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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 10309, 'field_bad_primes': [13, 61], 'field_label': '4.4.10309.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.10309.1-17.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [17], 'level_ideal': '[17,17,-w^2 - w + 5]', 'level_label': '17.2', 'level_norm': 17, 'parallel_weight': 2, 'short_label': '17.2-a', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[17,17,-w^2 - w + 5]', 1]], 'hecke_eigenvalues': [2, 2, 0, 6, 1, 0, -1, 6, 0, -6, 6, 0, 6, -10, 8, -6, -6, 0, 0, -6, 0, 12, 0, 0, 12, 0, -6, -12, -6, 12, -6, -6, 4, -14, -14, 4, -6, -6, 2, 20, 12, -24, 12, 12, 18, 6, -12, 12, -8, -26, 24, 12, 24, -12, -2, -24, -6, 6, -6, -30, 18, -30, -12, 18, 18, 34, -20, -8, 26, 10, 8, 6, 0, 0, -18, 6, -30, 30, -6, -36, 36, -42, 24, -24, -24, 6, -12, -34, 20, 46, -26, -44, -6, 12, 12, -12, 12, -24, 22, -14, 40, -14, 6, 42, -24, 12, -18, 36, -36, 18, 36, 36, -10, 26, 6, -42, -42, 48, -4, -40, -4, 32, 54, -6, 18, -6, -42, 42, -6, -30, -30, 6, -30, 42, 4, -14, -50, 12, 12, -24, -12, -6, -12, -24, -6, 12, -24, 0, -24, 54, 0, 6, 6, -24, 12, 12, -30, -26, -26, 42, 42, 6, 36, -4, -40, -38, -38, -30, 18, 0, -30, 0, 42, 2, 38, -2, 52, 52, -38, -12, -54, 0, -66, 24, -48, -48, 0, 46, -44, -10, -10, -24, -24, -24, 60, -24, 30, -24, 0, 18, 48, 48, 24, 54, 6, 48, 6, -58, 4, 50, -50, 12, -60, 26, -28, 30, 6, -72, -48, -4, -22, -16, 70, 38, -20, 12, 30, -60, 48, 12, -72, 36, 0, 12, 36, 66, -24, -36, 0, 0, 18, -54, -72, -42, 54, 66, -6, -36, 66, 18, 66, -36, 24, -30, 36, 24, 18, 60, 48, -36, 36, -36, -18, 66, 30, 18, -42, -40, -4, -18, 30, 24, -54, 24, 24, -24, -60, 12, 12, -40, 18, -78, 24, -48, 18, 36, 24, -30, -12, -12, 18, 42, 36, 78, -48, -30, -12, -30, -6, -24, 84, 36, -60, 12, 58, -50, -58, -40, -20, 52, -52, -52], 'hecke_polynomial': 'x', 'label': '4.4.10309.1-17.2-a'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 10309, 'ideals': ['[1, 1, 1]', '[9, 3, w^3 - 5*w + 3]', '[9, 3, w^3 - 5*w + 2]', '[13, 13, w + 1]', '[13, 13, w^3 - 6*w + 4]', '[16, 2, 2]', '[17, 17, w^2 + w - 2]', '[17, 17, w^2 + w - 5]', '[23, 23, w^3 - w^2 - 6*w + 6]', '[23, 23, w^3 + w^2 - 4*w - 1]', '[25, 5, -w^2 + 3]', '[25, 5, -w^3 - w^2 + 5*w + 1]', '[29, 29, -w^2 - 2*w + 3]', '[29, 29, -w^3 + w^2 + 7*w - 7]', '[43, 43, 2*w^3 + w^2 - 10*w + 3]', '[43, 43, -w^3 + w^2 + 5*w - 7]', '[53, 53, w^3 - w^2 - 7*w + 5]', '[53, 53, w^2 + 2*w - 5]', '[61, 61, 2*w^3 + w^2 - 10*w]', '[61, 61, w^3 - 7*w + 3]', '[61, 61, 2*w^3 + w^2 - 9*w + 3]', '[79, 79, -w^3 + w^2 + 6*w - 5]', '[79, 79, w^3 + w^2 - 4*w - 2]', '[81, 3, 3]', '[81, 9, -w^3 + 5*w + 1]', '[81, 9, w^3 - 5*w + 6]', '[101, 101, -2*w^3 + 12*w - 7]', '[101, 101, -2*w - 1]', '[107, 107, -w^3 + 4*w - 5]', '[107, 107, 3*w^3 - 17*w + 5]', '[107, 107, 2*w^3 - 11*w + 8]', '[107, 107, -3*w^3 - w^2 + 17*w - 4]', '[117, 39, 2*w^3 + w^2 - 11*w + 3]', '[117, 39, 2*w^3 + w^2 - 10*w + 4]', '[117, 39, w^3 - w^2 - 5*w + 8]', '[117, 39, -w^2 + w + 4]', '[127, 127, 3*w^3 - 16*w + 11]', '[127, 127, w^3 + w^2 - 7*w + 3]', '[127, 127, w^3 - 6*w - 1]', '[127, 127, w - 4]', '[139, 139, w^2 + 2*w - 6]', '[139, 139, w^3 - w^2 - 7*w + 4]', '[144, 6, 2*w^3 - 10*w + 6]', '[144, 6, 2*w^3 - 10*w + 4]', '[153, 51, 2*w^3 - w^2 - 13*w + 11]', '[153, 51, w^3 + w^2 - 3*w - 2]', '[153, 51, -2*w^3 + w^2 + 12*w - 8]', '[153, 51, -w^2 - 3*w + 2]', '[157, 157, -w^3 + w^2 + 6*w - 4]', '[157, 157, w^3 + w^2 - 4*w - 3]', '[169, 13, -w^3 + 3*w + 2]', '[169, 13, 2*w^3 - 10*w + 5]', '[169, 13, 3*w^3 - 17*w + 4]', '[173, 173, 3*w^3 + w^2 - 15*w + 5]', '[173, 173, -2*w^2 - w + 9]', '[181, 181, -2*w^3 - w^2 + 10*w - 5]', '[181, 181, -w^3 + w^2 + 5*w - 9]', '[191, 191, -w^2 - 3*w + 4]', '[191, 191, w^3 - w^2 - 7*w + 2]', '[207, 69, 3*w^3 + w^2 - 15*w + 4]', '[207, 69, -w^2 - 2*w + 7]', '[207, 69, -w^3 + w^2 + 7*w - 3]', '[207, 69, -2*w^3 + w^2 + 10*w - 8]', '[208, 26, 2*w + 2]', '[208, 26, 2*w^3 - 12*w + 8]', '[211, 211, -2*w^3 + w^2 + 13*w - 10]', '[211, 211, w^2 + 3*w - 3]', '[221, 221, w^3 + 2*w^2 - 4*w - 5]', '[221, 221, w^3 - w^2 - 6*w + 3]', '[221, 221, -w^3 - w^2 + 4*w + 4]', '[221, 221, 2*w^2 + w - 6]', '[225, 15, 2*w^3 - 13*w + 4]', '[225, 15, w^3 - 8*w + 5]', '[225, 15, w^3 - w^2 - 8*w + 8]', '[225, 15, w^3 - w^2 - 8*w + 5]', '[233, 233, -3*w^3 + 16*w - 6]', '[233, 233, 2*w^3 - 9*w + 3]', '[251, 251, w^2 - w - 5]', '[251, 251, -2*w^3 - w^2 + 11*w - 4]', '[256, 4, 4]', '[261, 87, -w^3 - 2*w^2 + 4*w + 3]', '[261, 87, w^3 - 8*w + 3]', '[261, 87, 2*w^2 + w - 8]', '[261, 87, -2*w^3 + 13*w - 6]', '[272, 34, 2*w^2 + 2*w - 4]', '[272, 34, 2*w^2 + 2*w - 10]', '[277, 277, w^3 + w^2 - 7*w - 2]', '[277, 277, -2*w^3 - w^2 + 12*w - 4]', '[283, 283, -w^3 + 8*w - 4]', '[283, 283, w^3 + 2*w^2 - 4*w - 4]', '[283, 283, 2*w^3 - 13*w + 5]', '[283, 283, 2*w^2 + w - 7]', '[289, 17, -w^3 + 5*w + 2]', '[289, 17, -w^3 + 5*w - 7]', '[289, 289, -2*w - 3]', '[289, 289, -2*w^3 + 12*w - 9]', '[299, 299, 3*w^3 + w^2 - 17*w + 5]', '[299, 299, w^2 - 2*w - 3]', '[299, 299, -w^3 + w^2 + 8*w - 6]', '[299, 299, w^3 - w^2 - 8*w + 7]', '[311, 311, 3*w^3 - 16*w + 8]', '[311, 311, 2*w^3 + 2*w^2 - 10*w - 3]', '[313, 313, -2*w^3 + 9*w - 4]', '[313, 313, -3*w^3 + 16*w - 7]', '[325, 65, -w^3 - w^2 + 3*w + 3]', '[325, 65, -w^3 + 4*w + 3]', '[325, 65, -2*w^3 + 11*w]', '[325, 65, 2*w^3 - w^2 - 12*w + 7]', '[337, 337, -2*w^3 + w^2 + 13*w - 6]', '[337, 337, 3*w^3 - 17*w + 10]', '[347, 347, 3*w^3 - 18*w + 10]', '[347, 347, -3*w - 1]', '[347, 347, 2*w^3 + 2*w^2 - 11*w - 4]', '[347, 347, 4*w^3 + w^2 - 21*w + 5]', '[361, 19, 2*w^2 + w - 13]', '[361, 19, -2*w^3 + w^2 + 10*w - 12]', '[367, 367, -2*w^3 - w^2 + 9*w + 1]', '[367, 367, 3*w^3 - w^2 - 18*w + 16]', '[367, 367, -2*w^3 + w^2 + 11*w - 6]', '[367, 367, 4*w^3 - 22*w + 9]', '[368, 46, 2*w^3 - 2*w^2 - 12*w + 12]', '[368, 46, 2*w^3 + 2*w^2 - 8*w - 2]', '[373, 373, -w^3 + w^2 + 4*w - 7]', '[373, 373, -3*w^3 - w^2 + 16*w - 6]', '[377, 377, -w^3 - 2*w^2 + 5*w + 2]', '[377, 377, -2*w^2 - 3*w + 9]', '[377, 377, -w^3 + 2*w^2 + 8*w - 8]', '[377, 377, w^3 + 2*w^2 - 5*w - 6]', '[387, 129, w^3 + w^2 - 2*w + 4]', '[387, 129, -w^3 + 8*w + 1]', '[387, 129, -3*w^3 + w^2 + 18*w - 17]', '[387, 129, -2*w^3 + 13*w - 10]', '[389, 389, w^3 - 6*w - 2]', '[389, 389, w - 5]', '[391, 391, w^3 + 2*w^2 - 7*w - 1]', '[391, 391, -3*w^3 - 2*w^2 + 17*w + 1]', '[391, 391, 2*w^3 + w^2 - 11*w + 5]', '[391, 391, w^2 - w - 6]', '[400, 10, -2*w^2 + 6]', '[400, 10, -2*w^3 - 2*w^2 + 10*w + 2]', '[419, 419, w^3 + 2*w^2 - 6*w - 5]', '[419, 419, -2*w^2 - 2*w + 11]', '[425, 85, -w^3 - 2*w^2 + 3*w + 6]', '[425, 85, -w^3 - w^2 + 5*w + 6]', '[425, 85, w^2 + 2]', '[425, 85, w^3 - 2*w^2 - 7*w + 8]', '[433, 433, 3*w^3 + w^2 - 15*w - 1]', '[433, 433, 2*w^3 - w^2 - 10*w + 3]', '[464, 58, -2*w^2 - 4*w + 6]', '[464, 58, -2*w^3 + 2*w^2 + 14*w - 14]', '[467, 467, -3*w^3 - 2*w^2 + 17*w]', '[467, 467, -w^3 + w^2 + 5*w - 12]', '[477, 159, -w^3 - 3*w^2 + 2*w + 9]', '[477, 159, -2*w^3 - 2*w^2 + 9*w + 4]', '[477, 159, -w^3 + 3*w^2 + 8*w - 12]', '[477, 159, -w^3 + 2*w^2 + 6*w - 7]', '[493, 493, w^3 + w^2 - 7*w - 3]', '[493, 493, -3*w^3 - w^2 + 14*w - 6]', '[493, 493, 3*w^3 - w^2 - 16*w + 13]', '[493, 493, 2*w^3 + w^2 - 12*w + 5]', '[503, 503, w^3 + 2*w^2 - 5*w - 3]', '[503, 503, 3*w^3 + w^2 - 18*w + 6]', '[503, 