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hmf_forms • Show schema
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{'deg': 3, 'dimension': 1, 'disc': 1101, 'field_bad_primes': [3, 367], 'field_label': '3.3.1101.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1101.1-18.2-g', 'label_nsuffix': 6, 'label_suffix': 'g', 'level_bad_primes': [2, 3], 'level_ideal': '[18, 6, w^2 + 2*w - 6]', 'level_label': '18.2', 'level_norm': 18, 'parallel_weight': 2, 'short_label': '18.2-g', 'weight': '[2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2, 2, w - 2]', 1], ['[3, 3, -w + 3]', -1], ['[3, 3, w - 1]', -1]], 'hecke_eigenvalues': [-1, 1, 1, -1, 4, -8, -8, 8, -8, -2, -12, 8, -10, 4, -4, 4, -12, -6, -10, -2, -8, -12, -18, -10, 14, -8, -4, -14, 14, -2, 0, -10, -20, 10, 10, 4, 22, 4, 20, 20, 0, -18, -8, 4, -14, -14, 10, 8, 8, -16, -2, -4, -16, 0, 0, 18, 14, -14, -10, 2, 26, 18, 28, 2, 2, 14, 12, 14, 16, -4, -22, 38, 8, -8, -10, -20, -24, 30, 18, 30, 34, -4, 10, -8, 18, 42, 18, 40, -4, 24, -20, -12, 20, -4, -36, 14, 28, -2, 4, 10, -4, -18, 10, 10, 26, 2, -22, -30, 42, 46, -4, -44, -26, -10, -36, 20, 12, -50, -46, -6, 14, 0, -24, 0, 16, -10, 20, 24, -32, -50, -46, -20, -42, 36, -12, -36, 30, 34, -14, 24, -42, -36, -40, 14, -20, -36, 12, 32, -6, -26, -14, 28, 8, -36, 0, -38], 'hecke_polynomial': 'x', 'label': '3.3.1101.1-18.2-g'}
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hmf_fields • Show schema
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{'degree': 3, 'discriminant': 1101, 'ideals': ['[1, 1, 1]', '[2, 2, w - 2]', '[3, 3, -w + 3]', '[3, 3, w - 1]', '[4, 2, w^2 + w - 7]', '[4, 4, w^2 + 2*w - 4]', '[6, 6, w^2 + w - 6]', '[6, 6, -w^2 + 10]', '[8, 2, 2]', '[8, 8, -w^2 + 8]', '[9, 3, -w^2 + 9]', '[9, 3, w^2 + 2*w - 3]', '[9, 9, 2*w - 5]', '[12, 6, w^2 + w - 9]', '[12, 6, w^2 + w - 5]', '[12, 12, w]', '[12, 12, w^2 + w - 8]', '[16, 4, 2*w - 4]', '[16, 4, -w^2 + w + 5]', '[16, 16, w^2 - w - 4]', '[18, 6, w^2 - 6]', '[18, 6, w^2 + 2*w - 6]', '[18, 18, w + 2]', '[19, 19, w + 1]', '[23, 23, w^2 - 2*w - 1]', '[24, 6, -2*w + 6]', '[24, 6, 2*w - 2]', '[24, 24, w^2 - 2*w]', '[24, 24, -w + 4]', '[27, 3, 3]', '[27, 9, w^2 - 3]', '[27, 9, 2*w^2 + w - 15]', '[27, 27, 2*w^2 + 3*w - 11]', '[31, 31, -2*w^2 + 19]', '[31, 31, -w^2 + 5]', '[31, 31, -3*w + 5]', '[32, 4, 2*w^2 + 2*w - 14]', '[32, 8, 2*w^2 + 4*w - 8]', '[32, 32, w + 4]', '[36, 6, w^2 - 3*w + 3]', '[36, 6, w^2 - w - 3]', '[36, 12, -w^2 + 3*w]', '[36, 12, w^2 + 2*w - 