 7*w^2 + 12*w - 15]', '[509, 509, 4*w^3 - w^2 - 14*w + 1]', '[541, 541, 3*w^3 - 2*w^2 - 9*w]', '[557, 557, 2*w^3 - 3*w^2 - 7*w + 2]', '[563, 563, 4*w^3 - 2*w^2 - 17*w + 3]', '[569, 569, 2*w^3 - w^2 - 9*w - 5]', '[577, 577, -3*w^3 + 3*w^2 + 7*w]', '[577, 577, 3*w^3 - 2*w^2 - 9*w + 3]', '[601, 601, -3*w^3 + 3*w^2 + 13*w - 1]', '[607, 607, w^2 + 2*w - 6]', '[613, 613, -2*w^3 - 2*w^2 + 9*w + 4]', '[613, 613, -3*w^3 + 4*w^2 + 13*w - 8]', '[619, 619, 4*w^3 - 4*w^2 - 13*w + 5]', '[619, 619, -2*w^3 + 2*w^2 + 10*w - 5]', '[631, 631, -w^3 + w^2 + 7*w - 2]', '[641, 641, -w - 5]', '[641, 641, -3*w^3 + 2*w^2 + 14*w - 5]', '[659, 659, -w^3 + 2*w^2 + w - 7]', '[661, 661, 3*w^2 - 5]', '[673, 673, -w^3 + 4*w^2 + 4*w - 8]', '[673, 673, -4*w^3 + w^2 + 15*w]', '[677, 677, -w^3 + 4*w^2 + 3*w - 6]', '[683, 683, -w^3 + 4*w^2 - 7]', '[701, 701, -4*w^3 + 4*w^2 + 13*w - 6]', '[701, 701, 2*w^3 - 2*w^2 - 8*w + 9]', '[701, 701, -w^3 + 2*w^2 + 7*w - 3]', '[701, 701, -3*w^3 + 4*w^2 + 9*w - 3]', '[709, 709, -w^2 + 2*w - 4]', '[709, 709, -4*w^3 + 5*w^2 + 15*w - 8]', '[727, 727, -2*w^3 + 3*w^2 + 10*w - 5]', '[727, 727, -w^3 + 2*w^2 + 6*w - 8]', '[727, 727, -4*w^3 + 3*w^2 + 17*w - 4]', '[727, 727, -3*w^3 + 14*w + 1]', '[733, 733, 2*w^2 - 4*w - 5]', '[739, 739, 3*w^2 - 3*w - 5]', '[739, 739, -w^3 + 4*w^2 + w - 5]', '[739, 739, 2*w^3 - 6*w - 5]', '[739, 739, -2*w^3 + 5*w^2 - 5]', '[743, 743, w^3 - 3*w - 7]', '[743, 743, w^3 + w^2 - 3*w - 8]', '[751, 751, -w^3 + w^2 + 2*w - 7]', '[751, 751, w^2 + 2*w - 7]', '[757, 757, -3*w^3 + 3*w^2 + 8*w - 3]', '[769, 769, 3*w^3 - 5*w^2 - 11*w + 8]', '[787, 787, -2*w^3 + 4*w^2 + 3*w - 7]', '[787, 787, -3*w^3 + w^2 + 11*w - 3]', '[797, 797, -3*w^3 + 2*w^2 + 10*w - 9]', '[809, 809, 2*w^2 - 2*w - 11]', '[809, 809, 3*w^2 - w - 8]', '[809, 809, -3*w^3 + 3*w^2 + 7*w - 4]', '[809, 809, -2*w^3 + 4*w^2 + 8*w - 5]', '[821, 821, 3*w^3 - 11*w]', '[821, 821, -w^3 + 4*w^2 + 3*w - 10]', '[823, 823, -4*w^3 + 4*w^2 + 15*w - 4]', '[829, 829, 2*w^3 + w^2 - 8*w]', '[853, 853, -w^3 + 2*w^2 - 5]', '[857, 857, 6*w^3 - 6*w^2 - 25*w + 16]', '[857, 857, 3*w^2 - w - 5]', '[859, 859, 4*w + 5]', '[859, 859, w^3 - w^2 - 2*w - 5]', '[877, 877, 2*w^3 - 3*w^2 - 9*w + 1]', '[877, 877, -w^3 + 3*w^2 + w - 10]', '[883, 883, w^3 + 2*w^2 - 3*w - 8]', '[883, 883, -3*w^3 + 4*w^2 + 10*w - 4]', '[907, 907, -5*w^3 + 8*w^2 + 15*w - 18]', '[911, 911, -w^3 + 3*w - 5]', '[937, 937, -3*w^3 + w^2 + 16*w - 5]', '[937, 937, -2*w^3 + 9*w - 4]', '[941, 941, -4*w^3 + 5*w^2 + 10*w - 3]', '[947, 947, -w^3 + 4*w^2 + 3*w - 7]', '[947, 947, 3*w^2 - 2*w - 7]', '[947, 947, -2*w^3 + 4*w^2 + 11*w - 9]', '[947, 947, -4*w^3 + 3*w^2 + 13*w - 5]', '[967, 967, 3*w^2 - w - 6]', '[971, 971, 3*w^3 - 2*w^2 - 8*w + 2]', '[983, 983, -3*w^2 + 6*w + 5]', '[983, 983, -w^3 + 4*w^2 + w - 6]', '[983, 983, 4*w^3 - 3*w^2 - 13*w + 1]', '[983, 983, -2*w^3 + w^2 + 11*w]', '[997, 997, 3*w^3 - 3*w^2 - 7*w + 3]', '[997, 997, w^3 - w - 5]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 2, -4, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 3981, 'disc_rad': 3981, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [0]], [5, [[3, 1], [1, 1]]], [7, [[4, 1]]], [11, [[4, 1]]], [13, [[3, 1], [1, 1]]], [17, [[4, 1]]], [19, [[4, 1]]], [23, [[3, 1], [1, 1]]], [29, [[4, 1]]], [31, [[4, 1]]], [37, [[2, 1], [1, 2]]], [41, [[3, 1], [1, 1]]], [43, [[3, 1], [1, 1]]], [47, [[4, 1]]], [53, [[3, 1], [1, 1]]], [59, [[3, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 63.095166217389426, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.3981.1', 'local_algs': ['3.2.0.1', '3.2.1.2', 'm1327.1.2.0', 'm1327.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [3, 1327], 'rd': 7.94324657916, 'regulator': {'__RealLiteral__': 0, 'data': '3.18893941247', 'prec': 44}, 'res': {'gal': ['-21599,237032,-681954,-528778,4065354,-558104,-9683833,2607608,12690714,-2798742,-10050534,1186870,4912007,-90506,-1471086,-79050,268314,25772,-29455,-3272,1890,188,-66,-4,1'], 'sib': ['-1,25,-163,99,485,-256,-500,111,187,-11,-25,0,1', '-192,-468,541,31,-49,-1,1', '144,0,-1941,0,6721,0,-3546,0,611,0,-42,0,1', '3,-10,2,15,-5,-3,1', '35605,31343,-16049,-4471,1872,181,-77,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a - 1 \\)', '\\( a^{3} - a^{2} - 3 a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}