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hmf_forms • Show schema
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{'deg': 4, 'dimension': 6, 'disc': 15125, 'field_bad_primes': [5, 11], 'field_label': '4.4.15125.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.15125.1-19.2-h', 'label_nsuffix': 7, 'label_suffix': 'h', 'level_bad_primes': [19], 'level_ideal': '[19,19,-w^3 - w^2 + 9*w + 3]', 'level_label': '19.2', 'level_norm': 19, 'parallel_weight': 2, 'short_label': '19.2-h', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[19,19,-w^3 - w^2 + 9*w + 3]', 1]], 'hecke_eigenvalues': ['e', '-1/27*e^5 + 19/27*e^3 - 10/3*e', '2/27*e^5 - 29/27*e^3 + 1/3*e', '-1/9*e^4 + 10/9*e^2 + 1', '-4/9*e^4 + 58/9*e^2 - 4', -1, '1/3*e^3 - 13/3*e', '1/27*e^5 - 19/27*e^3 + 10/3*e', '1/9*e^4 - 19/9*e^2 + 12', '5/9*e^4 - 77/9*e^2 + 14', '-1/27*e^5 + 10/27*e^3 + 3*e', '2/9*e^5 - 35/9*e^3 + 35/3*e', '1/9*e^5 - 13/9*e^3 - 5/3*e', '-2/27*e^5 + 29/27*e^3 - 4/3*e', '-2/27*e^5 + 20/27*e^3 + 5*e', '5/27*e^5 - 95/27*e^3 + 41/3*e', '-2/3*e^4 + 29/3*e^2 - 2', '11/9*e^4 - 164/9*e^2 + 22', '-8/9*e^4 + 125/9*e^2 - 22', '-2/9*e^4 + 11/9*e^2 + 14', '-7/9*e^4 + 97/9*e^2 - 4', '2/9*e^5 - 23/9*e^3 - 23/3*e', '-4/9*e^4 + 76/9*e^2 - 20', '-2/9*e^5 + 35/9*e^3 - 29/3*e', '-2/9*e^4 + 29/9*e^2 - 8', '5/27*e^5 - 104/27*e^3 + 15*e', '-5/9*e^4 + 59/9*e^2 + 12', '1/27*e^5 + 8/27*e^3 - 29/3*e', '-e^4 + 15*e^2 - 10', '-4/3*e^3 + 52/3*e', '-1/3*e^5 + 19/3*e^3 - 26*e', '1/9*e^4 - 1/9*e^2 - 2', 'e^4 - 15*e^2 + 28', '-5/9*e^4 + 59/9*e^2 + 14', '2/9*e^4 - 20/9*e^2 + 6', '1/27*e^5 + 17/27*e^3 - 12*e', '-5/27*e^5 + 68/27*e^3 + 1/3*e', '-4/9*e^5 + 58/9*e^3 - 3*e', '7/27*e^5 - 142/27*e^3 + 80/3*e', '7/27*e^5 - 115/27*e^3 + 23/3*e', '-2/27*e^5 + 92/27*e^3 - 89/3*e', '1/27*e^5 - 1/27*e^3 - 37/3*e', '-4/27*e^5 + 103/27*e^3 - 58/3*e', '2/3*e^3 - 23/3*e', '-1/27*e^5 + 10/27*e^3 + 4*e', '11/9*e^4 - 137/9*e^2 - 6', '-2/9*e^5 + 17/9*e^3 + 37/3*e', '4/9*e^5 - 70/9*e^3 + 64/3*e', '10/9*e^4 - 136/9*e^2 - 8', '-1/3*e^4 + 10/3*e^2 + 12', '-2/9*e^4 + 47/9*e^2 - 24', '-2*e^4 + 27*e^2 + 2', '-5/9*e^4 + 86/9*e^2 - 34', '4/3*e^4 - 64/3*e^2 + 36', '14/9*e^4 - 194/9*e^2 + 4', '2*e^2 - 4', '2/3*e^4 - 32/3*e^2 + 20', '-16/27*e^5 + 259/27*e^3 - 68/3*e', '1/27*e^5 + 53/27*e^3 - 103/3*e', '1/9*e^5 - 34/9*e^3 + 80/3*e', '4/27*e^5 - 103/27*e^3 + 82/3*e', '-10/27*e^5 + 190/27*e^3 - 88/3*e', '-2/3*e^4 + 20/3*e^2 + 16', '22/9*e^4 - 346/9*e^2 + 66', '-5/27*e^5 + 95/27*e^3 - 14/3*e', '-22/27*e^5 + 400/27*e^3 - 140/3*e', '-10/9*e^4 + 154/9*e^2 - 12', '-1/3*e^5 + 7/3*e^3 + 28*e', '-11/9*e^4 + 137/9*e^2 + 6', '-17/27*e^5 + 323/27*e^3 - 122/3*e', '-2/9*e^5 + 23/9*e^3 + 17/3*e', '1/27*e^5 + 35/27*e^3 - 74/3*e', '-5/27*e^5 + 95/27*e^3 - 56/3*e', '-2/27*e^5 - 7/27*e^3 + 19*e', '-1/27*e^5 + 64/27*e^3 - 19*e', '-2/9*e^4 + 38/9*e^2 + 2', '-4/9*e^4 + 76/9*e^2 - 12', '-2/27*e^5 + 65/27*e^3 - 71/3*e', '-8/27*e^5 + 89/27*e^3 + 23/3*e', '-2/27*e^5 + 83/27*e^3 - 73/3*e', '5/9*e^5 - 53/9*e^3 - 68/3*e', '2/3*e^3 - 8/3*e', '-2/9*e^4 + 56/9*e^2 - 26', '-11/27*e^5 + 110/27*e^3 + 17*e', '-1/3*e^4 + 19/3*e^2 - 4', '17/27*e^5 - 233/27*e^3 - 2/3*e', '14/27*e^5 - 176/27*e^3 - 14/3*e', '-1/9*e^4 + 1/9*e^2 + 42', 'e^4 - 13*e^2 - 10', '10/27*e^5 - 118/27*e^3 - 19/3*e', '-11/27*e^5 + 92/27*e^3 + 80/3*e', '8/9*e^5 - 143/9*e^3 + 50*e', '-7/9*e^5 + 124/9*e^3 - 44*e', '-2*e^4 + 26*e^2 + 6', '7/3*e^4 - 97/3*e^2 + 12', '-7/27*e^5 + 196/27*e^3 - 161/3*e', '10/3*e^3 - 136/3*e', '5/3*e^4 - 62/3*e^2 - 6', '1/9*e^4 - 46/9*e^2 + 24', '8/9*e^4 - 125/9*e^2 - 8', '32/9*e^4 - 455/9*e^2 + 26', '-26/27*e^5 + 413/27*e^3 - 80/3*e', '4/27*e^5 - 67/27*e^3 + 10*e', '-2/27*e^5 - 52/27*e^3 + 125/3*e', '14/27*e^5 - 275/27*e^3 + 42*e', '7/27*e^5 - 133/27*e^3 + 34/3*e', '11/3*e^3 - 167/3*e', '-10/9*e^4 + 154/9*e^2 - 32', '-2/9*e^4 + 20/9*e^2 + 28', '-2/3*e^4 + 35/3*e^2 - 20', '-16/9*e^4 + 223/9*e^2 - 10', '-e^4 + 18*e^2 - 44', '-4/9*e^4 + 49/9*e^2 - 28', '5/9*e^4 - 50/9*e^2 - 4', '14/9*e^4 - 185/9*e^2 - 2', '2/9*e^4 + 25/9*e^2 - 