12]', '[36, 18, -w^2 - w + 11]', '[36, 36, w^2 - 4]', '[38, 38, w^2 - w - 2]', '[41, 41, w^2 + 2*w - 7]', '[43, 43, w^2 - 11]', '[46, 46, w^2 + 2*w - 2]', '[47, 47, 3*w - 7]', '[48, 12, 2*w^2 + 2*w - 12]', '[48, 12, 3*w^2 + 5*w - 15]', '[48, 12, -2*w^2 + 20]', '[48, 12, w^2 + 3*w - 1]', '[48, 48, 3*w^2 + 4*w - 16]', '[48, 48, 3*w^2 + 2*w - 24]', '[53, 53, -3*w^2 - 6*w + 11]', '[54, 6, 3*w - 6]', '[54, 18, 4*w^2 + 3*w - 30]', '[54, 18, -w^2 + w + 6]', '[54, 54, w^2 + w - 2]', '[57, 57, w^2 - 1]', '[57, 57, -w^2 + 2*w + 3]', '[59, 59, 2*w - 1]', '[62, 62, w^2 - 4*w + 2]', '[62, 62, 2*w^2 + w - 14]', '[62, 62, -3*w^2 - 2*w + 22]', '[64, 4, 4]', '[64, 8, w^2 + 3*w - 5]', '[64, 16, -2*w^2 + 16]', '[64, 64, w^2 + 2*w - 8]', '[67, 67, 2*w^2 + w - 19]', '[67, 67, 3*w^2 + 2*w - 25]', '[67, 67, w - 5]', '[69, 69, 4*w^2 + 6*w - 19]', '[69, 69, 2*w^2 + 2*w - 15]', '[72, 6, -2*w^2 + 18]', '[72, 6, 2*w^2 + 4*w - 6]', '[72, 18, 4*w - 10]', '[72, 24, 2*w^2 + 3*w - 12]', '[72, 24, -w^2 + w + 12]', '[72, 72, -w^2 + 5*w - 4]', '[73, 73, -4*w^2 - 3*w + 29]', '[73, 73, 2*w^2 - w - 11]', '[73, 73, w^2 + 2*w - 11]', '[76, 38, 3*w^2 + 3*w - 19]', '[76, 76, 4*w^2 + 7*w - 16]', '[79, 79, 2*w^2 + 2*w - 11]', '[81, 9, -3*w + 9]', '[81, 9, 4*w^2 + 6*w - 21]', '[81, 9, 3*w - 3]', '[81, 27, w^2 + 2*w - 9]', '[81, 81, -2*w^2 + 17]', '[82, 82, w^2 - 2*w + 2]', '[83, 83, 2*w^2 - 13]', '[86, 86, -w^2 - 2*w + 10]', '[89, 89, -2*w + 7]', '[92, 46, -w^2 + w + 7]', '[92, 92, w^2 + 3*w - 8]', '[93, 93, w + 5]', '[93, 93, -4*w^2 - 4*w + 27]', '[93, 93, 2*w^2 + 2*w - 9]', '[93, 93, -2*w - 7]', '[93, 93, -4*w + 7]', '[93, 93, -3*w^2 - 4*w + 15]', '[94, 94, w^2 + 3*w - 2]', '[96, 12, 2*w^2 + 2*w - 18]', '[96, 12, 2*w^2 + 2*w - 10]', '[96, 24, 2*w]', '[96, 24, 2*w^2 + 2*w - 16]', '[96, 96, -w^2 - w + 12]', '[96, 96, w^2 + 3*w - 4]', '[97, 97, -2*w^2 + 4*w - 1]', '[101, 101, -2*w - 5]', '[103, 103, 2*w^2 + w - 13]', '[106, 106, -3*w^2 - 4*w + 14]', '[107, 107, -2*w^2 - 2*w + 17]', '[108, 6, 3*w^2 + 3*w - 21]', '[108, 12, 3*w^2 + 6*w - 12]', '[108, 18, w^2 + 3*w - 3]', '[108, 18, -w^2 + 7*w - 9]', '[108, 36, -w^2 + 12]', '[108, 36, 4*w^2 + 5*w - 24]', '[108, 54, -w^2 + 3*w + 1]', '[108, 108, -w^2 - 3*w + 16]', '[109, 109, -4*w^2 - 2*w + 31]', '[113, 113, w^2 + 2*w - 1]', '[114, 114, -2*w^2 + w + 22]', '[114, 114, 3*w^2 + 4*w - 18]', '[118, 118, 2*w^2 - 5*w + 2]', '[123, 123, 2*w^2 - 5]', '[123, 123, 4*w - 9]', '[124, 62, w^2 - w + 1]', '[124, 62, w^2 - w - 11]', '[124, 62, -w^2 - w + 