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hmf_forms • Show schema
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{'deg': 3, 'dimension': 4, 'disc': 1492, 'field_bad_primes': [2, 373], 'field_label': '3.3.1492.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1492.1-7.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [7], 'level_ideal': '[7, 7, w^2 - 2*w - 8]', 'level_label': '7.1', 'level_norm': 7, 'parallel_weight': 2, 'short_label': '7.1-b', 'weight': '[2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[7, 7, w^2 - 2*w - 8]', 1]], 'hecke_eigenvalues': ['-1/3*e^2 + 3', 'e', -1, '1/9*e^3 - e', '-1/9*e^3 + e', '2/9*e^3 - 3*e', '-1/9*e^3', '-1/3*e^2', '2/9*e^3 - 5*e', -2, '-2/9*e^3 + 4*e', '-1/9*e^3 + e', '2/3*e^2 - 12', '1/3*e^2 - 8', 'e', '-5/9*e^3 + 6*e', -8, '-2/3*e^3 + 9*e', '-4/3*e^2 + 16', '4/9*e^3 - 8*e', '-8/9*e^3 + 10*e', '-e^3 + 10*e', '1/3*e^2 + 8', -12, '4/9*e^3 - 6*e', 'e^3 - 12*e', '-2*e^2 + 12', '10/9*e^3 - 15*e', 0, '-2/3*e^2 + 14', '1/3*e^3 - 2*e', '-1/3*e^2 - 6', '-10/9*e^3 + 9*e', '-e^2 - 2', '-1/3*e^3 + 9*e', '2/3*e^3 - 11*e', -6, '5/9*e^3 - 5*e', 'e^3 - 16*e', '-5/9*e^3 + 4*e', '8/9*e^3 - 9*e', '13/3*e^2 - 44', '-8/9*e^3 + 16*e', '2/3*e^2 + 4', '-4/3*e^2 + 16', '4*e^2 - 40', '-8/9*e^3 + 11*e', '-1/9*e^3 - 2*e', '-7/3*e^2 + 18', '16/3*e^2 - 48', '13/3*e^2 - 36', '-8/3*e^2 + 6', '-13/9*e^3 + 22*e', '-7/9*e^3 + 9*e', '-4/9*e^3 + 7*e', '2*e^2 - 6', '-16/3*e^2 + 48', '-10/3*e^2 + 42', '13/9*e^3 - 14*e', '2/9*e^3 - 3*e', '4*e^2 - 44', '2*e^2 - 10', '-1/3*e^3 - e', '17/9*e^3 - 18*e', '2/3*e^3 - 7*e', '7/9*e^3 - 5*e', '-16/9*e^3 + 20*e', '1/9*e^3', '2/9*e^3 + 3*e', '-2/3*e^2 + 2', '-1/3*e^2 + 34', '2*e', '4/9*e^3 + e', '-2/9*e^3 + 7*e', '-4/3*e^3 + 21*e', '8/3*e^2 - 42', '2/3*e^2 - 2', '-1/3*e^2 + 18', '-4*e^2 + 32', '8/3*e^2 - 30', '5/9*e^3 - 4*e', 'e^3 - 6*e', '2/3*e^2', '-2/3*e^2 + 30', '-6*e^2 + 48', '1/3*e^2 - 18', '-4*e^2 + 40', '19/9*e^3 - 30*e', '1/3*e^3 - 2*e', '-1/3*e^3 + 13*e', '-7/9*e^3 + 8*e', '-7/3*e^2 + 42', '17/3*e^2 - 60', '4/3*e^2 - 12', '-7/3*e^2 + 12', '3*e^2 - 16', '-2*e^3 + 22*e', '-19/9*e^3 + 19*e', '-16/9*e^3 + 20*e', '20/9*e^3 - 24*e', '8/3*e^2 - 54', '2*e^2 - 26', '4*e^2 - 38', '1/3*e^2 - 16', 34, '10/9*e^3 - 23*e', '5/9*e^3 - 11*e', '-4/3*e^2 - 24', '22/9*e^3 - 28*e', '2*e^2 - 32', '-e^2 + 28', '-8/3*e^2 + 8', 6, '-17/9*e^3 + 22*e', '-5/3*e^3 + 27*e', '-8/3*e^2 + 24', '-8/9*e^3 + 18*e', '-2*e^2 + 32', '2*e^3 - 26*e', '4/3*e^2 - 6', '7/3*e^2 - 10', '-8/9*e^3 + 6*e', '-13/3*e^2 + 42', '-8/3*e^2 + 12', '-2*e^2 + 12', '-10/3*e^2 + 30', '-20/3*e^2 + 54', '10/9*e^3 - 20*e', '-2/3*e^3 + 10*e', '25/9*e^3 - 31*e', '5*e^2 - 36', '4/3*e^3 - 22*e', '-17/9*e^3 + 13*e', '-6*e^2 + 46', '-8/3*e^3 + 31*e', '3*e^3 - 34*e', '-e^3 + 26*e', '-4/3*e^3 + 10*e', '8/3*e^2 - 4', '16/3*e^2 - 38', '-3*e^2 + 20', '-20/9*e^3 + 19*e', '1/3*e^3 - 3*e', '8/3*e^3 - 28*e', '7/3*e^2 - 28', '-7*e^2 + 56', '-4*e^2 + 58', '-26/3*e^2 + 88', '10/9*e^3 - 10*e', '2*e^2 - 48', '-e^3 + 13*e', '16/3*e^2 - 46', '4*e^2 - 68', '11/3*e^3 - 38*e', '2/3*e^2 - 24', '-2*e^2 + 10', '2*e^2 + 22', '-14/3*e^2 + 30', '-1/3*e^3 + 17*e', '-4*e^2 + 72', '-e^3 + 12*e', '5/3*e^2 - 18', '20/3*e^2 - 84', '-e^3 + 12*e', '13/9*e^3 - 32*e'], 'hecke_polynomial': 'x^4 - 18*x^2 + 54', 'label': '3.3.1492.1-7.1-b'}