503, -3*w^3 - w^2 + 15*w - 9]', '[503, 503, w^3 + 2*w^2 - 5*w - 5]', '[521, 521, -w^3 - 2*w^2 + 6*w + 2]', '[521, 521, 2*w^3 + 2*w^2 - 11*w - 3]', '[523, 523, w^3 - 2*w^2 - 9*w + 14]', '[523, 523, w^3 - 2*w^2 - 9*w + 6]', '[529, 23, 2*w^3 - 10*w + 11]', '[529, 23, -3*w^3 + 15*w - 10]', '[529, 529, 2*w^3 - w^2 - 12*w + 6]', '[529, 529, -w^3 - w^2 + 3*w + 4]', '[547, 547, -2*w^3 - 3*w^2 + 8*w + 5]', '[547, 547, -4*w^3 + w^2 + 22*w - 17]', '[549, 183, -4*w^3 + 23*w - 5]', '[549, 183, -2*w^3 + w^2 + 13*w - 5]', '[549, 183, -w^3 - 2*w^2 + 5*w + 4]', '[549, 183, -2*w^3 - 2*w^2 + 12*w + 1]', '[549, 183, w^2 + 2*w + 2]', '[549, 183, 2*w^3 + 2*w^2 - 7*w + 5]', '[559, 559, w + 5]', '[559, 559, -w^3 + 6*w - 8]', '[559, 559, -4*w^3 + 3*w^2 + 22*w - 23]', '[559, 559, 5*w^3 + 3*w^2 - 23*w + 5]', '[571, 571, 2*w^3 + 2*w^2 - 12*w - 5]', '[571, 571, 4*w^3 + w^2 - 24*w + 8]', '[571, 571, -w^3 - w^2 + 9*w]', '[571, 571, 2*w^3 + 2*w^2 - 12*w + 3]', '[575, 115, -2*w^3 - 2*w^2 + 11*w + 1]', '[575, 115, 3*w^3 - 17*w + 11]', '[575, 115, w^3 + 2*w^2 - 6*w - 4]', '[575, 115, -w^3 + 3*w - 5]', '[599, 599, -3*w^3 - w^2 + 17*w - 6]', '[599, 599, w^2 - 2*w - 4]', '[607, 607, 2*w^3 + w^2 - 8*w - 1]', '[607, 607, -w^3 - 2*w^2 + 6*w + 3]', '[607, 607, 2*w^3 + 2*w^2 - 11*w - 2]', '[607, 607, -3*w^3 + w^2 + 17*w - 9]', '[625, 5, 5]', '[625, 25, -3*w^3 + w^2 + 19*w - 13]', '[625, 25, w^2 + 4*w - 3]', '[641, 641, w^3 - 9*w + 3]', '[641, 641, 3*w^3 - 19*w + 9]', '[647, 647, w^3 - w^2 - 9*w + 4]', '[647, 647, -2*w^3 + w^2 + 14*w - 12]', '[653, 653, -w^3 + 9*w - 6]', '[653, 653, 3*w^3 - 19*w + 6]', '[659, 659, -2*w^3 + w^2 + 13*w - 4]', '[659, 659, -w^3 + w^2 + 4*w - 8]', '[659, 659, -3*w^3 - w^2 + 16*w - 7]', '[659, 659, w^2 + 3*w - 9]', '[667, 667, 2*w^3 + w^2 - 13*w + 6]', '[667, 667, -2*w^3 - w^2 + 13*w + 1]', '[667, 667, w^3 + w^2 - 5*w + 5]', '[667, 667, -w^2 + 9]', '[673, 673, 3*w^3 - w^2 - 19*w + 12]', '[673, 673, w^2 + 4*w - 4]', '[677, 677, 2*w^3 + w^2 - 9*w - 3]', '[677, 677, 2*w^3 - w^2 - 11*w + 4]', '[688, 86, 4*w^3 + 2*w^2 - 20*w + 6]', '[688, 86, -2*w^3 + 2*w^2 + 10*w - 14]', '[689, 689, w^3 + 3*w^2 - 3*w - 5]', '[689, 689, w^3 - 2*w^2 - 10*w + 6]', '[689, 689, -2*w^3 + 2*w^2 + 15*w - 17]', '[689, 689, -3*w^2 - 2*w + 13]', '[701, 701, w^3 + w^2 - 7*w - 4]', '[701, 701, -2*w^3 - w^2 + 12*w - 6]', '[711, 237, w^3 + w^2 - 3*w - 5]', '[711, 237, 2*w^2 + 3*w - 10]', '[711, 237, -2*w^3 + w^2 + 12*w - 5]', '[711, 237, -w^3 + 2*w^2 + 8*w - 7]', '[725, 145, 2*w^3 - 2*w^2 - 11*w + 10]', '[725, 145, 3*w^3 - 14*w + 10]', '[725, 145, -4*w^3 + 21*w - 13]', '[725, 145, 3*w^3 + 2*w^2 - 14*w - 1]', '[729, 9, 3*w^3 - 15*w + 9]', '[729, 9, 3*w^3 - 15*w + 6]', '[729, 27, -w^3 + 5*w + 3]', '[729, 27, w^3 - 5*w + 8]', '[731, 731, 4*w^3 - 5*w^2 - 25*w + 34]', '[731, 731, w^3 - 2*w^2 - 10*w + 13]', '[731, 731, -2*w^3 + 2*w^2 + 15*w - 10]', '[731, 731, 4*w^3 + 5*w^2 - 15*w - 1]', '[751, 751, -2*w^3 + 2*w^2 + 12*w - 11]', '[751, 751, -2*w^3 - w^2 + 6*w + 1]', '[751, 751, -5*w^3 + w^2 + 29*w - 15]', '[751, 751, 2*w^3 + 2*w^2 - 8*w - 3]', '[757, 757, w^3 + 2*w^2 - 3*w - 7]', '[757, 757, 5*w^3 + 2*w^2 - 27*w + 6]', '[757, 757, -w^3 + 2*w^2 + 7*w - 7]', '[757, 757, -4*w^3 + w^2 + 23*w - 12]', '[793, 793, w^3 - 3*w + 6]', '[793, 793, 5*w^3 + 4*w^2 - 22*w + 5]', '[793, 793, -3*w^3 + 19*w - 7]', '[793, 793, 5*w^3 + 3*w^2 - 26*w + 2]', '[793, 793, -w^3 - w^2 + 3*w + 6]', '[793, 793, 2*w^3 - w^2 - 12*w + 4]', '[797, 797, 3*w^3 - 19*w + 8]', '[797, 797, 3*w^3 + 2*w^2 - 16*w + 4]', '[797, 797, -w^3 + 9*w - 4]', '[797, 797, 2*w^2 - w - 9]', '[809, 809, 2*w^3 - 7*w - 1]', '[809, 809, -3*w^3 + 2*w^2 + 15*w - 14]', '[809, 