1]', '[124, 124, -w^2 + 2*w + 4]', '[124, 124, -3*w^2 - 5*w + 16]', '[124, 124, w^2 - w - 8]', '[125, 5, -5]', '[127, 127, 2*w^2 + 3*w - 13]', '[128, 8, 4*w - 8]', '[128, 8, -2*w^2 + 2*w + 10]', '[128, 32, 2*w^2 - 2*w - 8]', '[128, 128, w^2 - 3*w + 4]', '[129, 129, -2*w - 1]', '[129, 129, 2*w^2 + 2*w - 21]', '[134, 134, -w^2 - 2*w + 14]', '[134, 134, w^2 - 7*w + 10]', '[134, 134, -w^2 - 3*w + 14]', '[137, 137, -2*w^2 + 7*w - 7]', '[138, 138, 3*w^2 + w - 22]', '[138, 138, -w + 6]', '[139, 139, 2*w^2 + w - 7]', '[141, 141, -6*w^2 - 2*w + 53]', '[141, 141, 3*w^2 + 2*w - 21]', '[144, 12, 2*w^2 - 12]', '[144, 12, 2*w^2 + 4*w - 12]', '[144, 12, w^2 + 3*w - 9]', '[144, 12, -w^2 + w + 9]', '[144, 36, 2*w + 4]', '[144, 36, 3*w^2 + 5*w - 11]', '[144, 48, w^2]', '[144, 48, 2*w^2 + w - 12]', '[144, 144, -3*w^2 - w + 28]', '[146, 146, w^2 - w - 10]', '[146, 146, -w^2 + w + 14]', '[146, 146, w^2 - 6*w + 10]', '[149, 149, -6*w^2 - 9*w + 31]', '[152, 38, 2*w + 2]', '[152, 152, -2*w^2 - w + 20]', '[157, 157, w^2 - 4*w + 1]', '[158, 158, 3*w - 2]', '[159, 159, -2*w - 3]', '[159, 159, -4*w^2 - 3*w + 31]', '[162, 18, 3*w^2 + 3*w - 18]', '[162, 18, 2*w^2 + 3*w - 6]', '[162, 18, -3*w^2 + 30]', '[162, 54, w^2 - 4*w + 6]', '[162, 162, 2*w^2 - w - 10]', '[163, 163, 2*w^2 + 5*w - 5]', '[164, 82, w^2 + 3*w + 1]', '[164, 164, 7*w^2 + 11*w - 32]', '[166, 166, -2*w^2 + 5*w + 2]', '[171, 57, -2*w^2 + 21]', '[171, 57, 4*w^2 + 8*w - 15]', '[171, 171, 2*w^2 - 3*w - 5]', '[172, 86, -7*w^2 - 5*w + 53]', '[172, 172, -3*w^2 - 7*w + 8]', '[173, 173, 5*w^2 + 4*w - 37]', '[177, 177, 2*w^2 - 3*w + 1]', '[177, 177, -2*w^2 + 7*w - 3]', '[178, 178, 4*w^2 + 5*w - 22]', '[179, 179, 2*w^2 + w - 11]', '[179, 179, 3*w^2 - 2*w - 17]', '[179, 179, -4*w^2 - w + 37]', '[184, 46, 2*w^2 - 4*w - 2]', '[184, 184, 2*w^2 - 5*w + 4]', '[186, 186, -w - 6]', '[186, 186, 5*w - 6]', '[186, 186, -2*w^2 - 3*w + 14]', '[186, 186, -5*w^2 - 3*w + 38]', '[186, 186, w^2 + 3*w - 10]', '[186, 186, -w^2 - 4*w + 6]', '[188, 94, -w^2 - w + 13]', '[188, 188, -5*w^2 - w + 40]', '[191, 191, -6*w^2 - 9*w + 29]', '[192, 12, -4*w + 12]', '[192, 12, 4*w - 4]', '[192, 24, -w^2 + 5*w - 3]', '[192, 24, w^2 + 3*w - 13]', '[192, 48, 2*w^2 - 4*w]', '[192, 48, -2*w + 8]', '[192, 192, 5*w - 12]', '[192, 192, 2*w^2 - w - 4]', '[193, 193, -2*w^2 - 4*w + 5]', '[194, 194, -8*w^2 - 13*w + 34]', '[201, 201, w^2 - 6*w + 5]', '[201, 201, w^2 - 2*w - 5]', '[201, 201, 2*w^2 - 11]', '[201, 201, -w^2 + 8*w - 15]', '[201, 201, -5*w + 