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hmf_fields • Show schema
Hide schema
{'degree': 3, 'discriminant': 1492, 'ideals': ['[1, 1, 1]', '[2, 2, -w - 1]', '[4, 2, w^2 - 2*w - 7]', '[5, 5, w]', '[7, 7, w^2 - 2*w - 8]', '[7, 7, -2*w^2 + 3*w + 16]', '[7, 7, -w^2 + 2*w + 6]', '[8, 2, 2]', '[10, 10, 2*w^2 - 3*w - 15]', '[11, 11, w^2 - 2*w - 2]', '[14, 14, -w^2 + 3*w + 4]', '[14, 14, w - 3]', '[14, 14, w - 1]', '[16, 4, -2*w - 2]', '[19, 19, -w + 2]', '[20, 10, -w^2 + 2*w + 5]', '[22, 22, w^2 - w - 8]', '[23, 23, -w^2 + 3*w + 1]', '[25, 5, w^2 - w - 9]', '[25, 25, 3*w^2 - 5*w - 25]', '[27, 3, 3]', '[28, 14, -w^2 + 2*w + 1]', '[28, 14, -w^2 + 2*w + 3]', '[28, 14, -w^2 + 1]', '[29, 29, -w^2 - w + 1]', '[29, 29, w^2 - 2*w - 4]', '[29, 29, -w^2 + w + 11]', '[32, 4, 2*w^2 - 4*w - 14]', '[35, 35, -w^2 + w + 5]', '[35, 35, w^2 - 3*w - 5]', '[35, 35, w^2 - 2*w - 10]', '[38, 38, w^2 - w - 2]', '[40, 10, 2*w]', '[43, 43, 2*w^2 - 3*w - 18]', '[44, 22, -w^2 + 3]', '[46, 46, 4*w^2 - 7*w - 31]', '[47, 47, -2*w + 7]', '[49, 7, w^2 - 4*w - 4]', '[49, 7, w^2 - 5*w - 3]', '[49, 7, -w^2 + 2]', '[49, 49, -w - 4]', '[49, 49, -4*w^2 + 7*w + 32]', '[49, 49, -w^2 - w - 1]', '[50, 10, -w^2 + w + 4]', '[50, 50, -w + 5]', '[53, 53, w^2 - w - 3]', '[54, 6, -3*w - 3]', '[55, 55, 2*w^2 - 4*w - 15]', '[56, 14, 2*w^2 - 4*w - 16]', '[56, 14, -4*w^2 + 6*w + 32]', '[56, 14, -2*w^2 + 4*w + 12]', '[58, 58, -3*w^2 + 5*w + 22]', '[58, 58, -3*w - 1]', '[58, 58, w^2 - 3*w - 6]', '[61, 61, w^2 + 2*w + 2]', '[64, 4, 4]', '[67, 67, -2*w^2 + 5*w + 8]', '[70, 70, w^2 - 3*w]', '[70, 70, 2*w^2 - 5*w - 5]', '[70, 70, w^2 - w]', '[76, 38, 3*w^2 - 4*w - 23]', '[77, 77, -3*w - 4]', '[77, 77, -2*w + 1]', '[77, 77, w^2 - 3*w - 7]', '[79, 79, w^2 - 3*w - 9]', '[80, 20, 4*w^2 - 6*w - 30]', '[86, 86, -w^2 + 3*w + 8]', '[88, 22, 2*w^2 - 4*w - 4]', '[92, 46, -w^2 + 2*w + 11]', '[94, 94, 2*w^2 - 5*w - 7]', '[95, 95, -w^2 + 2*w]', '[97, 97, -w^2 - 2*w + 2]', '[98, 14, -4*w^2 + 7*w + 29]', '[98, 14, 3*w^2 - 5*w - 26]', '[98, 14, -2*w^2 + 3*w + 13]', '[98, 98, 2*w^2 - 5*w - 11]', '[98, 98, w^2 - w - 12]', '[98, 98, 2*w^2 - 5*w - 3]', '[100, 10, 3*w^2 - 8*w - 7]', '[100, 50, w^2 - 4*w - 5]', '[106, 106, -w^2 - 5*w - 2]', '[108, 6, 3*w^2 - 6*w - 21]', '[109, 109, -2*w^2 + 4*w + 11]', '[109, 109, -3*w^2 + 4*w + 26]', '[109, 109, -3*w^2 + 4*w + 28]', '[110, 110, w + 5]', '[112, 28, -2*w^2 + 6*w + 8]', '[112, 28, 2*w - 6]', '[112, 28, 2*w - 2]', '[113, 113, -4*w^2 + 8*w + 27]', '[115, 115, 2*w^2 - 8*w - 5]', '[116, 58, w^2 - 7]', '[116, 58, -w^2 + 13]', '[116, 58, w^2 + 1]', '[121, 11, 5*w^2 - 8*w - 38]', '[121, 121, w - 6]', '[122, 122, -2*w^2 + 3*w + 19]', '[125, 5, 5]', '[125, 125, -2*w^2 + 2*w + 15]', '[127, 127, -3*w^2 + 4*w + 24]', '[128, 8, -4*w - 4]', '[131, 131, -4*w^2 + 5*w + 38]', '[133, 133, 3*w^2 - 5*w - 21]', '[133, 133, -2*w^2 + 4*w + 19]', '[133, 133, -5*w^2 + 8*w + 42]', '[134, 134, -w^2 + 5*w + 2]', '[135, 15, 3*w]', '[139, 139, 2*w - 3]', '[140, 70, 3*w^2 - 4*w - 25]', '[140, 70, -3*w^2 + 6*w + 25]', '[140, 70, w^2 - 6*w - 5]', '[145, 145, -w^2 + 5*w + 5]', '[145, 145, -6*w^2 + 11*w + 50]', '[145, 