809, -w^3 + 3*w^2 + 9*w - 17]', '[809, 809, 5*w^3 - 28*w + 8]', '[823, 823, 2*w^3 + w^2 - 12*w + 7]', '[823, 823, w^3 + w^2 - 7*w - 5]', '[841, 29, -3*w^3 + 15*w - 8]', '[841, 29, -3*w^3 + 15*w - 7]', '[841, 841, 4*w^3 - w^2 - 22*w + 14]', '[841, 841, 3*w^3 + w^2 - 13*w + 4]', '[848, 106, 2*w^3 - 2*w^2 - 14*w + 10]', '[848, 106, 2*w^2 + 4*w - 10]', '[859, 859, -w^3 - w^2 + 4*w - 5]', '[859, 859, -w^3 + w^2 + 6*w - 12]', '[859, 859, w^3 + 2*w^2 - 2*w - 6]', '[859, 859, -2*w^3 + 2*w^2 + 13*w - 11]', '[883, 883, w^3 - 4*w - 4]', '[883, 883, 2*w^3 - 11*w - 1]', '[887, 887, -2*w^3 + w^2 + 14*w - 11]', '[887, 887, -w^3 + w^2 + 9*w - 5]', '[901, 901, 4*w^3 + w^2 - 17*w + 11]', '[901, 901, 4*w^3 - 2*w^2 - 23*w + 26]', '[901, 901, -3*w^3 - 2*w^2 + 12*w - 9]', '[901, 901, -6*w^3 + w^2 + 33*w - 24]', '[907, 907, 3*w^3 - 17*w + 13]', '[907, 907, -w^3 + 3*w - 7]', '[909, 303, w^3 + 2*w^2 - 7*w - 6]', '[909, 303, -w^3 + 2*w^2 + 5*w - 13]', '[909, 303, -3*w^3 - 2*w^2 + 15*w - 5]', '[909, 303, -3*w^3 - 2*w^2 + 17*w - 4]', '[911, 911, 2*w^3 - w^2 - 14*w + 8]', '[911, 911, w^3 - 6*w - 3]', '[911, 911, -w^3 + w^2 + 9*w - 8]', '[911, 911, w - 6]', '[953, 953, -2*w^3 - w^2 + 15*w - 4]', '[953, 953, 4*w^3 + w^2 - 25*w + 7]', '[963, 321, -3*w^3 - w^2 + 16*w - 8]', '[963, 321, -4*w^3 - w^2 + 20*w - 13]', '[963, 321, -3*w^3 - 2*w^2 + 15*w + 4]', '[963, 321, -6*w^3 - 2*w^2 + 32*w - 1]', '[963, 321, w^3 - w^2 - 4*w + 9]', '[963, 321, 3*w^3 - w^2 - 15*w + 17]', '[963, 321, -5*w^3 - 2*w^2 + 30*w - 2]', '[963, 321, -2*w^3 - w^2 + 13*w + 2]', '[971, 971, w^2 - 3*w - 3]', '[971, 971, -5*w^3 + 30*w - 12]', '[971, 971, -3*w^3 + 3*w^2 + 18*w - 19]', '[971, 971, 4*w^3 + w^2 - 23*w + 8]', '[976, 122, 4*w^3 + 2*w^2 - 20*w]', '[976, 122, 2*w^3 - 14*w + 6]', '[976, 122, 4*w^3 + 2*w^2 - 18*w + 6]', '[989, 989, -3*w^2 - 2*w + 10]', '[989, 989, -5*w^3 + 4*w^2 + 33*w - 37]', '[989, 989, w^3 + 4*w^2 + 3*w - 3]', '[989, 989, -w^3 - 3*w^2 + 3*w + 8]', '[997, 997, 4*w^3 + w^2 - 20*w + 8]', '[997, 997, -3*w^3 + w^2 + 15*w - 12]', '[1013, 1013, -2*w^3 - w^2 + 8*w + 2]', '[1013, 1013, 3*w^3 - w^2 - 17*w + 8]', '[1027, 1027, -w^3 + w^2 + 9*w - 6]', '[1027, 1027, 3*w^3 + 3*w^2 - 14*w - 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7]', '[1849, 43, -4*w^3 + 20*w - 13]', '[1849, 1849, 3*w^3 + 2*w^2 - 14*w - 3]', '[1849, 1849, 2*w^3 - 2*w^2 - 11*w + 8]', '[1863, 69, 3*w^3 - 3*w^2 - 18*w + 18]', '[1863, 69, 3*w^3 + 3*w^2 - 12*w - 3]', '[1863, 207, -w^3 - w^2 + 2*w + 8]', '[1863, 207, 3*w^3 - 2*w^2 - 16*w + 11]', '[1863, 207, 4*w^3 + 2*w^2 - 19*w]', '[1863, 207, -3*w^3 + w^2 + 18*w - 5]', '[1871, 1871, -2*w^3 + 2*w^2 + 12*w - 9]', '[1871, 1871, 2*w^3 + 2*w^2 - 8*w - 5]', '[1871, 1871, -3*w^3 - 2*w^2 + 16*w - 6]', '[1871, 1871, 2*w^2 - w - 11]', '[1872, 78, 4*w^3 + 2*w^2 - 22*w + 6]', '[1872, 78, 4*w^3 + 2*w^2 - 20*w + 8]', '[1872, 78, 2*w^3 - 2*w^2 - 10*w + 16]', '[1872, 78, -2*w^2 + 2*w + 8]', '[1873, 1873, w^3 - 4*w - 5]', '[1873, 1873, 2*w^3 - 11*w - 2]', '[1889, 1889, -4*w^3 + 22*w - 17]', '[1889, 1889, -4*w^2 - 3*w + 9]', '[1899, 633, -w^3 + 4*w^2 + 8*w - 20]', '[1899, 633, w^3 + 3*w^2 - 5*w - 10]', '[1899, 633, 2*w^3 + 4*w^2 - 7*w - 5]', '[1899, 633, 2*w^3 + 3*w^2 - 10*w - 2]', '[1901, 1901, 3*w^3 - 11*w + 4]', '[1901, 1901, -7*w^3 + 39*w - 16]', '[1907, 1907, -2*w^3 + 2*w^2 + 15*w - 14]', '[1907, 1907, w^3 + 3*w^2 - 6*w - 9]', '[1907, 1907, w^3 - 2*w^2 - 10*w + 9]', '[1907, 1907, 3*w^3 + 3*w^2 - 16*w]', '[1949, 1949, -3*w^3 + 20*w - 10]', '[1949, 1949, -2*w^3 + 2*w^2 + 15*w - 13]', '[1949, 1949, -w^3 + 2*w^2 + 10*w - 10]', '[1949, 1949, 2*w^3 - 15*w + 5]', '[1973, 1973, 6*w^3 + 2*w^2 - 31*w + 2]', '[1973, 