9]', '[201, 201, w^2 - 2*w + 3]', '[202, 202, -2*w^2 - w + 10]', '[206, 206, -w^2 + 3*w + 2]', '[207, 69, 2*w^2 + w - 9]', '[207, 69, 2*w^2 + 3*w - 21]', '[207, 207, -w^2 + 13]', '[212, 106, -w^2 - 3*w + 11]', '[212, 212, -3*w^2 + 20]', '[214, 214, 3*w - 10]', '[216, 6, 6]', '[216, 18, 2*w^2 - 6]', '[216, 18, 4*w^2 + 2*w - 30]', '[216, 24, -3*w^2 + 24]', '[216, 54, 4*w^2 + 6*w - 22]', '[216, 72, w^2 + 3*w - 12]', '[216, 72, w^2 + 2*w]', '[216, 216, 4*w^2 + 3*w - 28]', '[218, 218, 2*w^2 - w - 14]', '[219, 219, -5*w^2 - 2*w + 39]', '[219, 219, 5*w^2 + 6*w - 29]', '[219, 219, 4*w^2 + 7*w - 15]', '[219, 219, 2*w^2 - 4*w - 1]', '[219, 219, -3*w^2 - 4*w + 19]', '[219, 219, 8*w - 21]', '[223, 223, -2*w^2 + 2*w + 7]', '[226, 226, w^2 + 4*w - 10]', '[227, 227, 6*w^2 + 4*w - 47]', '[228, 114, 3*w^2 + 5*w - 17]', '[228, 114, 3*w^2 + w - 21]', '[228, 228, 3*w^2 + 2*w - 20]', '[228, 228, w^2 + w]', '[233, 233, 2*w^2 + 4*w - 13]', '[233, 233, -4*w^2 - 4*w + 25]', '[233, 233, 4*w + 13]', '[236, 118, 3*w^2 + 3*w - 17]', '[236, 236, 5*w^2 + 8*w - 20]', '[237, 237, 2*w^2 + 5*w - 13]', '[237, 237, 2*w^2 - w - 9]', '[239, 239, -4*w^2 - 8*w + 13]', '[239, 239, 2*w^2 + 2*w - 5]', '[239, 239, -w^2 + 8*w - 11]', '[241, 241, 3*w - 1]', '[243, 9, -3*w^2 + 27]', '[243, 9, 3*w^2 + 6*w - 9]', '[243, 27, 2*w^2 + 3*w - 15]', '[243, 27, 6*w - 15]', '[243, 81, 2*w^2 - 2*w - 3]', '[243, 243, -w + 7]', '[246, 246, 5*w^2 + 5*w - 34]', '[246, 246, 2*w^2 + 5*w - 6]', '[248, 62, -4*w^2 + 38]', '[248, 62, -2*w^2 + 10]', '[248, 62, -6*w + 10]', '[248, 248, 5*w^2 + 7*w - 28]', '[248, 248, -3*w^2 - 3*w + 28]', '[248, 248, -2*w^2 + 3*w + 4]', '[249, 249, 4*w^2 - 5*w - 15]', '[249, 249, 5*w - 11]', '[250, 10, -5*w + 10]', '[251, 251, w^2 + 4*w - 19]', '[254, 254, w^2 - w + 2]', '[256, 8, 4*w^2 + 4*w - 28]', '[256, 16, 4*w^2 + 8*w - 16]', '[256, 16, 5*w^2 + 7*w - 25]', '[256, 64, 2*w + 8]', '[256, 256, -5*w^2 - w + 44]', '[258, 258, -6*w^2 - 5*w + 42]', '[258, 258, 11*w^2 + 3*w - 98]', '[263, 263, -2*w^2 + 2*w + 25]', '[263, 263, -5*w^2 - 4*w + 35]', '[263, 263, 3*w^2 - 25]', '[267, 267, 11*w^2 + 6*w - 89]', '[267, 267, -2*w^2 + w + 21]', '[268, 134, 3*w^2 - 13*w + 11]', '[268, 134, 3*w^2 - 9*w + 5]', '[268, 134, -3*w^2 - 3*w + 23]', '[268, 268, -2*w^2 + 11*w - 16]', '[268, 268, -w^2 + 9*w - 16]', '[268, 268, -2*w^2 - 5*w + 8]', '[269, 269, 6*w^2 + 3*w - 47]', '[269, 269, -w^2 - 1]', '[269, 269, 2*w^2 - 7]', '[274, 274, 3*w^2 - 26]', '[276, 138, w^2 - 3*w + 5]', '[276, 138, -3*w^2 + 5*w + 9]', '[276, 276, -w^2 + 8*w - 12]', '[276, 276, -2*w^2 + 3*w + 8]', '[277, 277, 2*w^2 - w - 5]', '[277, 277, -5*w^2 - 6*w + 31]', '[277, 277, 2*w^2 - 2*w - 11]', '[278, 278, -w^2 + 9*w - 10]', '[279, 93, 2*w^2 - 3*w - 3]', '[279, 93, -w^2 - 2*w + 15]', '[279, 93, -4*w^2 - 3*w + 33]', '[279, 93, -4*w^2 - 5*w + 21]', '[279, 93, 2*w^2 + w - 21]', '[279, 93, -2*w^2 + 9]', '[279, 279, w^2 + 4*w - 5]', '[279, 279, -2*w^2 - 5*w + 7]', '[279, 279, w^2 - 2*w - 17]', '[281, 281, 4*w^2 + 5*w - 25]', '[282, 282, 4*w^2 + 3*w - 34]', '[282, 282, -w^2 + 2*w + 6]', '[288, 12, 2*w^2 - 6*w + 6]', '[288, 12, 2*w^2 - 2*w - 6]', '[288, 24, -2*w^2 + 6*w]', '[288, 24, 2*w^2 + 4*w - 24]', '[288, 36, -2*w^2 - 2*w + 22]', '[288, 72, 2*w^2 - 8]', '[288, 96, -w^2 + 4*w]', '[288, 96, -w^2 + 9*w - 12]', '[288, 288, 2*w^2 + 3*w - 20]', '[291, 291, -w^2 - 4*w - 1]', '[291, 291, -4*w^2 - 7*w + 21]', '[292, 146, 3*w^2 + 3*w - 31]', '[292, 146, 3*w^2 + 3*w - 13]', '[292, 146, -3*w^2 - w + 29]', '[292, 292, -2*w^2 + w + 8]', '[292, 292, 3*w^2 + 3*w - 16]', '[292, 292, 2*w^2 + 3*w - 16]', '[298, 298, -3*w^2 - 5*w + 10]', '[303, 303, -2*w^2 - 3*w + 5]', '[303, 303, 2*w^2 - w - 15]', '[304, 76, -w^2 - 3*w + 17]', '[304, 76, 2*w^2 - 2*w - 4]', '[304, 304, w^2 + 4*w - 16]', '[307, 307, 4*w^2 + 2*w - 37]', '[309, 309, 3*w^2 - 2*w - 15]', '[309, 309, w^2 + 4*w - 11]', '[314, 314, -5*w^2 - 8*w + 26]', '[316, 158, w^2 - 7*w + 13]', '[316, 316, 3*w^2 - 8*w + 4]', '[317, 317, -w - 7]', '[317, 317, 3*w^2 + 2*w - 19]', '[317, 317, -2*w^2 + 2*w + 5]', '[318, 318, w^2 + w - 14]', '[318, 318, -2*w^2 + w + 6]', '[321, 321, -2*w^2 + w + 7]', '[321, 321, -2*w^2 - 5*w + 27]', '[324, 18, 3*w^2 + 3*w - 27]', '[324, 18, -w^2 + 3*w + 3]', '[324, 18, 3*w^2 + 3*w - 15]', '[324, 36, 3*w]', '[324, 36, -2*w^2 - 3*w + 24]', '[324, 36, 3*w^2 + 3*w - 24]', '[324, 54, -w^2 + w + 15]', '[324, 108, 5*w^2 + 7*w - 24]', '[324, 162, 7*w^2 + 13*w - 29]', '[324, 324, w^2 + 4*w + 4]', '[326, 326, 3*w^2 + 3*w - 14]', '[327, 327, -4*w + 3]', '[327, 327, -2*w^2 - 3*w + 17]', '[328, 82, 2*w^2 + 4*w - 14]', '[328, 328, 3*w^2 + w - 20]', '[331, 331, 2*w^2 + 3*w - 19]', '[332, 166, -5*w^2 - w + 43]', '[332, 332, 3*w^2 + 4*w - 20]', '[337, 337, w^2 - 4*w + 7]', '[339, 339, -2*w + 9]', '[339, 339, 2*w^2 + 6*w - 11]', '[342, 114, 2*w^2 + 3*w - 18]', '[342, 114, 4*w^2 + 5*w - 18]', '[342, 342, w^2 + 3*w + 2]', '[343, 7, -7]', '[344, 86, 2*w^2 - 22]', '[344, 344, 9*w^2 + 3*w - 76]', '[346, 346, -w^2 + 14]', '[347, 