145, 2*w - 5]', '[149, 149, -w^2 + 3*w - 1]', '[151, 151, w^2 - 4*w - 6]', '[152, 38, -2*w + 4]', '[154, 154, 5*w^2 - 9*w - 38]', '[154, 154, 2*w^2 + w - 1]', '[154, 154, w^2 + w + 2]', '[157, 157, 2*w^2 - 3*w - 12]', '[158, 158, w^2 + 3*w + 4]', '[160, 20, -2*w^2 + 4*w + 10]', '[161, 161, w^2 - 8]', '[161, 161, -2*w^2 + 5*w + 12]', '[161, 161, 2*w^2 - 2*w - 19]', '[167, 167, -3*w^2 + 6*w + 22]', '[172, 86, -w^2 - 2*w - 3]', '[173, 173, -3*w^2 + 8*w + 8]', '[175, 35, 2*w^2 - 2*w - 3]', '[175, 35, w^2 - w + 1]', '[175, 35, 6*w^2 - 11*w - 44]', '[175, 175, -2*w^2 + 4*w + 5]', '[175, 175, -4*w - 5]', '[175, 175, -w^2 - w + 5]', '[176, 44, 2*w^2 - 2*w - 16]', '[181, 181, w^2 - 2*w - 12]', '[181, 181, w^2 - 12]', '[181, 181, -4*w - 1]', '[184, 46, -2*w^2 + 6*w + 2]', '[188, 94, w^2 - 6*w - 3]', '[189, 21, 3*w^2 - 6*w - 24]', '[189, 21, -6*w^2 + 9*w + 48]', '[189, 21, -3*w^2 + 6*w + 18]', '[190, 190, 5*w^2 - 9*w - 40]', '[191, 191, 2*w^2 - 6*w - 9]', '[193, 193, -8*w^2 + 12*w + 67]', '[194, 194, -6*w^2 + 9*w + 49]', '[196, 14, -w^2 + 4*w + 11]', '[196, 14, w^2 - 9]', '[196, 14, w^2 + 2*w - 3]', '[196, 98, -3*w^2 + 6*w + 23]', '[196, 98, w^2 - 2*w + 1]', '[196, 98, -w^2 + 4*w + 7]', '[197, 197, 2*w^2 - 3*w - 4]', '[199, 199, 2*w^2 - 2*w - 11]', '[200, 10, 2*w^2 - 2*w - 18]', '[200, 50, 6*w^2 - 10*w - 50]', '[203, 203, w + 6]', '[203, 203, -2*w^2 + 2*w + 17]', '[203, 203, 5*w^2 - 9*w - 39]', '[203, 203, 5*w + 2]', '[203, 203, 2*w - 9]', '[203, 203, 2*w^2 - 4*w - 9]', '[203, 203, -w^2 + w + 13]', '[203, 203, -2*w^2 + 8*w + 7]', '[203, 203, -w^2 + 5*w + 1]', '[209, 209, 3*w^2 - 11*w - 9]', '[211, 211, 4*w^2 - 6*w - 29]', '[212, 106, -w^2 + 11]', '[215, 215, -w^2 + 10]', '[216, 6, 6]', '[218, 218, 2*w^2 - 5*w - 13]', '[218, 218, 3*w - 1]', '[218, 218, 2*w^2 - 3*w - 11]', '[220, 110, -3*w^2 + 8*w + 5]', '[223, 223, 3*w^2 - 5*w - 27]', '[224, 28, -2*w^2 + 4*w + 2]', '[224, 28, -2*w^2 + 4*w + 6]', '[224, 28, -2*w^2 + 2]', '[226, 226, w - 7]', '[227, 227, -4*w^2 + 7*w + 28]', '[229, 229, 3*w^2 - 8*w - 14]', '[229, 229, w^2 - 4*w - 8]', '[229, 229, -2*w - 7]', '[230, 230, -3*w^2 + 5*w + 20]', '[232, 58, -2*w^2 - 2*w + 2]', '[232, 58, 2*w^2 - 4*w - 8]', '[232, 58, -2*w^2 + 2*w + 22]', '[233, 233, -5*w^2 + 7*w + 43]', '[235, 235, -2*w^2 + 7*w]', '[241, 241, 2*w^2 - 4*w - 7]', '[242, 22, -3*w^2 + 7*w + 14]', '[242, 242, -w^2 + 5*w + 6]', '[244, 122, w^2 - 4*w - 9]', '[245, 35, -w^2 - 7*w - 5]', '[245, 35, 6*w^2 - 10*w - 45]', '[245, 35, -2*w^2 + 3*w + 20]', '[245, 245, 4*w^2 - 8*w - 25]', '[245, 245, 3*w^2 - 4*w - 20]', '[245, 245, -w^2 - 4*w]', '[250, 10, -5*w - 5]', '[250, 250, -w^2 + 5*w]', '[251, 251, w^2 + 2]', '[251, 251, -2*w^2 + 2*w + 1]', '[251, 251, 2*w^2 - 5*w - 2]', '[253, 253, 5*w^2 - 7*w - 39]', '[254, 254, 2*w^2 - w - 9]', '[256, 8, 4*w^2 - 8*w - 28]', '[262, 262, -3*w^2 + 7*w + 18]', '[263, 263, 2*w^2 - 5*w - 14]', '[265, 265, 6*w + 5]', '[266, 266, -w^2 - w + 6]', '[266, 266, -w^2 + 3*w - 2]', '[266, 266, 2*w^2 - 5*w - 17]', '[268, 134, w^2 + 2*w - 21]', '[269, 269, -w^2 + 5*w - 1]', '[270, 30, 6*w^2 - 9*w - 45]', '[271, 271, -2*w^2 - w + 2]', '[275, 55, -2*w^2 + 7*w + 8]', '[275, 275, -2*w^2 + 3*w + 10]', '[277, 277, -3*w^2 + 7*w + 