36', '-23/9*e^4 + 338/9*e^2 - 52', '-1/9*e^4 - 17/9*e^2 + 14', '-19/27*e^5 + 235/27*e^3 + 22/3*e', '5/27*e^5 - 122/27*e^3 + 53/3*e', '-7/3*e^4 + 97/3*e^2 - 10', '20/9*e^4 - 317/9*e^2 + 74', '-5/9*e^4 + 104/9*e^2 - 44', '14/9*e^4 - 221/9*e^2 + 52', '26/9*e^4 - 341/9*e^2 - 14', '28/9*e^4 - 424/9*e^2 + 50', '-11/3*e^4 + 161/3*e^2 - 52', '-4/27*e^5 + 130/27*e^3 - 142/3*e', '2/3*e^5 - 9*e^3 + 13/3*e', '10/3*e^3 - 100/3*e', '-2/9*e^4 + 56/9*e^2 + 2', '10/9*e^4 - 190/9*e^2 + 34', '-4*e^3 + 58*e', '20/9*e^4 - 281/9*e^2 + 38', '-1/3*e^4 + 10/3*e^2 + 38', '1/3*e^4 - 28/3*e^2 + 44', '-e^2 + 24', '-11/3*e^3 + 137/3*e', '13/3*e^3 - 157/3*e', '1/3*e^5 - 29/3*e^3 + 172/3*e', '-4/27*e^5 + 103/27*e^3 - 55/3*e', '-2/27*e^5 - 25/27*e^3 + 53/3*e', '-1/3*e^4 + 7/3*e^2 + 46', '-1/27*e^5 + 37/27*e^3 - 8*e', '4/9*e^4 - 76/9*e^2 + 64', '2/27*e^5 - 11/27*e^3 - 4/3*e', '-e^5 + 40/3*e^3 + 8/3*e', '-5/27*e^5 + 158/27*e^3 - 48*e', '20/27*e^5 - 362/27*e^3 + 53*e', '-8/27*e^5 + 215/27*e^3 - 63*e', '23/27*e^5 - 293/27*e^3 - 38/3*e', '29/27*e^5 - 389/27*e^3 - 16/3*e', '5/9*e^5 - 119/9*e^3 + 206/3*e'], 'hecke_polynomial': 'x^6 - 28*x^4 + 207*x^2 - 162', 'label': '4.4.15125.1-19.2-h'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 15125, 'ideals': ['[1, 1, 1]', '[5, 5, 4*w^3 + 7*w^2 - 37*w - 45]', '[11, 11, 2*w^3 + 3*w^2 - 18*w - 16]', '[11, 11, -w + 2]', '[16, 2, 2]', '[19, 19, 4*w^3 + 7*w^2 - 36*w - 45]', '[19, 19, -w^3 - w^2 + 9*w + 3]', '[19, 19, -2*w^3 - 4*w^2 + 17*w + 23]', '[19, 19, w^3 + 2*w^2 - 10*w - 10]', '[25, 5, 2*w^3 + 4*w^2 - 18*w - 25]', '[29, 29, -w - 2]', '[29, 29, -w^3 - 2*w^2 + 8*w + 15]', '[29, 29, 2*w^3 + 3*w^2 - 18*w - 20]', '[29, 29, -3*w^3 - 5*w^2 + 27*w + 28]', '[31, 31, 3*w^3 + 5*w^2 - 27*w - 31]', '[31, 31, -3*w^3 - 5*w^2 + 27*w + 30]', '[31, 31, -2*w^3 - 3*w^2 + 18*w + 17]', '[31, 31, 2*w^3 + 3*w^2 - 18*w - 18]', '[55, 55, 2*w^3 + 3*w^2 - 18*w - 14]', '[55, 55, w - 4]', '[71, 71, -w^3 - 2*w^2 + 10*w + 8]', '[71, 71, 4*w^3 + 8*w^2 - 35*w - 50]', '[71, 71, -4*w^3 - 7*w^2 + 36*w + 47]', '[71, 71, -w^3 - 2*w^2 + 8*w + 17]', '[79, 79, w^3 + 2*w^2 - 10*w - 14]', '[79, 79, -w^3 - w^2 + 9*w + 7]', '[79, 79, -2*w^3 - 4*w^2 + 17*w + 27]', '[79, 79, -4*w^3 - 7*w^2 + 36*w + 41]', '[80, 10, 8*w^3 + 14*w^2 - 74*w - 90]', '[81, 3, -3]', '[95, 95, -2*w^3 - 4*w^2 + 19*w + 26]', '[95, 95, -3*w^3 - 6*w^2 + 26*w + 39]', '[95, 95, 5*w^3 + 9*w^2 - 45*w - 54]', '[95, 95, -w^2 + 6]', '[109, 109, -2*w^3 - 3*w^2 + 19*w + 13]', '[109, 109, 3*w^3 + 5*w^2 - 26*w - 26]', '[109, 109, 2*w^3 + 3*w^2 - 19*w - 22]', '[109, 109, 3*w^3 + 5*w^2 - 26*w - 35]', '[121, 11, 3*w^3 + 6*w^2 - 27*w - 38]', '[121, 11, 3*w^3 + 6*w^2 - 27*w - 37]', '[121, 11, -10*w^3 - 18*w^2 + 91*w + 113]', '[125, 5, -12*w^3 - 21*w^2 + 109*w + 133]', '[139, 139, 4*w^3 + 7*w^2 - 36*w - 40]', '[139, 139, -w^3 - w^2 + 9*w + 8]', '[139, 139, -w^3 - 2*w^2 + 10*w + 15]', '[139, 139, 2*w^3 + 4*w^2 - 17*w - 28]', '[145, 145, -19*w^3 - 33*w^2 + 175*w + 214]', '[145, 145, 5*w^3 + 9*w^2 - 46*w - 55]', '[145, 145, -22*w^3 - 39*w^2 + 202*w + 249]', '[145, 145, 10*w^3 + 18*w^2 - 90*w - 113]', '[149, 149, 4*w^3 + 8*w^2 - 35*w - 52]', '[149, 149, -3*w^3 - 5*w^2 + 26*w + 34]', '[149, 149, -2*w^3 - 3*w^2 + 19*w + 14]', '[149, 149, -6*w^3 - 11*w^2 + 54*w + 66]', '[155, 155, -22*w^3 - 39*w^2 + 201*w + 248]', '[155, 155, -14*w^3 - 25*w^2 + 128*w + 159]', '[155, 155, 18*w^3 + 32*w^2 - 164*w - 203]', '[155, 155, 10*w^3 + 18*w^2 - 91*w - 114]', '[176, 22, 4*w^3 + 6*w^2 - 36*w - 32]', '[176, 22, -2*w + 4]', '[181, 181, w^3 + 2*w^2 - 11*w - 13]', '[181, 181, -3*w^3 - 4*w^2 + 27*w + 24]', '[181, 181, -7*w^3 - 12*w^2 + 63*w + 72]', '[181, 181, 3*w^3 + 6*w^2 - 25*w - 39]', '[191, 191, -7*w^3 - 12*w^2 + 66*w + 80]', '[191, 191, 5*w^3 + 9*w^2 - 47*w - 57]', '[191, 191, -2*w^3 - 2*w^2 + 18*w + 9]', '[191, 191, 2*w^3 + 2*w^2 - 17*w - 13]', '[209, 209, 5*w^3 + 10*w^2 - 43*w - 60]', '[209, 209, 2*w^3 + 4*w^2 - 19*w - 27]', '[209, 209, 5*w^3 + 9*w^2 - 45*w - 53]', '[209, 209, -9*w^3 - 16*w^2 + 81*w + 101]', '[209, 209, -3*w^3 - 6*w^2 + 29*w + 34]', '[209, 209, -w^2 + 5]', '[209, 209, 3*w^3 + 6*w^2 - 26*w - 40]', '[209, 209, w^3 - 9*w + 5]', '[239, 239, 7*w^3 + 13*w^2 - 62*w - 81]', '[239, 239, -2*w^3 - 5*w^2 + 17*w + 32]', '[239, 239, 6*w^3 + 11*w^2 - 55*w - 67]', '[239, 239, -w^3 - 3*w^2 + 10*w + 20]', '[251, 251, 7*w^3 + 13*w^2 - 63*w - 82]', '[251, 251, -5*w^3 - 10*w^2 + 44*w + 61]', '[251, 251, 4*w^3 + 8*w^2 - 37*w - 48]', '[251, 251, -2*w^3 - 5*w^2 + 18*w + 34]', '[256, 4, 4]', '[275, 55, 2*w^3 + 5*w^2 - 16*w - 34]', '[275, 55, -2*w^3 - 2*w^2 + 17*w + 12]', '[304, 38, 8*w^3 + 14*w^2 - 72*w - 90]', '[304, 38, -2*w^3 - 2*w^2 + 18*w + 6]', '[304, 38, -4*w^3 - 8*w^2 + 34*w + 46]', '[304, 38, 2*w^3 + 4*w^2 - 20*w - 20]', '[311, 311, 5*w^3 + 9*w^2 - 44*w - 50]', '[311, 311, -4*w^3 - 7*w^2 + 37*w + 48]', '[311, 311, 2*w^3 + 4*w^2 - 19*w - 19]', '[311, 311, w^3 + w^2 - 8*w - 11]', '[319, 319, -w^3 - 4*w^2 + 12*w + 22]', '[319, 319, w^2 - 4]', '[319, 319, w^3 + 2*w^2 - 13*w - 1]', '[319, 319, 2*w^3 + 5*w^2 - 16*w - 37]', '[319, 319, -3*w^3 - 6*w^2 + 26*w + 41]', '[319, 319, -9*w^3 - 16*w^2 + 80*w + 94]', '[319, 319, -w^3 - 5*w^2 + 7*w + 39]', '[319, 319, -7*w^3 - 10*w^2 + 63*w + 48]', '[331, 331, 4*w^3 + 6*w^2 - 36*w - 37]', '[331, 331, -6*w^3 - 10*w^2 + 54*w + 59]', '[331, 331, -2*w - 1]', '[331, 331, -2*w^3 - 4*w^2 + 16*w + 27]', '[341, 341, -3*w^3 - 3*w^2 + 28*w + 7]', '[341, 341, -2*w^3 - 5*w^2 + 19*w + 31]', '[341, 341, w^3 + w^2 - 9*w]', '[341, 341, 2*w^3 + 5*w^2 - 18*w - 33]', '[341, 341, -3*w^3 - 4*w^2 + 27*w + 16]', '[341, 341, -w^3 - 4*w^2 + 10*w + 26]', '[341, 341, w^3 - 10*w + 9]', '[341, 341, w^3 + 4*w^2 - 9*w - 28]', '[349, 349, -3*w^3 - 5*w^2 + 28*w + 27]', '[349, 349, 4*w^3 + 8*w^2 - 35*w - 53]', '[349, 349, -3*w^3 - 6*w^2 + 28*w + 40]', '[349, 349, 6*w^3 + 11*w^2 - 54*w - 65]', '[355, 355, 42*w^3 + 74*w^2 - 385*w - 472]', '[355, 355, -w^3 - 2*w^2 + 11*w + 12]', '[355, 355, -13*w^3 - 23*w^2 + 117*w + 142]', '[355, 355, 13*w^3 + 23*w^2 - 120*w - 145]', '[359, 359, -w^3 - 3*w^2 + 8*w + 19]', '[359, 359, -6*w^3 - 11*w^2 + 53*w + 69]', '[359, 359, 5*w^3 + 9*w^2 - 46*w - 54]', '[359, 359, w^2 - w - 8]', '[361, 19, w^3 + 3*w^2 - 7*w - 23]', '[361, 19, -4*w^3 - 7*w^2 + 38*w + 45]', '[361, 19, -4*w^3 - 8*w^2 + 36*w + 51]', '[361, 19, -8*w^3 - 14*w^2 + 71*w + 83]', '[361, 19, -3*w^3 - 4*w^2 + 26*w + 26]', '[361, 19, -4*w^3 - 8*w^2 + 36*w + 49]', '[361, 361, w + 5]', '[361, 361, -2*w^3 - 3*w^2 + 18*w + 23]', '[361, 361, 3*w^3 + 5*w^2 - 27*w - 25]', '[361, 361, -w^3 - 2*w^2 + 8*w + 18]', '[395, 395, -23*w^3 - 40*w^2 + 211*w + 258]', '[395, 395, 14*w^3 + 25*w^2 - 129*w - 160]', '[395, 395, 9*w^3 + 16*w^2 - 82*w - 99]', '[395, 395, 18*w^3 + 32*w^2 - 163*w - 202]', '[400, 10, 4*w^3 + 8*w^2 - 36*w - 50]', '[401, 401, 5*w^3 + 8*w^2 - 45*w - 50]', '[401, 401, w^3 + 2*w^2 - 7*w - 15]', '[401, 401, w^3 + 2*w^2 - 7*w - 11]', '[401, 401, 5*w^3 + 8*w^2 - 45*w - 46]', '[405, 15, -12*w^3 - 21*w^2 + 111*w + 135]', '[409, 409, -9*w^3 - 16*w^2 + 81*w + 97]', '[409, 409, w^3 + w^2 - 11*w - 10]', '[409, 409, 6*w^3 + 10*w^2 - 53*w - 66]', '[409, 409, -3*w^3 - 6*w^2 + 29*w + 38]', '[421, 421, -3*w^3 - 4*w^2 + 26*w + 23]', '[421, 421, -4*w^3 - 6*w^2 + 35*w + 39]', '[421, 421, 8*w^3 + 14*w^2 - 71*w - 86]', '[421, 421, -7*w^3 - 12*w^2 + 62*w + 70]', '[439, 439, w^3 + w^2 - 10*w - 9]', '[439, 439, -4*w^3 - 7*w^2 + 35*w + 47]', '[439, 439, 3*w^3 + 5*w^2 - 28*w - 26]', '[439, 439, 2*w^3 + 3*w^2 - 17*w - 14]', '[464, 58, -2*w - 4]', '[464, 58, -2*w^3 - 4*w^2 + 16*w + 30]', '[464, 58, 4*w^3 + 6*w^2 - 36*w - 40]', '[464, 58, -6*w^3 - 10*w^2 + 54*w + 56]', '[475, 95, -6*w^3 - 11*w^2 + 56*w + 71]', '[475, 95, -3*w^3 - 7*w^2 + 25*w + 49]', '[475, 95, -10*w^3 - 18*w^2 + 89*w + 107]', '[475, 95, -w^3 + 8*w + 2]', '[479, 479, 3*w^3 + 6*w^2 - 29*w - 33]', '[479, 479, 5*w^3 + 10*w^2 - 43*w - 59]', '[479, 479, w^3 - 9*w + 6]', '[479, 479, 9*w^3 + 16*w^2 - 81*w - 102]', '[496, 62, 6*w^3 + 10*w^2 - 54*w - 62]', '[496, 62, -6*w^3 - 10*w^2 + 54*w + 60]', '[496, 62, -4*w^3 - 6*w^2 + 36*w + 34]', '[496, 62, 4*w^3 + 6*w^2 - 36*w - 36]', '[521, 521, 4*w^3 + 7*w^2 - 38*w - 44]', '[521, 521, 3*w^3 + 4*w^2 - 26*w - 25]', '[521, 521, 5*w^3 + 8*w^2 - 44*w - 46]', '[521, 521, -8*w^3 - 14*w^2 + 71*w + 84]', '[545, 545, -41*w^3 - 72*w^2 + 377*w + 463]', '[545, 545, -27*w^3 - 48*w^2 + 248*w + 304]', '[545, 545, 5*w^3 + 9*w^2 - 44*w - 58]', '[545, 545, 9*w^3 + 15*w^2 - 85*w - 101]', '[551, 551, -w^3 - w^2 + 11*w + 2]', '[551, 551, -5*w^3 - 8*w^2 + 44*w + 51]', '[551, 551, 2*w^3 + 3*w^2 - 20*w - 20]', '[551, 551, 2*w^3 + 3*w^2 - 17*w - 24]', '[551, 551, -3*w^3 - 5*w^2 + 28*w + 36]', '[551, 551, -19*w^3 - 34*w^2 + 173*w + 214]', '[551, 551, -3*w^3 - 8*w^2 + 31*w + 45]', '[551, 551, 7*w^3 + 9*w^2 - 64*w - 40]', '[551, 551, -17*w^3 - 29*w^2 + 154*w + 187]', '[551, 551, w^3 + 6*w^2 - 7*w - 48]', '[551, 551, 17*w^3 + 32*w^2 - 149*w - 193]', '[551, 551, 4*w^3 + 7*w^2 - 35*w - 37]', '[551, 551, -w^3 - w^2 + 10*w - 1]', '[551, 551, 6*w^3 + 10*w^2 - 53*w - 58]', '[551, 551, 10*w^3 + 19*w^2 - 85*w - 108]', '[551, 551, w^2 - 5*w + 5]', '[569, 569, 21*w^3 + 37*w^2 - 191*w - 236]', '[569, 569, -13*w^3 - 23*w^2 + 120*w + 149]', '[569, 569, 10*w^3 + 17*w^2 - 92*w - 111]', '[569, 569, -18*w^3 - 32*w^2 + 164*w + 201]', '[589, 589, -7*w^3 - 13*w^2 + 62*w + 82]', '[589, 589, -2*w^3 - 5*w^2 + 20*w + 31]', '[589, 589, 9*w^3 + 17*w^2 - 79*w - 105]', '[589, 589, -14*w^3 - 24*w^2 + 128*w + 155]', '[589, 589, 13*w^3 + 24*w^2 - 115*w - 147]', '[589, 589, -3*w^3 - 3*w^2 + 29*w + 8]', '[589, 589, 4*w^3 + 4*w^2 - 38*w - 11]', '[589, 589, 5*w^3 + 7*w^2 - 46*w - 34]', '[589, 589, -w^3 - 4*w^2 + 11*w + 25]', '[589, 589, 2*w^2 - w - 15]', '[589, 589, -9*w^3 - 15*w^2 + 82*w + 97]', '[589, 589, 5*w^3 + 8*w^2 - 46*w - 52]', '[589, 589, w^3 + 3*w^2 - 10*w - 21]', '[589, 589, -11*w^3 - 20*w^2 + 98*w + 124]', '[589, 589, 10*w^3 + 17*w^2 - 92*w - 110]', '[589, 589, -4*w^3 - 6*w^2 + 37*w + 31]', '[605, 55, 5*w^3 + 8*w^2 - 45*w - 48]', '[605, 55, -w^3 - 4*w^2 + 6*w + 34]', '[605, 55, -3*w^3 - 2*w^2 + 28*w + 2]', '[625, 5, 5]', '[631, 631, -2*w^3 - 3*w^2 + 20*w + 25]', '[631, 631, 7*w^3 + 12*w^2 - 64*w - 80]', '[631, 631, -9*w^3 - 17*w^2 + 80*w + 106]', '[631, 631, 19*w^3 + 33*w^2 - 175*w - 215]', '[641, 641, 4*w^3 + 6*w^2 - 35*w - 35]', '[641, 641, 4*w^3 + 6*w^2 - 35*w - 38]', '[641, 641, 7*w^3 + 12*w^2 - 62*w - 71]', '[641, 641, 7*w^3 + 12*w^2 - 62*w - 74]', '[659, 659, 6*w^3 + 11*w^2 - 54*w - 63]', '[659, 659, 4*w^3 + 6*w^2 - 37*w - 38]', '[659, 659, 4*w^3 + 8*w^2 - 35*w - 55]', '[659, 659, 3*w^3 + 6*w^2 - 28*w - 42]', '[661, 661, -27*w^3 - 48*w^2 + 247*w + 306]', '[661, 661, 14*w^3 + 24*w^2 - 129*w - 158]', '[661, 661, 11*w^3 + 19*w^2 - 102*w - 126]', '[661, 661, 2*w^3 + 3*w^2 - 19*w - 24]', '[691, 691, 6*w^3 + 12*w^2 - 53*w - 73]', '[691, 691, 8*w^3 + 15*w^2 - 72*w - 95]', '[691, 691, -5*w^3 - 10*w^2 + 46*w + 60]', '[691, 691, -3*w^3 - 7*w^2 + 27*w + 47]', '[695, 695, -14*w^3 - 25*w^2 + 126*w + 157]', '[695, 695, 18*w^3 + 32*w^2 - 166*w - 205]', '[695, 695, 27*w^3 + 47*w^2 - 248*w - 303]', '[695, 695, -13*w^3 - 23*w^2 + 119*w + 144]', '[725, 145, -10*w^3 - 18*w^2 + 89*w + 112]', '[725, 145, -w^3 + 8*w - 3]', '[725, 145, -6*w^3 - 11*w^2 + 56*w + 66]', '[725, 145, -3*w^3 - 7*w^2 + 25*w + 44]', '[739, 739, -2*w^3 - 5*w^2 + 19*w + 34]', '[739, 739, 7*w^3 + 13*w^2 - 64*w - 78]', '[739, 739, -3*w^3 - 7*w^2 + 26*w + 43]', '[739, 739, 8*w^3 + 15*w^2 - 71*w - 95]', '[745, 745, -21*w^3 - 37*w^2 + 191*w + 232]', '[745, 745, 9*w^3 + 16*w^2 - 81*w - 103]', '[745, 745, 30*w^3 + 53*w^2 - 272*w - 335]', '[745, 745, 23*w^3 + 41*w^2 - 211*w - 259]', '[751, 751, -4*w^3 - 9*w^2 + 37*w + 59]', '[751, 751, -5*w^3 - 9*w^2 + 43*w + 48]', '[751, 751, -6*w^3 - 10*w^2 + 55*w + 68]', '[751, 751, -10*w^3 - 17*w^2 + 93*w + 114]', '[769, 769, 6*w^3 + 11*w^2 - 52*w - 69]', '[769, 769, w^3 + w^2 - 7*w - 5]', '[769, 769, 2*w^3 + 2*w^2 - 19*w - 11]', '[769, 769, 7*w^3 + 12*w^2 - 64*w - 72]', '[775, 155, -3*w^3 - 5*w^2 + 29*w + 31]', '[775, 155, w^3 + w^2 - 11*w - 6]', '[775, 155, -w^2 - 2*w + 9]', '[775, 155, -2*w^3 - 3*w^2 + 20*w + 16]', '[781, 781, w^3 - 2*w - 15]', '[781, 781, 3*w^3 + w^2 - 29*w + 7]', '[781, 781, -5*w^3 - 6*w^2 + 45*w + 27]', '[781, 781, -4*w^3 - 5*w^2 + 36*w + 24]', '[781, 781, 3*w^3 + 6*w^2 - 31*w - 30]', '[781, 781, 9*w^3 + 20*w^2 - 76*w - 130]', '[781, 781, 5*w^3 + 7*w^2 - 46*w - 39]', '[781, 781, w^3 + 2*w^2 - 15*w + 3]', '[809, 809, -3*w^3 - 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42*w - 64]', '[991, 991, -4*w^3 - 5*w^2 + 36*w + 29]', '[991, 991, -11*w^3 - 19*w^2 + 99*w + 115]', '[991, 991, 10*w^3 + 17*w^2 - 90*w - 108]', '[1009, 1009, -6*w^3 - 10*w^2 + 55*w + 58]', '[1009, 1009, -5*w^3 - 9*w^2 + 43*w + 58]', '[1009, 1009, 5*w^3 + 9*w^2 - 46*w - 52]', '[1009, 1009, 6*w^3 + 11*w^2 - 53*w - 71]', '[1019, 1019, -17*w^3 - 30*w^2 + 154*w + 191]', '[1019, 1019, -17*w^3 - 30*w^2 + 157*w + 194]', '[1019, 1019, 14*w^3 + 24*w^2 - 129*w - 156]', '[1019, 1019, -22*w^3 - 39*w^2 + 201*w + 246]', '[1021, 1021, 3*w^3 + 3*w^2 - 27*w - 14]', '[1021, 1021, -6*w^3 - 12*w^2 + 51*w + 74]', '[1021, 1021, 8*w^3 + 13*w^2 - 72*w - 83]', '[1021, 1021, 12*w^3 + 21*w^2 - 108*w - 130]', '[1045, 1045, 3*w^3 + 4*w^2 - 29*w - 15]', '[1045, 1045, 2*w^3 + 5*w^2 - 17*w - 30]', '[1045, 1045, 7*w^3 + 12*w^2 - 61*w - 66]', '[1045, 1045, -5*w^3 - 8*w^2 + 43*w + 56]', '[1045, 1045, 5*w^3 + 8*w^2 - 47*w - 55]', '[1045, 1045, -6*w^3 - 11*w^2 + 55*w + 65]', '[1045, 1045, w^3 + 3*w^2 - 10*w - 22]', '[1045, 1045, 7*w^3 + 13*w^2 - 62*w - 83]', '[1061, 1061, 3*w^3 + 7*w^2 - 28*w - 43]', '[1061, 1061, 9*w^3 + 17*w^2 - 80*w - 104]', '[1061, 1061, -4*w^3 - 9*w^2 + 35*w + 59]', '[1061, 1061, -8*w^3 - 15*w^2 + 73*w + 94]', '[1069, 1069, -3*w^3 - 4*w^2 + 29*w + 16]', '[1069, 1069, -5*w^3 - 8*w^2 + 43*w + 55]', '[1069, 1069, -11*w^3 - 20*w^2 + 99*w + 121]', '[1069, 1069, 7*w^3 + 14*w^2 - 61*w - 90]', '[1129, 1129, -18*w^3 - 31*w^2 + 166*w + 202]', '[1129, 1129, 4*w^3 + 7*w^2 - 34*w - 51]', '[1129, 1129, 4*w^3 + 6*w^2 - 37*w - 43]', '[1129, 1129, -26*w^3 - 46*w^2 + 239*w + 295]', '[1136, 142, -2*w^3 - 4*w^2 + 20*w + 16]', '[1136, 142, 8*w^3 + 16*w^2 - 70*w - 100]', '[1136, 142, -8*w^3 - 14*w^2 + 72*w + 94]', '[1136, 142, -2*w^3 - 4*w^2 + 16*w + 34]', '[1171, 1171, 7*w^3 + 12*w^2 - 63*w - 81]', '[1171, 1171, 12*w^3 + 22*w^2 - 108*w - 137]', '[1171, 1171, 2*w^3 + 6*w^2 - 18*w - 41]', '[1171, 1171, 3*w^3 + 4*w^2 - 27*w - 15]', '[1181, 1181, 5*w^3 + 8*w^2 - 45*w - 40]', '[1181, 1181, w^3 + 2*w^2 - 7*w - 21]', '[1181, 1181, -w^3 - 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6*w - 48]', '[1539, 57, -12*w^3 - 21*w^2 + 108*w + 135]', '[1539, 57, 3*w^3 + 3*w^2 - 27*w - 9]', '[1539, 57, 6*w^3 + 12*w^2 - 51*w - 69]', '[1539, 57, -3*w^3 - 6*w^2 + 30*w + 30]', '[1555, 1555, 57*w^3 + 100*w^2 - 523*w - 641]', '[1555, 1555, -54*w^3 - 95*w^2 + 495*w + 606]', '[1555, 1555, -22*w^3 - 38*w^2 + 203*w + 244]', '[1555, 1555, w^3 + 2*w^2 - 12*w - 13]', '[1559, 1559, 7*w^3 + 13*w^2 - 62*w - 84]', '[1559, 1559, -6*w^3 - 10*w^2 + 55*w + 57]', '[1559, 1559, 6*w^3 + 11*w^2 - 55*w - 64]', '[1559, 1559, -5*w^3 - 9*w^2 + 43*w + 59]', '[1571, 1571, -32*w^3 - 57*w^2 + 293*w + 362]', '[1571, 1571, 31*w^3 + 54*w^2 - 285*w - 350]', '[1571, 1571, 20*w^3 + 36*w^2 - 181*w - 226]', '[1571, 1571, -7*w^3 - 12*w^2 + 64*w + 81]', '[1579, 1579, -10*w^3 - 19*w^2 + 89*w + 122]', '[1579, 1579, -5*w^3 - 11*w^2 + 44*w + 66]', '[1579, 1579, 4*w^3 + 9*w^2 - 37*w - 61]', '[1579, 1579, 9*w^3 + 17*w^2 - 82*w - 101]', '[1595, 1595, -9*w^3 - 16*w^2 + 78*w + 90]', '[1595, 1595, -3*w^3 - 2*w^2 + 24*w + 18]', '[1595, 1595, w^3 + 2*w^2 - 3*w - 29]', '[1595, 1595, w^3 - 10*w + 1]', '[1595, 1595, -3*w^3 - 9*w^2 + 23*w + 69]', '[1595, 1595, 4*w^3 + 5*w^2 - 38*w - 19]', '[1595, 1595, -13*w^3 - 20*w^2 + 117*w + 104]', '[1595, 1595, -w^2 + 2*w + 8]', '[1619, 1619, 9*w^3 + 17*w^2 - 80*w - 109]', '[1619, 1619, -3*w^3 - 7*w^2 + 28*w + 48]', '[1619, 1619, 8*w^3 + 15*w^2 - 73*w - 