347, 4*w^2 + 2*w - 29]', '[349, 349, 3*w^2 - 19]', '[354, 354, -w^2 + 2*w + 14]', '[354, 354, 3*w^2 + 5*w - 18]', '[356, 178, 3*w^2 + 3*w - 25]', '[356, 356, 8*w^2 + 3*w - 64]', '[358, 358, -w^2 + 5*w - 2]', '[358, 358, 3*w^2 + 3*w - 26]', '[358, 358, -5*w^2 - 4*w + 38]', '[361, 19, w^2 - 2*w - 7]', '[361, 361, w^2 + 2*w + 1]', '[367, 367, 4*w^2 + 5*w - 19]', '[367, 367, -6*w + 11]', '[368, 92, 5*w^2 + 3*w - 37]', '[368, 92, 2*w^2 + 4*w - 4]', '[368, 368, -2*w^2 + w + 20]', '[369, 123, 4*w^2 + 3*w - 27]', '[369, 123, 8*w^2 + 13*w - 39]', '[369, 369, w^2 - 6*w + 11]', '[372, 186, 3*w^2 - 5*w - 7]', '[372, 186, 3*w^2 - w - 21]', '[372, 186, 3*w^2 + 7*w - 9]', '[372, 186, -3*w^2 + w + 17]', '[372, 186, -w^2 - w - 1]', '[372, 186, -w^2 + 5*w - 9]', '[372, 372, -2*w^2 + w + 24]', '[372, 372, 2*w^2 - w - 16]', '[372, 372, -w^2 - 4*w + 12]', '[372, 372, -w^2 + 2*w - 4]', '[372, 372, 2*w^2 - 7*w + 8]', '[372, 372, 3*w^2 - 4*w - 12]', '[373, 373, -4*w^2 + w + 25]', '[375, 15, 5*w - 15]', '[375, 15, -5*w + 5]', '[376, 94, 6*w - 14]', '[376, 376, 4*w^2 - 3*w - 20]', '[379, 379, -5*w^2 - 10*w + 19]', '[381, 381, 3*w^2 + 2*w - 11]', '[381, 381, w^2 + 4*w - 15]', '[382, 382, -3*w^2 - 7*w + 14]', '[383, 383, 4*w^2 + 6*w - 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13*w + 14]', '[9978, 9978, w - 22]', '[9981, 3327, 16*w^2 + 15*w - 105]', '[9981, 3327, 40*w^2 + 65*w - 189]', '[9981, 9981, w^2 - 8*w + 25]', '[9983, 9983, 8*w^2 - 10*w - 35]', '[9983, 9983, 15*w^2 + 22*w - 83]', '[9983, 9983, 23*w^2 + 22*w - 157]', '[9986, 9986, 2*w^2 - 7*w - 14]', '[9987, 9987, -13*w^2 - 16*w + 69]', '[9987, 9987, 4*w^2 - 6*w - 61]', '[9991, 9991, 7*w^2 + 16*w - 91]', '[9994, 9994, 11*w^2 + 13*w - 74]', '[9994, 9994, -4*w^2 - 11*w + 50]', '[9994, 9994, -3*w - 22]'], 'label': '3.3.1101.1', 'narrow_class_no': 1, 'primes': ['[2, 2, w - 2]', '[3, 3, -w + 3]', '[3, 3, w - 1]', '[4, 2, w^2 + w - 7]', '[19, 19, w + 1]', '[23, 23, w^2 - 2*w - 1]', '[31, 31, -2*w^2 + 19]', '[31, 31, -w^2 + 5]', '[31, 31, -3*w + 5]', '[41, 41, w^2 + 2*w - 7]', '[43, 43, w^2 - 11]', '[47, 47, 3*w - 7]', '[53, 53, -3*w^2 - 6*w + 11]', '[59, 59, 2*w - 1]', '[67, 67, 2*w^2 + w - 19]', '[67, 67, 3*w^2 + 2*w - 25]', '[67, 67, w - 5]', '[73, 73, -4*w^2 - 3*w + 29]', '[73, 73, 2*w^2 - w - 11]', '[73, 73, w^2 + 2*w - 11]', '[79, 79, 2*w^2 + 2*w - 11]', '[83, 83, 2*w^2 - 13]', '[89, 89, -2*w + 7]', '[97, 97, -2*w^2 + 4*w - 1]', '[101, 101, -2*w - 5]', '[103, 103, 2*w^2 + w - 13]', '[107, 