7]', '[278, 278, -2*w^2 + w + 3]', '[280, 70, -2*w^2 + 2*w + 10]', '[280, 70, 2*w^2 - 6*w - 10]', '[280, 70, 2*w^2 - 4*w - 20]', '[281, 281, -5*w^2 + 10*w + 34]', '[290, 290, 2*w^2 - 5*w - 15]', '[290, 290, -4*w^2 + 7*w + 35]', '[290, 290, -2*w^2 + 3*w + 5]', '[293, 293, -2*w^2 + 5*w + 16]', '[297, 33, 3*w^2 - 6*w - 6]', '[298, 298, -w^2 + 7*w + 6]', '[301, 301, w^2 - 6*w - 6]', '[301, 301, -3*w + 2]', '[301, 301, -w^2 - 5*w - 1]', '[302, 302, 2*w^2 + w + 1]', '[304, 76, 2*w^2 - 2*w - 4]', '[305, 305, -6*w^2 + 8*w + 45]', '[308, 154, -w^2 + 2*w + 13]', '[308, 154, 3*w^2 - 6*w - 17]', '[308, 154, -3*w^2 + 4*w + 29]', '[311, 311, w^2 + w + 3]', '[313, 313, 2*w^2 + w - 4]', '[314, 314, -w^2 - 3*w + 2]', '[316, 158, -5*w^2 + 8*w + 43]', '[317, 317, -7*w^2 + 13*w + 49]', '[319, 319, -3*w^2 + 6*w + 28]', '[319, 319, 4*w^2 - 10*w - 7]', '[319, 319, w^2 + 2*w - 4]', '[320, 20, 4*w]', '[322, 322, -2*w^2 - w + 3]', '[322, 322, -w^2 + w - 2]', '[322, 322, -2*w^2 + 3*w + 9]', '[329, 329, -3*w^2 + 6*w + 4]', '[329, 329, -4*w^2 + 12*w + 7]', '[329, 329, -6*w^2 + 17*w + 14]', '[331, 331, w^2 - 5*w - 7]', '[334, 334, -w - 7]', '[335, 335, 3*w^2 - 10*w - 10]', '[337, 337, -w^2 + 2*w - 2]', '[337, 337, 7*w^2 - 12*w - 52]', '[337, 337, -2*w^2 + 3]', '[343, 7, 7]', '[343, 49, 3*w^2 - 7*w - 13]', '[343, 49, 2*w^2 - 3*w - 6]', '[343, 49, -w^2 + 16]', '[343, 49, 3*w^2 - 5*w - 19]', '[343, 49, w^2 + 2*w + 4]', '[343, 49, 2*w^2 - w - 8]', '[343, 343, 6*w^2 - 11*w - 42]', '[343, 343, -w^2 + 6*w + 2]', '[343, 343, 2*w^2 - 6*w - 1]', '[344, 86, 4*w^2 - 6*w - 36]', '[346, 346, -5*w^2 + 7*w + 42]', '[347, 347, -10*w^2 + 17*w + 76]', '[349, 349, 2*w^2 - 2*w - 9]', '[350, 70, 3*w^2 - 3*w - 22]', '[350, 70, -6*w^2 + 11*w + 49]', '[350, 70, -w^2 + w + 14]', '[350, 350, 6*w^2 - 11*w - 45]', '[350, 350, -2*w^2 + 9*w + 5]', '[350, 350, -5*w^2 + 7*w + 40]', '[352, 44, -2*w^2 + 6]', '[353, 353, 2*w^2 - 3*w - 8]', '[359, 359, -4*w^2 + 5*w + 36]', '[361, 19, w^2 + w - 7]', '[361, 361, w^2 - 4*w + 4]', '[362, 362, -2*w^2 + 3*w + 7]', '[362, 362, 5*w + 7]', '[362, 362, -2*w^2 + w + 23]', '[367, 367, -4*w^2 + 8*w + 29]', '[368, 92, 8*w^2 - 14*w - 62]', '[371, 371, -2*w^2 + w + 14]', '[371, 371, 4*w^2 - 8*w - 33]', '[371, 371, w - 8]', '[373, 373, 2*w^2 - 6*w - 11]', '[373, 373, 8*w^2 - 14*w - 59]', '[376, 94, -4*w + 14]', '[378, 42, -3*w^2 + 9*w + 12]', '[378, 42, 3*w - 9]', '[378, 42, 3*w - 3]', '[379, 379, -2*w^2 + w + 4]', '[380, 190, -3*w^2 + 8*w + 15]', '[382, 382, 2*w^2 - 3*w - 1]', '[383, 383, -3*w^2 + 2*w + 34]', '[383, 383, 5*w^2 - 7*w - 41]', '[383, 383, 3*w^2 - 7*w - 19]', '[385, 385, -2*w^2 + 2*w + 5]', '[385, 385, -2*w^2 + w]', '[385, 385, 4*w^2 - 15*w - 10]', '[386, 386, 4*w^2 - 7*w - 27]', '[388, 194, 3*w^2 - 4*w - 19]', '[392, 14, 2*w^2 - 8*w - 8]', '[392, 14, 2*w^2 - 10*w - 6]', '[392, 14, -2*w^2 + 4]', '[392, 98, -2*w - 8]', '[392, 98, -8*w^2 + 14*w + 64]', '[392, 98, -2*w^2 - 2*w - 2]', '[394, 394, -w^2 - 11*w - 6]', '[395, 395, -2*w^2 + 5]', '[397, 397, -7*w^2 + 13*w + 51]', '[398, 398, -2*w^2 - 5*w + 1]', '[400, 20, -2*w^2 + 2*w + 8]', '[400, 100, -2*w + 10]', '[406, 406, -4*w^2 + 11*w + 17]', '[406, 406, w^2 + w - 16]', '[406, 406, -2*w^2 + 7*w + 