89]', '[1619, 1619, 4*w^3 + 9*w^2 - 35*w - 54]', '[1621, 1621, -5*w^3 - 10*w^2 + 42*w + 61]', '[1621, 1621, 6*w^3 + 9*w^2 - 51*w - 55]', '[1621, 1621, 12*w^3 + 21*w^2 - 105*w - 128]', '[1621, 1621, 7*w^3 + 11*w^2 - 63*w - 69]', '[1639, 1639, -2*w^2 - w + 14]', '[1639, 1639, 5*w^3 + 8*w^2 - 42*w - 54]', '[1639, 1639, -4*w^3 - 2*w^2 + 38*w - 7]', '[1639, 1639, 5*w^3 + 14*w^2 - 40*w - 98]', '[1639, 1639, 2*w^3 + 6*w^2 - 24*w - 25]', '[1639, 1639, w^3 + 3*w^2 - 4*w - 34]', '[1639, 1639, -4*w^3 - 5*w^2 + 38*w + 20]', '[1639, 1639, -9*w^3 - 16*w^2 + 78*w + 91]', '[1655, 1655, -26*w^3 - 45*w^2 + 239*w + 293]', '[1655, 1655, -2*w^3 - 3*w^2 + 19*w + 25]', '[1655, 1655, -32*w^3 - 57*w^2 + 293*w + 363]', '[1655, 1655, 32*w^3 + 57*w^2 - 291*w - 361]', '[1669, 1669, 5*w^3 + 7*w^2 - 44*w - 49]', '[1669, 1669, -13*w^3 - 24*w^2 + 115*w + 148]', '[1669, 1669, -15*w^3 - 27*w^2 + 133*w + 166]', '[1669, 1669, 3*w^3 + 8*w^2 - 24*w - 53]', '[1681, 41, 6*w^3 + 12*w^2 - 54*w - 77]', '[1681, 41, 6*w^3 + 12*w^2 - 54*w - 73]', '[1705, 1705, 7*w^3 + 11*w^2 - 63*w - 62]', '[1705, 1705, 4*w^3 + 5*w^2 - 36*w - 27]', '[1705, 1705, -3*w^3 - 2*w^2 + 26*w + 10]', '[1705, 1705, -9*w^3 - 14*w^2 + 81*w + 76]', '[1705, 1705, 5*w^3 + 6*w^2 - 46*w - 27]', '[1705, 1705, 3*w^3 + 2*w^2 - 27*w - 6]', '[1705, 1705, -7*w^3 - 9*w^2 + 64*w + 41]', '[1705, 1705, -4*w^3 - 5*w^2 + 35*w + 31]', '[1721, 1721, -32*w^3 - 56*w^2 + 293*w + 361]', '[1721, 1721, -20*w^3 - 35*w^2 + 183*w + 227]', '[1721, 1721, -7*w^3 - 12*w^2 + 62*w + 83]', '[1721, 1721, -16*w^3 - 28*w^2 + 147*w + 183]', '[1741, 1741, 40*w^3 + 71*w^2 - 365*w - 450]', '[1741, 1741, 23*w^3 + 40*w^2 - 210*w - 259]', '[1741, 1741, 15*w^3 + 26*w^2 - 139*w - 172]', '[1741, 1741, 12*w^3 + 22*w^2 - 109*w - 138]', '[1744, 218, -4*w^3 - 6*w^2 + 38*w + 26]', '[1744, 218, 6*w^3 + 10*w^2 - 52*w - 52]', '[1744, 218, 4*w^3 + 6*w^2 - 38*w - 44]', '[1744, 218, 6*w^3 + 10*w^2 - 52*w - 70]', '[1745, 1745, -25*w^3 - 44*w^2 + 228*w + 277]', '[1745, 1745, 17*w^3 + 30*w^2 - 154*w - 192]', '[1745, 1745, 39*w^3 + 68*w^2 - 357*w - 436]', '[1745, 1745, -26*w^3 - 46*w^2 + 235*w + 290]', '[1759, 1759, -8*w^3 - 13*w^2 + 73*w + 85]', '[1759, 1759, 6*w^3 + 9*w^2 - 55*w - 46]', '[1759, 1759, 12*w^3 + 22*w^2 - 107*w - 138]', '[1759, 1759, -3*w^3 - 5*w^2 + 24*w + 38]', '[1775, 355, -3*w^3 - 8*w^2 + 28*w + 48]', '[1775, 355, 6*w^3 + 10*w^2 - 53*w - 52]', '[1775, 355, 10*w^3 + 19*w^2 - 92*w - 121]', '[1775, 355, 3*w^3 + 8*w^2 - 28*w - 53]', '[1789, 1789, -8*w^3 - 14*w^2 + 72*w + 81]', '[1789, 1789, -9*w^3 - 16*w^2 + 79*w + 100]', '[1789, 1789, 3*w^3 + 4*w^2 - 25*w - 22]', '[1789, 1789, -7*w^3 - 12*w^2 + 65*w + 71]', '[1795, 1795, 31*w^3 + 55*w^2 - 282*w - 346]', '[1795, 1795, -13*w^3 - 22*w^2 + 119*w + 143]', '[1795, 1795, -37*w^3 - 65*w^2 + 337*w + 415]', '[1795, 1795, -9*w^3 - 16*w^2 + 84*w + 106]', '[1805, 95, 20*w^3 + 35*w^2 - 181*w - 221]', '[1805, 95, -9*w^3 - 17*w^2 + 81*w + 104]', '[1805, 95, 6*w^3 + 12*w^2 - 55*w - 76]', '[1805, 95, 5*w^3 + 9*w^2 - 44*w - 48]', '[1805, 95, -4*w^3 - 9*w^2 + 36*w + 56]', '[1805, 95, -12*w^3 - 21*w^2 + 112*w + 136]', '[1805, 1805, -7*w^3 - 11*w^2 + 62*w + 71]', '[1805, 1805, -w^2 - 3*w + 13]', '[1805, 1805, 2*w^3 + 3*w^2 - 21*w - 22]', '[1805, 1805, -9*w^3 - 15*w^2 + 80*w + 86]', '[1831, 1831, -10*w^3 - 17*w^2 + 89*w + 99]', '[1831, 1831, 12*w^3 + 21*w^2 - 106*w - 129]', '[1831, 1831, 5*w^3 + 7*w^2 - 43*w - 41]', '[1831, 1831, 7*w^3 + 12*w^2 - 66*w - 72]', '[1871, 1871, -12*w^3 - 20*w^2 + 109*w + 120]', '[1871, 1871, 4*w^3 + 5*w^2 - 34*w - 33]', '[1871, 1871, 7*w^3 + 13*w^2 - 59*w - 82]', '[1871, 1871, -8*w^3 - 14*w^2 + 75*w + 89]', '[1889, 1889, 8*w^3 + 13*w^2 - 73*w - 86]', '[1889, 1889, -15*w^3 - 27*w^2 + 134*w + 168]', '[1889, 1889, -13*w^3 - 24*w^2 + 116*w + 151]', '[1889, 1889, 8*w^3 + 15*w^2 - 75*w - 90]', '[1901, 1901, 9*w^3 + 17*w^2 - 81*w - 107]', '[1901, 1901, 6*w^3 + 12*w^2 - 55*w - 73]', '[1901, 1901, -7*w^3 - 14*w^2 + 62*w + 86]', '[1901, 1901, -4*w^3 - 9*w^2 + 36*w + 59]', '[1936, 