107, -2*w^2 - 2*w + 17]', '[109, 109, -4*w^2 - 2*w + 31]', '[113, 113, w^2 + 2*w - 1]', '[125, 5, -5]', '[127, 127, 2*w^2 + 3*w - 13]', '[137, 137, -2*w^2 + 7*w - 7]', '[139, 139, 2*w^2 + w - 7]', '[149, 149, -6*w^2 - 9*w + 31]', '[157, 157, w^2 - 4*w + 1]', '[163, 163, 2*w^2 + 5*w - 5]', '[173, 173, 5*w^2 + 4*w - 37]', '[179, 179, 2*w^2 + w - 11]', '[179, 179, 3*w^2 - 2*w - 17]', '[179, 179, -4*w^2 - w + 37]', '[191, 191, -6*w^2 - 9*w + 29]', '[193, 193, -2*w^2 - 4*w + 5]', '[223, 223, -2*w^2 + 2*w + 7]', '[227, 227, 6*w^2 + 4*w - 47]', '[233, 233, 2*w^2 + 4*w - 13]', '[233, 233, -4*w^2 - 4*w + 25]', '[233, 233, 4*w + 13]', '[239, 239, -4*w^2 - 8*w + 13]', '[239, 239, 2*w^2 + 2*w - 5]', '[239, 239, -w^2 + 8*w - 11]', '[241, 241, 3*w - 1]', '[251, 251, w^2 + 4*w - 19]', '[263, 263, -2*w^2 + 2*w + 25]', '[263, 263, -5*w^2 - 4*w + 35]', '[263, 263, 3*w^2 - 25]', '[269, 269, 6*w^2 + 3*w - 47]', '[269, 269, -w^2 - 1]', '[269, 269, 2*w^2 - 7]', '[277, 277, 2*w^2 - w - 5]', '[277, 277, -5*w^2 - 6*w + 31]', '[277, 277, 2*w^2 - 2*w - 11]', '[281, 281, 4*w^2 + 5*w - 25]', '[307, 307, 4*w^2 + 2*w - 37]', '[317, 317, -w - 7]', '[317, 317, 3*w^2 + 2*w - 19]', '[317, 317, -2*w^2 + 2*w + 5]', '[331, 331, 2*w^2 + 3*w - 19]', '[337, 337, w^2 - 4*w + 7]', '[343, 7, -7]', '[347, 347, 4*w^2 + 2*w - 29]', '[349, 349, 3*w^2 - 19]', '[361, 19, w^2 - 2*w - 7]', '[367, 367, 4*w^2 + 5*w - 19]', '[367, 367, -6*w + 11]', '[373, 373, -4*w^2 + w + 25]', '[379, 379, -5*w^2 - 10*w + 19]', '[383, 383, 4*w^2 + 6*w - 23]', '[401, 401, -3*w + 11]', '[401, 401, -3*w - 1]', '[401, 401, -3*w - 7]', '[409, 409, -w^2 - 4*w + 13]', '[419, 419, 2*w^2 - w - 17]', '[421, 421, -3*w^2 + 31]', '[431, 431, w^2 + 4*w - 1]', '[449, 449, -w^2 + 4*w + 1]', '[457, 457, -w^2 + 2*w + 13]', '[461, 461, 4*w^2 - 4*w - 19]', '[463, 463, 2*w^2 + 4*w - 23]', '[467, 467, 2*w^2 - 5*w + 5]', '[479, 479, 3*w + 11]', '[491, 491, 8*w^2 + 9*w - 49]', '[499, 499, -6*w^2 - 6*w + 41]', '[499, 499, 2*w^2 + 2*w - 23]', '[499, 499, 2*w^2 + 5*w - 29]', '[523, 523, -4*w^2 + w + 41]', '[529, 23, 6*w^2 + 7*w - 35]', '[547, 547, -2*w^2 + 6*w + 1]', '[557, 557, 3*w^2 + 2*w - 13]', '[563, 563, -w^2 + 4*w + 23]', '[569, 569, 10*w^2 + 8*w - 73]', '[587, 587, 2*w^2 - 2*w - 13]', '[593, 593, -6*w^2 - 8*w + 31]', '[601, 601, 4*w^2 + 5*w - 41]', '[601, 601, 10*w^2 + 16*w - 49]', '[601, 601, w^2 - 2*w + 5]', '[613, 613, -8*w^2 - 7*w + 55]', '[617, 617, -8*w^2 - 12*w + 37]', '[617, 617, 2*w^2 + 3*w - 25]', '[617, 617, 3*w^2 - 17]', '[641, 641, 4*w^2 - 35]', '[643, 643, 4*w^2 + 4*w - 37]', '[659, 659, -3*w^2 - 4*w + 23]', '[661, 661, -w^2 - 4*w - 5]', '[673, 673, 4*w^2 + 4*w - 31]', '[683, 683, 2*w^2 + 4*w - 19]', '[683, 683, 2*w^2 + w - 23]', '[683, 683, 3*w^2 + 6*w - 19]', '[701, 701, -6*w^2 - 12*w + 23]', '[701, 701, -2*w^2 + 7*w - 1]', '[701, 701, 3*w^2 + 2*w - 31]', '[709, 709, 5*w^2 + 4*w - 41]', '[719, 719, -6*w^2 - 2*w + 55]', '[719, 719, w^2 + 2*w - 17]', '[719, 719, 3*w^2 + 4*w - 29]', '[727, 727, -9*w^2 - 12*w + 49]', '[733, 733, 13*w^2 + 20*w - 65]', '[739, 739, 11*w^2 + 6*w - 91]', '[743, 743, -2*w^2 - 8*w + 35]', '[751, 751, 3*w^2 - 4*w - 13]', '[769, 769, 2*w^2 - 1]', '[797, 797, 2*w^2 - 8*w + 11]', '[811, 811, 4*w^2 - w - 29]', '[821, 821, 2*w^2 + 5*w - 17]', '[827, 827, -3*w^2 - 6*w + 7]', '[827, 827, -11*w^2 - 8*w + 83]', '[827, 827, -5*w^2 - 6*w + 25]', '[829, 829, -4*w^2 + 41]', '[829, 829, 4*w^2 + 8*w - 23]', '[829, 829, 8*w - 19]', '[839, 839, 2*w^2 + 6*w - 7]', '[853, 853, 10*w^2 + 6*w - 77]', '[859, 859, -5*w^2 - 2*w + 47]', '[863, 863, 12*w^2 + 19*w - 59]', '[877, 877, 8*w^2 + 6*w - 61]', '[907, 907, -4*w - 1]', '[907, 907, 9*w^2 + 4*w - 71]', '[907, 907, 2*w^2 + 7*w - 17]', '[919, 919, -10*w^2 - 5*w + 79]', '[929, 929, 2*w^2 + 7*w - 11]', '[937, 937, -4*w^2 + 6*w + 11]', '[941, 941, 3*w^2 - 11]', '[947, 947, 6*w - 5]', '[967, 967, -2*w^2 + 5*w + 5]', '[971, 971, 5*w^2 - 2*w - 29]', '[991, 991, 4*w^2 + 2*w - 25]', '[997, 997, 3*w^2 - 2*w - 11]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [12, -9, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1101, 'disc_rad': 1101, 'disc_sign': 1, 'frobs': [[2, [[2, 1], [1, 1]]], [3, [0]], [5, [[3, 1]]], [7, [[3, 1]]], [11, [[3, 1]]], [13, [[3, 1]]], [17, [[3, 1]]], [19, [[2, 1], [1, 1]]], [23, [[2, 1], [1, 1]]], [29, [[3, 1]]], [31, [[1, 3]]], [37, [[3, 1]]], [41, [[2, 1], [1, 1]]], [43, [[2, 1], [1, 1]]], [47, [[2, 1], [1, 1]]], [53, [[2, 1], [1, 1]]], [59, [[2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 33.18132004607411, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1101.1', 'local_algs': ['3.1.0.1', '3.2.1.1', 'm367.1.1.0', 'm367.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [3, 367], 'rd': 10.3259283287, 'regulator': {'__RealLiteral__': 0, 'data': '9.18395840633', 'prec': 44}, 'res': {'gal': ['-12,54,31,-66,-35,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} + 2 a - 5 \\)', '\\( 2 a^{2} + 4 a - 7 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}