9]', '[406, 406, w^2 - 5*w - 8]', '[406, 406, -3*w^2 + 5*w + 28]', '[406, 406, -w^2 - 7*w - 6]', '[406, 406, -3*w^2 + 11*w + 4]', '[406, 406, -5*w - 1]', '[406, 406, 8*w^2 - 13*w - 61]', '[418, 418, 2*w^2 - 3*w - 21]', '[422, 422, -2*w^2 - w + 9]', '[424, 106, 2*w^2 - 2*w - 6]', '[427, 427, -w^2 + 3*w - 3]', '[427, 427, -2*w^2 + 2*w + 7]', '[427, 427, -3*w^2 + 6*w + 16]', '[430, 430, 2*w^2 - w - 5]', '[431, 431, -8*w^2 + 14*w + 63]', '[432, 12, -6*w - 6]', '[433, 433, -2*w^2 + 9*w + 8]', '[436, 218, -3*w^2 - 2*w + 1]', '[436, 218, -w^2 - 4*w + 1]', '[436, 218, w^2 + 3]', '[437, 437, 2*w^2 - w - 6]', '[440, 110, 4*w^2 - 8*w - 30]', '[443, 443, -6*w^2 + 10*w + 51]', '[443, 443, 3*w - 4]', '[443, 443, w^2 - 7*w - 3]', '[446, 446, -w^2 + 5*w + 12]', '[448, 28, 4*w^2 - 8*w - 32]', '[448, 28, -8*w^2 + 12*w + 64]', '[448, 28, -4*w^2 + 8*w + 24]', '[449, 449, -7*w^2 + 10*w + 62]', '[452, 226, -w^2 + 6*w + 7]', '[454, 454, w^2 + w - 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7*w + 6]', '[9778, 9778, w^2 - 23*w - 12]', '[9778, 9778, 2*w^2 + 3*w + 13]', '[9779, 9779, 9*w^2 - 7*w - 51]', '[9779, 9779, -5*w^2 + 10*w + 54]', '[9779, 9779, 16*w^2 - 25*w - 118]', '[9781, 9781, 10*w^2 - 21*w - 72]', '[9781, 9781, -14*w^2 + 24*w + 99]', '[9781, 9781, -19*w^2 + 39*w + 119]', '[9784, 2446, -8*w^2 + 18*w + 64]', '[9787, 9787, -17*w - 6]', '[9787, 9787, -20*w^2 + 32*w + 151]', '[9787, 9787, 7*w^2 - 21*w - 33]', '[9791, 9791, 4*w^2 - 20*w - 7]', '[9791, 9791, -19*w^2 + 36*w + 136]', '[9791, 9791, 4*w^2 - 19*w - 4]', '[9800, 70, -6*w^2 + 16*w + 4]', '[9800, 70, 4*w^2 - 14*w - 36]', '[9800, 70, -8*w^2 + 18*w + 32]', '[9800, 350, -8*w^2 + 18*w + 60]', '[9800, 350, 4*w^2 - 50]', '[9800, 350, 2*w^2 + 4*w - 20]', '[9800, 490, -8*w^2 + 8*w + 62]', '[9800, 490, -6*w^2 + 6*w + 14]', '[9800, 490, -2*w^2 - 8*w + 8]', '[9800, 2450, -18*w^2 + 34*w + 130]', '[9800, 2450, -8*w^2 + 22*w + 40]', '[9800, 2450, -2*w^2 + 14*w + 30]', '[9803, 9803, 6*w^2 - 8*w - 17]', '[9806, 9806, 13*w^2 - 21*w - 114]', '[9808, 2452, -8*w^2 - 10*w + 2]', '[9811, 9811, 6*w^2 - 14*w - 63]', '[9812, 4906, 11*w^2 - 12*w - 71]', '[9814, 9814, -w^2 - w - 16]', '[9814, 9814, -5*w^2 - 11*w - 12]', '[9814, 9814, -6*w^2 + 5*w + 13]', '[9818, 9818, 3*w^2 - 25*w - 14]', '[9820, 4910, -7*w^2 + 28*w + 25]', '[9821, 9821, -w^2 + 15*w + 19]', '[9821, 9821, 6*w^2 + 16*w - 1]', '[9821, 9821, 3*w^2 + 4*w - 18]', '[9823, 9823, -2*w^2 + 14*w - 1]', '[9826, 34, 17*w + 17]', '[9829, 9829, 4*w^2 + 4*w - 19]', '[9830, 9830, -33*w^2 + 55*w + 270]', '[9832, 2458, -12*w^2 + 20*w + 106]', '[9833, 9833, 4*w^2 - 14*w - 33]', '[9835, 9835, -14*w^2 + 19*w + 120]', '[9835, 9835, 15*w^2 - 28*w - 120]', '[9835, 9835, -7*w^2 + 29*w + 25]', '[9836, 4918, -11*w^2 + 38*w + 33]', '[9836, 4918, 7*w^2 - 97]', '[9836, 4918, 3*w^2 + 6*w - 13]', '[9838, 9838, -5*w^2 + 19*w + 24]', '[9838, 9838, 5*w^2 + 25*w + 18]', '[9838, 9838, 2*w^2 + 19*w + 17]', '[9839, 9839, -11*w^2 + 14*w + 94]', '[9847, 9847, -16*w^2 + 36*w + 93]', '[9847, 9847, -7*w^2 - w - 1]', '[9847, 9847, 13*w^2 - 25*w - 99]', '[9850, 1970, -6*w^2 + w - 1]', '[9850, 9850, 11*w^2 - 29*w - 30]', '[9856, 616, 20*w^2 - 36*w - 152]', '[9856, 616, 8*w^2 + 4*w - 4]', '[9856, 