22, 6*w^3 + 12*w^2 - 54*w - 76]', '[1936, 22, 6*w^3 + 12*w^2 - 54*w - 74]', '[1936, 22, -20*w^3 - 36*w^2 + 182*w + 226]', '[1949, 1949, -12*w^3 - 21*w^2 + 107*w + 133]', '[1949, 1949, 7*w^3 + 13*w^2 - 59*w - 84]', '[1949, 1949, 7*w^3 + 10*w^2 - 64*w - 61]', '[1949, 1949, 12*w^3 + 20*w^2 - 109*w - 118]', '[1951, 1951, 7*w^3 + 14*w^2 - 65*w - 88]', '[1951, 1951, -13*w^3 - 24*w^2 + 117*w + 147]', '[1951, 1951, 31*w^3 + 54*w^2 - 284*w - 349]', '[1951, 1951, -9*w^3 - 18*w^2 + 79*w + 114]', '[1975, 395, -9*w^3 - 16*w^2 + 80*w + 102]', '[1975, 395, 5*w^3 + 9*w^2 - 47*w - 51]', '[1975, 395, -2*w^3 - 2*w^2 + 17*w + 7]', '[1975, 395, -2*w^3 - 5*w^2 + 16*w + 29]', '[1979, 1979, -7*w^3 - 14*w^2 + 60*w + 90]', '[1979, 1979, 13*w^3 + 23*w^2 - 117*w - 139]', '[1979, 1979, 2*w^3 + w^2 - 18*w - 5]', '[1979, 1979, 4*w^3 + 8*w^2 - 39*w - 51]', '[1991, 1991, -10*w^3 - 19*w^2 + 89*w + 115]', '[1991, 1991, -8*w^3 - 12*w^2 + 71*w + 57]', '[1991, 1991, w^3 + 7*w^2 - 12*w - 45]', '[1991, 1991, -3*w^3 - 5*w^2 + 31*w + 15]', '[1991, 1991, -w^3 + w^2 + 5*w + 5]', '[1991, 1991, 4*w^2 + 3*w - 43]', '[1991, 1991, 5*w^3 + 11*w^2 - 44*w - 73]', '[1991, 1991, 10*w^3 + 23*w^2 - 85*w - 151]', '[1999, 1999, 4*w^3 + 7*w^2 - 38*w - 37]', '[1999, 1999, 3*w^3 + 4*w^2 - 26*w - 18]', '[1999, 1999, w^3 + 3*w^2 - 7*w - 15]', '[1999, 1999, -8*w^3 - 14*w^2 + 71*w + 91]', '[2000, 10, -24*w^3 - 42*w^2 + 218*w + 266]', '[2005, 2005, 22*w^3 + 38*w^2 - 203*w - 249]', '[2005, 2005, -40*w^3 - 71*w^2 + 366*w + 452]', '[2005, 2005, 6*w^3 + 10*w^2 - 55*w - 69]', '[2005, 2005, -24*w^3 - 43*w^2 + 218*w + 272]', '[2011, 2011, 6*w^3 + 9*w^2 - 54*w - 55]', '[2011, 2011, 9*w^3 + 15*w^2 - 81*w - 89]', '[2011, 2011, -3*w - 1]', '[2011, 2011, -3*w^3 - 6*w^2 + 24*w + 40]', '[2025, 15, -6*w^3 - 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36*w - 40]', '[139, 139, -w^3 - w^2 + 9*w + 8]', '[139, 139, -w^3 - 2*w^2 + 10*w + 15]', '[139, 139, 2*w^3 + 4*w^2 - 17*w - 28]', '[149, 149, 4*w^3 + 8*w^2 - 35*w - 52]', '[149, 149, -3*w^3 - 5*w^2 + 26*w + 34]', '[149, 149, -2*w^3 - 3*w^2 + 19*w + 14]', '[149, 149, -6*w^3 - 11*w^2 + 54*w + 66]', '[181, 181, w^3 + 2*w^2 - 11*w - 13]', '[181, 181, -3*w^3 - 4*w^2 + 27*w + 24]', '[181, 181, -7*w^3 - 12*w^2 + 63*w + 72]', '[181, 181, 3*w^3 + 6*w^2 - 25*w - 39]', '[191, 191, -7*w^3 - 12*w^2 + 66*w + 80]', '[191, 191, 5*w^3 + 9*w^2 - 47*w - 57]', '[191, 191, -2*w^3 - 2*w^2 + 18*w + 9]', '[191, 191, 2*w^3 + 2*w^2 - 17*w - 13]', '[239, 239, 7*w^3 + 13*w^2 - 62*w - 81]', '[239, 239, -2*w^3 - 5*w^2 + 17*w + 32]', '[239, 239, 6*w^3 + 11*w^2 - 55*w - 67]', '[239, 239, -w^3 - 3*w^2 + 10*w + 20]', '[251, 251, 7*w^3 + 13*w^2 - 63*w - 82]', '[251, 251, -5*w^3 - 10*w^2 + 44*w + 61]', '[251, 251, 4*w^3 + 8*w^2 - 37*w - 48]', '[251, 251, -2*w^3 - 5*w^2 + 18*w + 34]', '[311, 311, 5*w^3 + 9*w^2 - 44*w - 50]', '[311, 311, -4*w^3 - 7*w^2 + 37*w + 48]', '[311, 311, 2*w^3 + 4*w^2 - 19*w - 19]', '[311, 311, w^3 + w^2 - 8*w - 11]', '[331, 331, 4*w^3 + 6*w^2 - 36*w - 37]', '[331, 331, -6*w^3 - 10*w^2 + 54*w + 59]', '[331, 331, -2*w - 1]', '[331, 331, -2*w^3 - 4*w^2 + 16*w + 27]', '[349, 349, -3*w^3 - 5*w^2 + 28*w + 27]', '[349, 349, 4*w^3 + 8*w^2 - 35*w - 53]', '[349, 349, -3*w^3 - 6*w^2 + 28*w + 40]', '[349, 349, 6*w^3 + 11*w^2 - 54*w - 65]', '[359, 359, -w^3 - 3*w^2 + 8*w + 19]', '[359, 359, -6*w^3 - 11*w^2 + 53*w + 69]', '[359, 359, 5*w^3 + 9*w^2 - 46*w - 54]', '[359, 359, w^2 - w - 8]', '[401, 401, 5*w^3 + 8*w^2 - 45*w - 50]', '[401, 401, w^3 + 2*w^2 - 7*w - 15]', '[401, 401, w^3 + 2*w^2 - 7*w - 11]', '[401, 401, 5*w^3 + 8*w^2 - 45*w - 46]', '[409, 409, -9*w^3 - 16*w^2 + 81*w + 97]', '[409, 409, w^3 + w^2 - 11*w - 10]', '[409, 409, 6*w^3 + 10*w^2 - 53*w - 66]', '[409, 409, -3*w^3 - 6*w^2 + 29*w + 38]', '[421, 421, -3*w^3 - 4*w^2 + 26*w + 23]', '[421, 421, -4*w^3 - 6*w^2 + 35*w + 39]', '[421, 421, 8*w^3 + 14*w^2 - 71*w - 86]', '[421, 421, -7*w^3 - 12*w^2 + 62*w + 70]', '[439, 439, w^3 + w^2 - 10*w - 9]', '[439, 439, -4*w^3 - 7*w^2 + 35*w + 