1973, 3*w^3 - 2*w^2 - 14*w + 7]', '[1975, 395, -3*w^3 + 19*w - 15]', '[1975, 395, -4*w^3 - w^2 + 22*w - 10]', '[1975, 395, w^3 - 9*w - 3]', '[1975, 395, -w^3 + w^2 + 3*w - 8]', '[1979, 1979, 2*w^3 - 4*w^2 - 12*w + 21]', '[1979, 1979, -4*w^3 - 4*w^2 + 18*w + 1]', '[1979, 1979, w^3 + 3*w^2 - 2*w - 11]', '[1979, 1979, -w^3 + 3*w^2 + 8*w - 10]', '[1989, 663, -3*w^3 + w^2 + 20*w - 10]', '[1989, 663, 5*w^3 + 3*w^2 - 28*w]', '[1989, 663, -2*w^3 - 2*w^2 + 7*w + 4]', '[1989, 663, -3*w^3 - w^2 + 13*w + 1]', '[1989, 663, 3*w^3 - 2*w^2 - 18*w + 13]', '[1989, 663, 4*w^3 - w^2 - 22*w + 9]', '[1989, 663, -w^3 + w^2 + 10*w - 9]', '[1989, 663, w^3 + 3*w^2 - 8*w - 3]', '[1993, 1993, w^3 + 3*w^2 - 4*w - 8]', '[1993, 1993, w^3 + 3*w^2 - 4*w - 7]', '[1993, 1993, 6*w^3 + 3*w^2 - 34*w + 6]', '[1993, 1993, -w^3 - 3*w^2 + 9*w + 6]', '[1999, 1999, 7*w^3 - 39*w + 21]', '[1999, 1999, 4*w^3 + w^2 - 19*w]', '[1999, 1999, w^3 + 2*w^2 - 8*w - 5]', '[1999, 1999, -4*w^3 - 2*w^2 + 23*w - 6]', '[2003, 2003, 4*w^3 - w^2 - 21*w + 13]', '[2003, 2003, -4*w^3 - w^2 + 19*w - 6]', '[2011, 2011, -5*w^3 - w^2 + 28*w - 11]', '[2011, 2011, -w^3 + w^2 + 2*w - 6]', '[2025, 15, -3*w^2 + 9]', '[2025, 15, -3*w^3 - 3*w^2 + 15*w + 3]', '[2025, 45, -5*w^3 - 3*w^2 + 28*w - 1]', '[2025, 45, -w^3 - 3*w^2 + 8*w + 4]', '[2025, 45, w^3 - 4*w^2 - 8*w + 17]', '[2025, 45, -2*w^3 - 4*w^2 + 7*w + 8]', '[2032, 254, 6*w^3 - 32*w + 22]', '[2032, 254, 2*w^3 + 2*w^2 - 14*w + 6]', '[2032, 254, 2*w^3 - 12*w - 2]', '[2032, 254, 2*w - 8]', '[2041, 2041, -w^3 + w^2 + 10*w - 5]', '[2041, 2041, 3*w^3 + 3*w^2 - 15*w - 2]', '[2041, 2041, 3*w^2 - 10]', '[2041, 2041, -3*w^3 + w^2 + 20*w - 14]', '[2053, 2053, w^3 + 2*w^2 - 2*w - 8]', '[2053, 2053, 2*w^3 - 2*w^2 - 13*w + 9]', '[2063, 2063, -4*w^3 - 3*w^2 + 19*w - 6]', '[2063, 2063, -2*w^3 + 3*w^2 + 11*w - 21]', '[2081, 2081, 2*w^3 + 4*w^2 - 9*w - 2]', '[2081, 2081, 5*w^3 + 2*w^2 - 25*w + 1]', '[2083, 2083, 4*w^3 - 21*w + 20]', '[2083, 2083, -3*w^3 + 14*w - 17]', '[2083, 2083, 4*w^3 - w^2 - 23*w + 10]', '[2083, 2083, 2*w^3 + w^2 - 7*w - 3]', '[2089, 2089, -2*w^3 + w^2 + 9*w - 13]', '[2089, 2089, 4*w^3 + w^2 - 21*w + 12]', '[2089, 2089, 4*w^3 - w^2 - 21*w + 15]', '[2089, 2089, 4*w^3 + w^2 - 19*w + 8]', '[2097, 699, 4*w^3 + w^2 - 21*w - 2]', '[2097, 699, w^3 + w^2 - 5*w - 8]', '[2097, 699, w^2 + 4]', '[2097, 699, -2*w^3 + w^2 + 9*w + 1]', '[2129, 2129, 3*w^3 + w^2 - 18*w + 9]', '[2129, 2129, w^3 + w^2 - 8*w - 4]', '[2141, 2141, -2*w^3 + 15*w - 8]', '[2141, 2141, 3*w^3 - 20*w + 7]', '[2159, 2159, w^3 + 4*w^2 - 6*w - 3]', '[2159, 2159, -2*w^3 + w^2 + 15*w - 12]', '[2159, 2159, w^3 - 3*w^2 - 6*w + 8]', '[2159, 2159, w^3 - 3*w^2 - 9*w + 20]', '[2159, 2159, -3*w^2 - 4*w + 4]', '[2159, 2159, -3*w^3 - 3*w^2 + 14*w + 7]', '[2159, 2159, 2*w^3 + 7*w^2 - 2*w - 16]', '[2159, 2159, -7*w^3 + 7*w^2 + 46*w - 49]', '[2161, 2161, -3*w^3 + 20*w - 16]', '[2161, 2161, -3*w^3 + 3*w^2 + 21*w - 22]', '[2197, 13, 4*w^3 + 2*w^2 - 21*w + 7]', '[2197, 13, w^3 - 2*w^2 - 4*w + 12]', '[2197, 169, -2*w^3 - 3*w^2 + 13*w + 1]', '[2197, 169, -4*w^3 - 3*w^2 + 23*w + 2]', '[2207, 2207, -2*w^3 + 3*w^2 + 13*w - 14]', '[2207, 2207, 2*w^3 + 3*w^2 - 7*w - 7]', '[2209, 47, 2*w^3 + 3*w^2 - 10*w - 7]', '[2209, 47, w^3 + 3*w^2 - 5*w - 5]', '[2213, 2213, 3*w^3 - 2*w^2 - 17*w + 12]', '[2213, 2213, 3*w^3 + 2*w^2 - 13*w - 2]', '[2224, 278, 2*w^2 + 4*w - 12]', '[2224, 278, 2*w^3 - 2*w^2 - 14*w + 8]', '[2237, 2237, 2*w^3 - 2*w^2 - 15*w + 6]', '[2237, 2237, 2*w^3 - 3*w^2 - 8*w + 14]', '[2237, 2237, w^3 - 2*w^2 - 10*w + 17]', '[2237, 2237, -4*w^3 - w^2 + 26*w - 9]', '[2239, 2239, -5*w^3 - w^2 + 29*w - 11]', '[2239, 2239, w^2 - 4*w - 3]', '[2249, 