616, 4*w^2 + 4*w + 8]', '[9857, 9857, -2*w^2 + 4*w - 11]', '[9859, 9859, -27*w^2 + 47*w + 201]', '[9862, 9862, -5*w^2 + 9*w + 54]', '[9863, 9863, 53*w^2 - 89*w - 427]', '[9863, 9863, -8*w^2 + 10*w + 81]', '[9863, 9863, 16*w^2 - 26*w - 137]', '[9863, 9863, -26*w^2 + 38*w + 201]', '[9863, 9863, 8*w^2 - 15*w - 76]', '[9863, 9863, 7*w^2 - 20*w - 36]', '[9863, 9863, 25*w^2 - 43*w - 187]', '[9863, 9863, -2*w^2 + 18*w - 37]', '[9863, 9863, -7*w^2 + 8*w + 38]', '[9871, 9871, -w^2 + 2*w - 16]', '[9872, 2468, 2*w^2 - 6*w + 12]', '[9875, 395, 5*w^2 - 15*w - 45]', '[9875, 9875, 15*w^2 - 19*w - 105]', '[9878, 9878, 6*w^2 - 25*w - 11]', '[9883, 9883, -23*w^2 + 41*w + 167]', '[9884, 4942, -9*w^2 + 16*w + 17]', '[9884, 4942, -7*w^2 - 4*w - 3]', '[9884, 4942, -5*w^2 + 10*w + 1]', '[9890, 9890, -9*w^2 + 19*w + 20]', '[9892, 4946, -7*w^2 + 12*w + 17]', '[9892, 4946, 3*w^2 - 10*w + 9]', '[9892, 4946, -5*w^2 + 67]', '[9895, 9895, -4*w^2 + 14*w + 35]', '[9895, 9895, -5*w^2 + 32*w + 20]', '[9895, 9895, -2*w^2 + 15*w + 20]', '[9896, 2474, 8*w^2 - 10*w - 48]', '[9902, 9902, -8*w^2 + 15*w + 9]', '[9904, 2476, 4*w^2 - 14*w - 34]', '[9908, 4954, -5*w^2 + 20*w + 23]', '[9908, 4954, 5*w^2 - 4*w + 1]', '[9908, 4954, -33*w^2 + 56*w + 261]', '[9909, 1101, -12*w^2 + 24*w + 87]', '[9910, 9910, 7*w^2 - 17*w - 50]', '[9913, 9913, 12*w^2 - 24*w - 109]', '[9914, 9914, 4*w^2 - 5*w + 3]', '[9914, 9914, -8*w^2 - 35*w - 17]', '[9914, 9914, -6*w^2 + 3*w + 23]', '[9917, 9917, 6*w^2 + 10*w + 9]', '[9925, 1985, -14*w^2 + 39*w + 36]', '[9925, 9925, -6*w^2 + 19*w + 30]', '[9929, 9929, -15*w^2 + 25*w + 129]', '[9931, 9931, -30*w^2 + 49*w + 232]', '[9934, 9934, 4*w^2 - 15*w - 27]', '[9936, 276, 24*w^2 - 42*w - 186]', '[9937, 9937, 2*w^2 - 19*w - 8]', '[9938, 9938, 17*w + 31]', '[9938, 9938, -4*w^2 - 15*w - 1]', '[9938, 9938, -13*w^2 + 17*w + 114]', '[9941, 9941, 11*w^2 - 25*w - 67]', '[9941, 9941, 7*w^2 - 14*w - 22]', '[9941, 9941, 9*w^2 - 22*w - 32]', '[9944, 2486, 6*w^2 - 6*w - 26]', '[9947, 203, -7*w^2 - 7*w + 7]', '[9947, 203, 7*w^2 - 14*w - 28]', '[9947, 203, -7*w^2 + 7*w + 77]', '[9947, 1421, 22*w^2 - 33*w - 178]', '[9947, 1421, 3*w^2 - 19*w - 19]', '[9947, 1421, 5*w^2 - 11*w - 1]', '[9947, 1421, 6*w^2 - 21*w + 2]', '[9947, 1421, -2*w^2 + w + 36]', '[9947, 1421, 12*w^2 - 28*w - 59]', '[9947, 1421, 12*w^2 - 20*w - 83]', '[9947, 1421, -2*w^2 + 3*w + 34]', '[9947, 1421, w^2 + 3*w + 17]', '[9947, 1421, 6*w^2 - 2*w - 11]', '[9947, 1421, -32*w^2 + 55*w + 264]', '[9947, 1421, -3*w^2 - 8]', '[9947, 1421, -w^2 - 10*w - 24]', '[9947, 1421, -6*w^2 + 7*w + 26]', '[9947, 1421, 15*w^2 - 21*w - 121]', '[9947, 1421, 10*w^2 - 22*w - 51]', '[9947, 1421, 2*w^2 - 21*w - 18]', '[9947, 1421, -16*w^2 + 43*w + 36]', '[9947, 9947, -21*w^2 + 38*w + 172]', '[9947, 9947, 13*w^2 - 36*w - 36]', '[9947, 9947, 4*w^2 - 8*w - 47]', '[9947, 9947, -8*w^2 + 30*w + 27]', '[9947, 9947, -7*w^2 + 5*w + 83]', '[9947, 9947, -8*w^2 + 18*w + 63]', '[9947, 9947, -4*w^2 + 19*w - 8]', '[9947, 9947, -7*w^2 + 3*w + 9]', '[9947, 9947, -12*w + 1]', '[9949, 9949, -8*w^2 + 18*w + 61]', '[9949, 9949, -20*w - 9]', '[9949, 9949, -12*w^2 + 22*w + 79]', '[9950, 1990, w^2 - 11*w - 34]', '[9950, 9950, 10*w^2 - 17*w - 65]', '[9952, 1244, 