47]', '[439, 439, 3*w^3 + 5*w^2 - 28*w - 26]', '[439, 439, 2*w^3 + 3*w^2 - 17*w - 14]', '[479, 479, 3*w^3 + 6*w^2 - 29*w - 33]', '[479, 479, 5*w^3 + 10*w^2 - 43*w - 59]', '[479, 479, w^3 - 9*w + 6]', '[479, 479, 9*w^3 + 16*w^2 - 81*w - 102]', '[521, 521, 4*w^3 + 7*w^2 - 38*w - 44]', '[521, 521, 3*w^3 + 4*w^2 - 26*w - 25]', '[521, 521, 5*w^3 + 8*w^2 - 44*w - 46]', '[521, 521, -8*w^3 - 14*w^2 + 71*w + 84]', '[569, 569, 21*w^3 + 37*w^2 - 191*w - 236]', '[569, 569, -13*w^3 - 23*w^2 + 120*w + 149]', '[569, 569, 10*w^3 + 17*w^2 - 92*w - 111]', '[569, 569, -18*w^3 - 32*w^2 + 164*w + 201]', '[631, 631, -2*w^3 - 3*w^2 + 20*w + 25]', '[631, 631, 7*w^3 + 12*w^2 - 64*w - 80]', '[631, 631, -9*w^3 - 17*w^2 + 80*w + 106]', '[631, 631, 19*w^3 + 33*w^2 - 175*w - 215]', '[641, 641, 4*w^3 + 6*w^2 - 35*w - 35]', '[641, 641, 4*w^3 + 6*w^2 - 35*w - 38]', '[641, 641, 7*w^3 + 12*w^2 - 62*w - 71]', '[641, 641, 7*w^3 + 12*w^2 - 62*w - 74]', '[659, 659, 6*w^3 + 11*w^2 - 54*w - 63]', '[659, 659, 4*w^3 + 6*w^2 - 37*w - 38]', '[659, 659, 4*w^3 + 8*w^2 - 35*w - 55]', '[659, 659, 3*w^3 + 6*w^2 - 28*w - 42]', '[661, 661, -27*w^3 - 48*w^2 + 247*w + 306]', '[661, 661, 14*w^3 + 24*w^2 - 129*w - 158]', '[661, 661, 11*w^3 + 19*w^2 - 102*w - 126]', '[661, 661, 2*w^3 + 3*w^2 - 19*w - 24]', '[691, 691, 6*w^3 + 12*w^2 - 53*w - 73]', '[691, 691, 8*w^3 + 15*w^2 - 72*w - 95]', '[691, 691, -5*w^3 - 10*w^2 + 46*w + 60]', '[691, 691, -3*w^3 - 7*w^2 + 27*w + 47]', '[739, 739, -2*w^3 - 5*w^2 + 19*w + 34]', '[739, 739, 7*w^3 + 13*w^2 - 64*w - 78]', '[739, 739, -3*w^3 - 7*w^2 + 26*w + 43]', '[739, 739, 8*w^3 + 15*w^2 - 71*w - 95]', '[751, 751, -4*w^3 - 9*w^2 + 37*w + 59]', '[751, 751, -5*w^3 - 9*w^2 + 43*w + 48]', '[751, 751, -6*w^3 - 10*w^2 + 55*w + 68]', '[751, 751, -10*w^3 - 17*w^2 + 93*w + 114]', '[769, 769, 6*w^3 + 11*w^2 - 52*w - 69]', '[769, 769, w^3 + w^2 - 7*w - 5]', '[769, 769, 2*w^3 + 2*w^2 - 19*w - 11]', '[769, 769, 7*w^3 + 12*w^2 - 64*w - 72]', '[809, 809, -3*w^3 - 4*w^2 + 29*w + 17]', '[809, 809, -5*w^3 - 8*w^2 + 43*w + 54]', '[809, 809, w^3 - 9*w + 9]', '[809, 809, 10*w^3 + 18*w^2 - 90*w - 109]', '[881, 881, -10*w^3 - 17*w^2 + 92*w + 113]', '[881, 881, -6*w^3 - 10*w^2 + 56*w + 69]', '[881, 881, -31*w^3 - 55*w^2 + 283*w + 350]', '[881, 881, -11*w^3 - 19*w^2 + 101*w + 125]', '[911, 911, 5*w^3 + 8*w^2 - 44*w - 49]', '[911, 911, -6*w^3 - 10*w^2 + 53*w + 60]', '[911, 911, 5*w^3 + 8*w^2 - 44*w - 48]', '[911, 911, 6*w^3 + 10*w^2 - 53*w - 61]', '[919, 919, 4*w^3 + 7*w^2 - 37*w - 38]', '[919, 919, 5*w^3 + 9*w^2 - 44*w - 60]', '[919, 919, 8*w^3 + 14*w^2 - 73*w - 85]', '[919, 919, -7*w^3 - 13*w^2 + 61*w + 81]', '[971, 971, 28*w^3 + 49*w^2 - 255*w - 312]', '[971, 971, 16*w^3 + 28*w^2 - 145*w - 176]', '[971, 971, -25*w^3 - 44*w^2 + 227*w + 278]', '[971, 971, 15*w^3 + 26*w^2 - 136*w - 165]', '[991, 991, 5*w^3 + 10*w^2 - 42*w - 64]', '[991, 991, -4*w^3 - 5*w^2 + 36*w + 29]', '[991, 991, -11*w^3 - 19*w^2 + 99*w + 115]', '[991, 991, 10*w^3 + 17*w^2 - 90*w - 108]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [31, 14, -14, -1, 1], 'conductor': 55, 'degree': 4, 'dirichlet_group': [32, 1, 34, 43], 'disc_abs': 15125, 'disc_rad': 55, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[4, 1]]], [5, [0]], [7, [[4, 1]]], [11, [0]], [13, [[4, 1]]], [17, [[4, 1]]], [19, [[1, 4]]], [23, [[4, 1]]], [29, [[1, 4]]], [31, [[1, 4]]], [37, [[4, 1]]], [41, [[2, 2]]], [43, [[4, 1]]], [47, [[4, 1]]], [53, [[4, 1]]], [59, [[2, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 2], 'galois_label': '4T1', 'galt': 1, 'grd': 11.08980336897316, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.15125.1', 'local_algs': ['5.4.3.2', '11.2.1.2', '11.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 11], 'rd': 11.089803369, 'regulator': {'__RealLiteral__': 0, 'data': '5.29445586371', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{3} + 2 a^{2} - 9 a - 13 \\)', '\\( a - 3 \\)', '\\( 2 a^{3} + 3 a^{2} - 18 a - 15 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}