2249, -2*w^3 - 3*w^2 + 8*w + 9]', '[2249, 2249, 6*w^3 - 4*w^2 - 36*w + 33]', '[2249, 2249, 7*w^3 + 4*w^2 - 34*w + 8]', '[2249, 2249, -w^2 + 2*w + 9]', '[2259, 753, -4*w^3 + 23*w - 15]', '[2259, 753, -4*w^3 - w^2 + 24*w - 10]', '[2259, 753, -w^3 + 2*w - 6]', '[2259, 753, w^3 + w^2 - 9*w - 2]', '[2279, 2279, 2*w^3 + 3*w^2 - 12*w - 6]', '[2279, 2279, 3*w^2 + 3*w - 17]', '[2279, 2279, 2*w^2 - w - 12]', '[2279, 2279, -3*w^3 - 2*w^2 + 16*w - 7]', '[2287, 2287, -3*w^3 + w^2 + 13*w - 8]', '[2287, 2287, 6*w^3 + w^2 - 32*w + 10]', '[2291, 2291, 4*w^3 - 3*w^2 - 22*w + 28]', '[2291, 2291, -3*w^3 + 13*w - 13]', '[2291, 2291, 5*w^3 - 27*w + 19]', '[2291, 2291, -5*w^3 - 3*w^2 + 23*w - 10]', '[2297, 2297, -6*w^3 + 2*w^2 + 35*w - 22]', '[2297, 2297, 6*w^3 + 3*w^2 - 31*w + 7]', '[2304, 12, 4*w^3 - 20*w + 12]', '[2304, 12, 4*w^3 - 20*w + 8]', '[2311, 2311, 3*w^3 - 20*w + 8]', '[2311, 2311, 2*w^3 - 15*w + 7]', '[2323, 2323, -3*w^3 + 5*w^2 + 18*w - 30]', '[2323, 2323, 3*w^3 - w^2 - 20*w + 11]', '[2323, 2323, -w^3 + w^2 + 10*w - 8]', '[2323, 2323, -5*w^3 - 5*w^2 + 22*w - 1]', '[2339, 2339, 5*w^3 + w^2 - 31*w + 9]', '[2339, 2339, -6*w^3 - w^2 + 31*w - 15]', '[2341, 2341, -4*w^3 + w^2 + 21*w - 5]', '[2341, 2341, 4*w^3 + w^2 - 19*w - 2]', '[2349, 87, -3*w^2 - 6*w + 9]', '[2349, 87, -3*w^3 + 3*w^2 + 21*w - 21]', '[2349, 261, -2*w^3 - 3*w^2 + 10*w + 3]', '[2349, 261, w^3 - w^2 - 10*w + 6]', '[2349, 261, w^3 + 3*w^2 - 5*w - 9]', '[2349, 261, -3*w^3 + w^2 + 20*w - 13]', '[2353, 2353, -w^3 + 4*w - 10]', '[2353, 2353, -2*w^3 + 11*w - 13]', '[2353, 2353, -5*w^3 - 3*w^2 + 21*w - 7]', '[2353, 2353, -6*w^3 + 3*w^2 + 34*w - 31]', '[2363, 2363, -6*w^3 + 32*w - 19]', '[2363, 2363, 4*w^3 - 18*w + 13]', '[2363, 2363, -3*w^3 - 3*w^2 + 11*w - 7]', '[2363, 2363, 4*w^3 - 3*w^2 - 24*w + 31]', '[2389, 2389, 6*w^3 + w^2 - 31*w + 18]', '[2389, 2389, 4*w^3 + 2*w^2 - 20*w - 3]', '[2393, 2393, -w - 7]', '[2393, 2393, -w^3 + 6*w - 10]', '[2393, 2393, -2*w^3 + 3*w^2 + 14*w - 14]', '[2393, 2393, w^3 + 3*w^2 - w - 10]', '[2401, 7, -7]', '[2417, 2417, -5*w^3 + w^2 + 27*w - 15]', '[2417, 2417, -4*w^3 - w^2 + 18*w - 5]', '[2441, 2441, -3*w^3 - 2*w^2 + 14*w + 4]', '[2441, 2441, -2*w^3 + 2*w^2 + 11*w - 7]', '[2441, 2441, -3*w^3 - 2*w^2 + 16*w - 8]', '[2441, 2441, 2*w^2 - w - 13]', '[2447, 2447, 3*w^3 - w^2 - 20*w + 12]', '[2447, 2447, -w^3 + w^2 + 10*w - 7]', '[2448, 102, 4*w^3 - 2*w^2 - 26*w + 22]', '[2448, 102, 2*w^3 + 2*w^2 - 6*w - 4]', '[2448, 102, -4*w^3 + 2*w^2 + 24*w - 16]', '[2448, 102, -2*w^2 - 6*w + 4]', '[2461, 2461, -4*w^3 - 6*w^2 + 14*w + 5]', '[2461, 2461, 4*w^2 + 7*w - 11]', '[2461, 2461, -3*w^3 + 4*w^2 + 22*w - 26]', '[2461, 2461, 4*w^3 - 6*w^2 - 26*w + 37]', '[2461, 2461, -5*w^3 + 32*w - 7]', '[2461, 2461, -8*w^3 - 2*w^2 + 43*w - 10]', '[2461, 2461, -2*w^3 - 3*w^2 + 11*w + 7]', '[2461, 2461, -w^3 - 2*w^2 + 4*w + 13]', '[2467, 2467, -4*w^3 + 19*w - 6]', '[2467, 2467, -4*w - 3]', '[2467, 2467, -4*w^3 + 24*w - 15]', '[2467, 2467, -5*w^3 + 26*w - 9]', '[2473, 2473, w^3 + 3*w^2 - 7*w - 4]', '[2473, 2473, -4*w^3 - 3*w^2 + 22*w + 2]', '[2483, 2483, -2*w^2 - 5*w + 12]', '[2483, 2483, -w^3 - 4*w^2 + w + 4]', '[2483, 2483, -3*w^3 - 3*w^2 + 16*w + 1]', '[2483, 2483, w^3 - 2*w^2 - 13*w + 3]', '[2493, 831, -5*w^3 - 2*w^2 + 30*w - 8]', '[2493, 831, -4*w^3 - w^2 + 23*w - 10]', '[2493, 831, 2*w^3 + 2*w^2 - 15*w - 1]', '[2493, 831, w^2 - 3*w - 5]', '[2512, 314, -2*w^3 + 2*w^2 + 12*w - 8]', '[2512, 314, 2*w^3 + 2*w^2 - 8*w - 6]', '[2521, 2521, -w^3 + w^2 + 7*w - 14]', '[2521, 2521, -w^2 - 2*w - 4]', '[2521, 2521, w^2 + w - 11]', '[2521, 2521, -w^2 - w - 4]', '[2525, 505, -4*w^3 + 3*w^2 + 22*w - 19]', '[2525, 505, -5*w^3 + w^2 + 29*w - 13]', '[2525, 505, 5*w^3 + 3*w^2 - 23*w + 1]', '[2525, 505, 2*w^3 + w^2 - 6*w - 3]', '[2531, 2531, -2*w^3 - 2*w^2 + 13*w + 5]', '[2531, 2531, -3*w^3 - 2*w^2 + 18*w - 6]', '[2539, 2539, 5*w^3 - 2*w^2 - 33*w + 15]', '[2539, 2539, -3*w^3 + w^2 + 17*w - 20]', '[2547, 849, w^3 + 3*w^2 - 5*w - 6]', '[2547, 849, 2*w^3 + 3*w^2 - 13*w - 2]', '[2547, 849, -2*w^3 + w^2 + 15*w - 8]', '[2547, 849, -w^3 + 3*w^2 + 11*w - 12]', '[2547, 849, -2*w^3 - 3*w^2 + 10*w + 6]', '[2547, 849, -4*w^3 - 3*w^2 + 23*w + 1]', '[2547, 849, -2*w^3 + w^2 + 15*w - 11]', '[2547, 849, -2*w^3 + 3*w^2 + 16*w - 18]', '[2551, 2551, 5*w^3 - 26*w + 16]', '[2551, 2551, -2*w^3 - 4*w^2 + 8*w + 11]', '[2591, 2591, 6*w^3 - 35*w + 8]', '[2591, 2591, -3*w^3 + 5*w^2 + 20*w - 26]', '[2601, 51, -4*w^3 + 20*w - 11]', '[2601, 51, 2*w^3 - 10*w + 13]', '[2601, 51, -5*w^3 + 25*w - 18]', '[2601, 51, 4*w^3 - 20*w + 9]', '[2601, 867, -5*w^3 - 2*w^2 + 25*w - 11]', '[2601, 867, -5*w^3 - 2*w^2 + 27*w - 8]', '[2601, 867, -3*w^3 + 2*w^2 + 15*w - 19]', '[2601, 867, -w^3 + 2*w^2 + 3*w - 10]', '[2609, 2609, -3*w^3 - w^2 + 19*w - 10]', '[2609, 2609, w^3 + w^2 - 4*w - 9]', '[2609, 2609, w^3 - w^2 - 6*w - 2]', '[2609, 2609, 2*w^3 + w^2 - 14*w - 2]', '[2617, 2617, 4*w^3 + 3*w^2 - 22*w - 1]', '[2617, 2617, w^3 + 3*w^2 - 7*w - 5]', '[2623, 2623, w^3 + 3*w^2 - 6*w - 14]', '[2623, 2623, 2*w^3 + 3*w^2 - 10*w - 4]', '[2623, 2623, -2*w^3 + w^2 + 9*w - 15]', '[2623, 2623, 4*w^3 + w^2 - 21*w + 14]', '[2623, 2623, w^3 + 3*w^2 - 5*w - 8]', '[2623, 2623, 2*w^3 - 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13]', '[1283, 1283, -w^2 - 2*w - 3]', '[1291, 1291, -w^3 + w^2 + 3*w - 7]', '[1291, 1291, 4*w^3 + w^2 - 22*w + 9]', '[1303, 1303, -w^2 - w - 3]', '[1303, 1303, w^2 + w - 10]', '[1303, 1303, -4*w^3 - w^2 + 24*w - 9]', '[1303, 1303, -w^3 - w^2 + 9*w + 1]', '[1327, 1327, -3*w^3 - 3*w^2 + 15*w + 5]', '[1327, 1327, -3*w^2 + 7]', '[1327, 1327, -2*w^3 - 3*w^2 + 10*w + 1]', '[1327, 1327, w^3 + 3*w^2 - 5*w - 11]', '[1361, 1361, 3*w^3 - 18*w + 13]', '[1361, 1361, 3*w^3 - 2*w^2 - 17*w + 13]', '[1361, 1361, -3*w - 4]', '[1361, 1361, -3*w^3 - 2*w^2 + 13*w + 1]', '[1381, 1381, -w^3 + 2*w^2 + 6*w - 3]', '[1381, 1381, -2*w^3 + 3*w^2 + 12*w - 14]', '[1381, 1381, 2*w^3 + 2*w^2 - 9*w - 8]', '[1381, 1381, 3*w^3 + 3*w^2 - 13*w - 4]', '[1427, 1427, 3*w^3 + w^2 - 17*w + 8]', '[1427, 1427, w^2 - 2*w - 6]', '[1429, 1429, 2*w^3 - 15*w + 4]', '[1429, 1429, -3*w^3 + 20*w - 11]', '[1433, 1433, -w^3 + 2*w^2 + 7*w - 5]', '[1433, 1433, w^3 + 2*w^2 - 3*w - 9]', '[1447, 1447, -2*w - 7]', '[1447, 1447, -2*w^3 + 12*w - 13]', '[1453, 1453, -4*w^3 - 2*w^2 + 24*w + 1]', '[1453, 1453, 5*w^3 + 2*w^2 - 26*w]', '[1459, 1459, 5*w^3 + w^2 - 26*w + 10]', '[1459, 1459, -w^2 + w - 4]', '[1459, 1459, 3*w^3 - w^2 - 14*w + 11]', '[1459, 1459, 2*w^3 + w^2 - 11*w - 5]', '[1481, 1481, -w^3 + w^2 + 10*w - 10]', '[1481, 1481, 3*w^3 - w^2 - 20*w + 9]', '[1499, 1499, -3*w^3 + 13*w - 8]', '[1499, 1499, 5*w^3 - 27*w + 14]', '[1511, 1511, -3*w^3 + 18*w - 14]', '[1511, 1511, -3*w - 5]', '[1511, 1511, -w^3 - w^2 + 3*w - 6]', '[1511, 1511, -2*w^3 + w^2 + 12*w - 16]', '[1531, 1531, 4*w^3 - w^2 - 25*w + 14]', '[1531, 1531, w^3 - 7*w - 4]', '[1543, 1543, -4*w^3 - w^2 + 21*w - 11]', '[1543, 1543, -2*w^3 + w^2 + 9*w - 12]', '[1559, 1559, -2*w^3 - 3*w^2 + 9*w + 3]', '[1559, 1559, -w^3 + w^2 + 10*w - 4]', '[1559, 1559, -3*w^3 + w^2 + 20*w - 15]', '[1559, 1559, 3*w^2 + w - 12]', '[1609, 1609, -w^3 + 2*w^2 + 7*w - 4]', '[1609, 1609, w^3 + 2*w^2 - 3*w - 10]', '[1613, 1613, 5*w^3 - 27*w + 11]', '[1613, 1613, w^3 + 2*w^2 - 7*w - 7]', '[1613, 1613, -3*w^3 - 2*w^2 + 17*w - 5]', '[1613, 1613, -3*w^3 + 13*w - 5]', '[1621, 1621, 4*w^3 + w^2 - 19*w + 5]', '[1621, 1621, 4*w^3 - w^2 - 21*w + 12]', '[1637, 1637, 2*w^3 - w^2 - 15*w + 6]', '[1637, 1637, -2*w^3 + w^2 + 15*w - 13]', '[1663, 1663, 5*w^3 + 3*w^2 - 28*w - 1]', '[1663, 1663, 5*w^3 - 26*w + 8]', '[1663, 1663, -6*w^3 - w^2 + 32*w - 8]', '[1663, 1663, 4*w^3 - 19*w + 5]', '[1681, 41, 5*w^3 + 2*w^2 - 26*w - 1]', '[1681, 41, -2*w^3 + 2*w^2 + 9*w - 4]', '[1699, 1699, -3*w^3 + 19*w - 14]', '[1699, 1699, w^3 + 4*w^2 - 2*w - 13]', '[1699, 1699, -4*w^3 - w^2 + 22*w + 1]', '[1699, 1699, w^3 - 9*w - 2]', '[1733, 1733, 3*w^2 + w - 11]', '[1733, 1733, 2*w^3 + 3*w^2 - 9*w - 4]', '[1733, 1733, 5*w^3 + w^2 - 26*w + 8]', '[1733, 1733, 3*w^3 - w^2 - 14*w + 9]', '[1741, 1741, -w^3 + 10*w - 6]', '[1741, 1741, 4*w^3 - 25*w + 9]', '[1759, 1759, -w^3 + 2*w^2 + 10*w - 11]', '[1759, 1759, -2*w^3 + 2*w^2 + 15*w - 12]', '[1777, 1777, 3*w^3 + 3*w^2 - 15*w - 4]', '[1777, 1777, -3*w^2 + 8]', '[1811, 1811, -3*w^3 + w^2 + 17*w - 5]', '[1811, 1811, 5*w^3 - 27*w + 12]', '[1811, 1811, -3*w^3 + 13*w - 6]', '[1811, 1811, 2*w^3 + w^2 - 8*w - 5]', '[1823, 1823, -5*w^3 - 2*w^2 + 23*w - 11]', '[1823, 1823, 5*w^3 - 2*w^2 - 27*w + 25]', '[1847, 1847, -3*w^3 - w^2 + 17*w - 9]', '[1847, 1847, w^2 - 2*w - 7]', '[1849, 43, -4*w^3 + 20*w - 7]', '[1871, 1871, -2*w^3 + 2*w^2 + 12*w - 9]', '[1871, 1871, 2*w^3 + 2*w^2 - 8*w - 5]', '[1871, 1871, -3*w^3 - 2*w^2 + 16*w - 6]', '[1871, 1871, 2*w^2 - w - 11]', '[1873, 1873, w^3 - 4*w - 5]', '[1873, 1873, 2*w^3 - 11*w - 2]', '[1889, 1889, -4*w^3 + 22*w - 17]', '[1889, 1889, -4*w^2 - 3*w + 9]', '[1901, 1901, 3*w^3 - 11*w + 4]', '[1901, 1901, -7*w^3 + 39*w - 16]', '[1907, 1907, -2*w^3 + 2*w^2 + 15*w - 14]', '[1907, 1907, w^3 + 3*w^2 - 6*w - 9]', '[1907, 1907, w^3 - 2*w^2 - 10*w + 9]', '[1907, 1907, 3*w^3 + 3*w^2 - 16*w]', '[1949, 1949, -3*w^3 + 20*w - 10]', '[1949, 1949, -2*w^3 + 2*w^2 + 15*w - 13]', '[1949, 1949, -w^3 + 2*w^2 + 10*w - 10]', '[1949, 1949, 2*w^3 - 15*w + 5]', '[1973, 1973, 6*w^3 + 2*w^2 - 31*w + 2]', '[1973, 1973, 3*w^3 - 2*w^2 - 14*w + 7]', '[1979, 1979, 2*w^3 - 4*w^2 - 12*w + 21]', '[1979, 1979, -4*w^3 - 4*w^2 + 18*w + 1]', '[1979, 1979, w^3 + 3*w^2 - 2*w - 11]', '[1979, 1979, -w^3 + 3*w^2 + 8*w - 10]', '[1993, 1993, w^3 + 3*w^2 - 4*w - 8]', '[1993, 1993, w^3 + 3*w^2 - 4*w - 7]', '[1993, 1993, 6*w^3 + 3*w^2 - 34*w + 6]', '[1993, 1993, -w^3 - 3*w^2 + 9*w + 6]', '[1999, 1999, 7*w^3 - 39*w + 21]', '[1999, 1999, 4*w^3 + w^2 - 19*w]', '[1999, 1999, w^3 + 2*w^2 - 8*w - 5]', '[1999, 1999, -4*w^3 - 2*w^2 + 23*w - 6]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 8, -6, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 10309, 'disc_rad': 793, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[2, 2]]], [5, [[2, 2]]], [7, [[4, 1]]], [11, [[4, 1]]], [13, [0]], [17, [[2, 1], [1, 2]]], [19, [[2, 2]]], [23, [[2, 1], [1, 2]]], [29, [[2, 1], [1, 2]]], [31, [[4, 1]]], [37, [[4, 1]]], [41, [[2, 2]]], [43, [[2, 1], [1, 2]]], [47, [[2, 2]]], [53, [[2, 1], [1, 2]]], [59, [[4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 28.160255680657446, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.10309.1', 'local_algs': ['13.2.1.1', '13.2.1.1', '61.1.0.1', '61.1.0.1', '61.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [13, 61], 'rd': 10.0763706654, 'regulator': {'__RealLiteral__': 0, 'data': '4.04659780603', 'prec': 44}, 'res': {'gal': ['169,0,-377,0,230,0,-32,0,1'], 'sib': ['5,9,-8,-2,1', '169,0,-377,0,230,0,-32,0,1']}, 'subfield_mults': [1], 'subfields': ['-3.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a^{3} - 6 a + 3 \\)', '\\( a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}