6*w^2 - 16*w - 42]', '[9955, 9955, -23*w^2 + 40*w + 170]', '[9955, 9955, 6*w^2 - 8*w - 25]', '[9955, 9955, -19*w^2 + 34*w + 150]', '[9956, 4978, -3*w^2 + 16*w - 1]', '[9959, 9959, -21*w^2 + 36*w + 176]', '[9961, 9961, 10*w^2 - 24*w - 43]', '[9961, 9961, -3*w^2 - w + 51]', '[9961, 9961, -w + 22]', '[9964, 4982, -19*w^2 + 34*w + 149]', '[9965, 9965, -19*w^2 + 32*w + 160]', '[9967, 9967, -w^2 + 16*w + 18]', '[9973, 9973, -18*w - 7]', '[9974, 9974, 11*w^2 + 3*w - 4]', '[9974, 9974, 5*w^2 - 15*w - 36]', '[9974, 9974, -8*w^2 - 11*w + 3]', '[9976, 2494, -16*w - 18]', '[9976, 2494, -14*w^2 + 26*w + 94]', '[9976, 2494, -2*w^2 + 14*w - 18]', '[9977, 9977, 7*w^2 - 10*w - 38]', '[9980, 4990, w^2 - 18*w + 55]', '[9983, 9983, 2*w^2 + 5*w - 16]', '[9985, 9985, -27*w^2 + 40*w + 210]', '[9988, 4994, -7*w^2 + 14*w + 69]', '[9989, 9989, 9*w^2 - 25*w - 13]', '[9989, 9989, 14*w^2 - 36*w - 31]', '[9989, 9989, 8*w^2 - 9*w - 6]', '[9992, 2498, -2*w^2 + 18*w + 18]', '[9992, 2498, 8*w^2 - 20*w - 74]', '[9992, 2498, -6*w^2 + 16*w + 52]', '[9994, 9994, -11*w + 3]', '[9995, 9995, -2*w^2 + 11*w - 20]', '[9995, 9995, -6*w^2 + 22*w + 25]', '[9995, 9995, 11*w^2 - 14*w - 90]', '[9998, 9998, 2*w^2 - 7*w + 13]', '[10000, 100, 8*w^2 - 18*w - 62]', '[10000, 100, 20*w^2 - 30*w - 150]', '[10000, 2500, 8*w^2 - 18*w - 10]'], 'label': '3.3.1492.1', 'narrow_class_no': 2, 'primes': ['[2, 2, -w - 1]', '[5, 5, w]', '[7, 7, w^2 - 2*w - 8]', '[7, 7, -2*w^2 + 3*w + 16]', '[7, 7, -w^2 + 2*w + 6]', '[11, 11, w^2 - 2*w - 2]', '[19, 19, -w + 2]', '[23, 23, -w^2 + 3*w + 1]', '[25, 5, w^2 - w - 9]', '[27, 3, 3]', '[29, 29, -w^2 - w + 1]', '[29, 29, w^2 - 2*w - 4]', '[29, 29, -w^2 + w + 11]', '[43, 43, 2*w^2 - 3*w - 18]', '[47, 47, -2*w + 7]', '[53, 53, w^2 - w - 3]', '[61, 61, w^2 + 2*w + 2]', '[67, 67, -2*w^2 + 5*w + 8]', '[79, 79, w^2 - 3*w - 9]', '[97, 97, -w^2 - 2*w + 2]', '[109, 109, -2*w^2 + 4*w + 11]', '[109, 109, -3*w^2 + 4*w + 26]', '[109, 109, -3*w^2 + 4*w + 28]', '[113, 113, -4*w^2 + 8*w + 27]', '[121, 11, 5*w^2 - 8*w - 38]', '[127, 127, -3*w^2 + 4*w + 24]', '[131, 131, -4*w^2 + 5*w + 38]', '[139, 139, 2*w - 3]', '[149, 149, -w^2 + 3*w - 1]', '[151, 151, w^2 - 4*w - 6]', '[157, 157, 2*w^2 - 3*w - 12]', '[167, 167, -3*w^2 + 6*w + 22]', '[173, 173, -3*w^2 + 8*w + 8]', '[181, 181, w^2 - 2*w - 12]', '[181, 181, w^2 - 12]', '[181, 181, -4*w - 1]', '[191, 191, 2*w^2 - 6*w - 9]', '[193, 193, -8*w^2 + 12*w + 67]', '[197, 197, 2*w^2 - 3*w - 4]', '[199, 199, 2*w^2 - 2*w - 11]', '[211, 211, 4*w^2 - 6*w - 29]', '[223, 223, 3*w^2 - 5*w - 27]', '[227, 227, -4*w^2 + 7*w + 28]', '[229, 229, 3*w^2 - 8*w - 14]', '[229, 229, w^2 - 4*w - 8]', '[229, 229, -2*w - 7]', '[233, 233, -5*w^2 + 7*w + 43]', '[241, 241, 2*w^2 - 4*w - 7]', '[251, 251, w^2 + 2]', '[251, 251, -2*w^2 + 2*w + 1]', '[251, 251, 2*w^2 - 5*w - 2]', '[263, 263, 2*w^2 - 5*w - 14]', '[269, 269, -w^2 + 5*w - 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1]', '[461, 461, w^2 - 5*w - 9]', '[463, 463, 7*w + 6]', '[463, 463, -5*w^2 + 8*w + 36]', '[463, 463, 3*w^2 - 2*w - 16]', '[467, 467, 3*w^2 - 7*w - 9]', '[467, 467, 4*w - 1]', '[467, 467, 6*w^2 - 11*w - 48]', '[479, 479, 2*w^2 - 4*w - 21]', '[479, 479, w^2 + 7*w + 7]', '[479, 479, w^2 - 2*w - 14]', '[487, 487, w^2 - 5*w - 11]', '[487, 487, 3*w^2 - 3*w - 23]', '[487, 487, w^2 + 3*w - 3]', '[491, 491, w^2 - 8*w - 4]', '[499, 499, -6*w^2 + 14*w + 31]', '[509, 509, -w - 8]', '[523, 523, 2*w^2 + 1]', '[529, 23, 2*w^2 - 5*w - 22]', '[541, 541, -w^2 + 5*w - 7]', '[547, 547, 2*w^2 - 6*w - 13]', '[563, 563, 2*w^2 - 9*w - 4]', '[569, 569, 4*w^2 - 7*w - 26]', '[569, 569, -3*w^2 + 5*w + 3]', '[569, 569, 4*w^2 - 6*w - 27]', '[577, 577, 3*w^2 - 7*w - 21]', '[577, 577, -8*w^2 + 12*w + 69]', '[577, 577, -2*w^2 + w + 26]', '[587, 587, w^2 - 6*w - 8]', '[593, 593, -2*w^2 + w + 16]', '[593, 593, 3*w^2 - 5*w - 17]', '[593, 593, 2*w^2 - 8*w - 9]', '[601, 601, -6*w^2 + 8*w + 53]', '[607, 607, -2*w - 9]', '[613, 613, w^2 + 2*w - 6]', '[617, 617, 5*w^2 - 11*w - 31]', '[619, 619, -4*w^2 + 6*w + 37]', '[641, 641, 3*w^2 - 6*w - 14]', '[647, 647, -2*w^2 + 3*w + 22]', '[653, 653, 2*w^2 - 7*w - 22]', '[653, 653, 2*w^2 + w + 2]', '[653, 653, -3*w^2 + 5*w + 29]', '[659, 659, 4*w^2 - 11*w - 18]', '[659, 659, 3*w^2 - 6*w - 8]', '[659, 659, 4*w^2 - 8*w - 23]', '[661, 661, w^2 + w - 11]', '[677, 677, -w^2 - 4]', '[701, 701, -2*w^2 - 5*w + 2]', '[727, 727, -2*w^2 + w + 18]', '[733, 733, -9*w^2 + 13*w + 79]', '[733, 733, -7*w^2 + 10*w + 56]', '[733, 733, 2*w^2 - 13]', '[739, 739, 6*w^2 - 10*w - 43]', '[739, 739, 4*w^2 - 4*w - 29]', '[739, 739, -8*w^2 + 15*w + 58]', '[751, 751, -11*w^2 + 19*w + 87]', '[757, 757, 3*w^2 - 10*w - 12]', '[761, 761, 4*w - 3]', '[769, 769, 3*w^2 - w - 13]', '[811, 811, 5*w^2 - 9*w - 33]', '[823, 823, 2*w^2 - 7*w - 12]', '[853, 853, -7*w - 8]', '[853, 853, -3*w^2 + 4*w + 2]', '[853, 853, 2*w^2 + 5*w + 6]', '[857, 857, 10*w^2 - 15*w - 82]', '[857, 857, 3*w^2 - 8*w - 18]', '[857, 857, -4*w^2 + 3*w + 44]', '[859, 859, -w^2 + 4*w - 6]', '[877, 877, -4*w^2 + 13*w + 14]', '[881, 881, 2*w^2 - 9*w - 2]', '[887, 887, 3*w - 14]', '[907, 907, -11*w^2 + 21*w + 77]', '[919, 919, 12*w^2 - 21*w - 92]', '[929, 929, w^2 - 18]', '[937, 937, 9*w + 4]', '[941, 941, -2*w^2 + 2*w - 1]', '[947, 947, 4*w^2 - 9*w - 18]', '[953, 953, -7*w^2 + 14*w + 48]', '[977, 977, w^2 - 2*w - 16]', '[983, 983, 4*w^2 - 7*w - 24]', '[991, 991, -3*w^2 - 2*w + 4]']}
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-5, -9, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1492, 'disc_rad': 746, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 1]]], [5, [[2, 1], [1, 1]]], [7, [[1, 3]]], [11, [[2, 1], [1, 1]]], [13, [[3, 1]]], [17, [[3, 1]]], [19, [[2, 1], [1, 1]]], [23, [[2, 1], [1, 1]]], [29, [[1, 3]]], [31, [[3, 1]]], [37, [[3, 1]]], [41, [[3, 1]]], [43, [[2, 1], [1, 1]]], [47, [[2, 1], [1, 1]]], [53, [[2, 1], [1, 1]]], [59, [[3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 30.657806562465872, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1492.1', 'local_algs': ['2.3.2.1', 'm373.1.1.0', 'm373.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 373], 'rd': 11.4267556639, 'regulator': {'__RealLiteral__': 0, 'data': '7.64636835507', 'prec': 44}, 'res': {'gal': ['7,-314,-5,160,-43,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 2 \\)', '\\( a^{2} - a - 1 \\)'], 'unitsGmodule': [[4, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}