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hmf_forms • Show schema
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{'deg': 3, 'dimension': 1, 'disc': 892, 'field_bad_primes': [2, 223], 'field_label': '3.3.892.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.892.1-8.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2], 'level_ideal': '[8, 2, 2]', 'level_label': '8.1', 'level_norm': 8, 'parallel_weight': 2, 'short_label': '8.1-a', 'weight': '[2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2, 2, -w + 2]', -1], ['[2, 2, -w + 1]', 1]], 'hecke_eigenvalues': [0, -1, 0, 4, 4, 4, 4, 4, 8, -8, 0, 4, -8, 0, -12, -12, 8, 8, 8, -12, -8, -6, 6, -6, 0, -12, -12, 2, -20, 16, 0, -20, -12, -6, 4, -12, 2, 20, -20, 4, -8, -12, 0, 2, 6, -12, -24, -8, 16, 8, -8, 24, 4, 6, 12, 24, -30, -10, 20, -6, 26, -34, 0, 24, 24, 30, -24, 16, 32, -22, -4, 28, 24, -18, -12, -22, 36, 38, -34, 16, 4, 12, -18, -22, -20, -24, -16, 20, 30, 24, 24, -24, 20, 20, 20, -8, -8, -30, 12, 12, 12, 6, 30, 12, -32, -20, -36, 20, -24, -36, 36, -44, 6, -48, -24, 12, 20, 28, -8, 4, 48, 8, -4, 20, 20, 0, 16, -22, 42, 6, -48, -4, -32, 40, 8, 4, -32, 28, 28, -6, 12, 0, 44, -32, 4, 2, 52, 44, 16, -12, -44, -48, 40, -16, 28, -58, 48, 24, -34, -8, -8, -40, 30, 24, -24, 0, 40, -44, 8, -58, 26, 26], 'hecke_polynomial': 'x', 'label': '3.3.892.1-8.1-a'}
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hmf_fields • Show schema
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{'degree': 3, 'discriminant': 892, 'ideals': ['[1, 1, 1]', '[2, 2, -w + 2]', '[2, 2, -w + 1]', '[4, 2, w^2 - 8]', '[4, 2, -w^2 - w + 6]', '[4, 4, -w + 3]', '[5, 5, -w^2 - w + 5]', '[7, 7, w^2 + w - 9]', '[8, 2, 2]', '[8, 4, w^2 - 6]', '[8, 4, w^2 + w - 4]', '[8, 8, -w^2 + 9]', '[10, 10, w]', '[10, 10, w^2 + 2*w - 5]', '[13, 13, -w^2 - w + 7]', '[14, 14, w + 2]', '[14, 14, 2*w^2 + 3*w - 9]', '[16, 4, -2*w + 4]', '[16, 4, w^2 + 2*w - 2]', '[16, 4, -2*w + 2]', '[16, 8, -w^2 - w + 8]', '[16, 16, -w - 1]', '[19, 19, w^2 - w - 1]', '[20, 10, -w^2 + 2*w]', '[20, 10, w^2 + w - 10]', '[20, 20, -w^2 + 5]', '[25, 5, -w^2 + w + 3]', '[25, 25, w^2 - w - 5]', '[26, 26, w^2 - 3]', '[26, 26, -w + 4]', '[27, 3, 3]', '[28, 14, -w^2 + 4]', '[28, 14, -w^2 - w + 2]', '[28, 28, -2*w^2 - w + 13]', '[31, 31, -w^2 + w + 11]', '[32, 4, 2*w^2 - 16]', '[32, 4, -2*w^2 - 2*w + 12]', '[32, 8, -w^2 - 2*w + 6]', '[32, 8, -2*w + 6]', '[32, 16, w^2 - w - 2]', '[32, 32, w^2 - 1]', '[35, 35, 2*w^2 - 15]', '[38, 38, w + 4]', '[38, 38, -3*w + 7]', '[40, 10, -2*w^2 - 2*w + 10]', '[40, 20, w^2 - 10]', '[40, 20, -w^2 + 3*w]', '[40, 40, 3*w - 5]', '[43, 43, -3*w^2 - w + 21]', '[47, 47, 2*w - 1]', '[49, 7, 4*w^2 + 2*w - 29]', '[49, 49, -2*w^2 - 4*w + 7]', '[50, 10, -2*w^2 - 3*w + 6]', '[50, 10, -3*w^2 - 2*w + 19]', '[50, 50, w^2 - 4*w + 5]', '[50, 50, -2*w^2 - 3*w + 10]', '[52, 26, -w^2 + w + 12]', '[52, 26, 3*w^2 + 4*w - 12]', '[52, 52, -w^2 - 2*w + 11]', '[54, 6, -3*w + 6]', '[54, 6, -3*w + 3]', '[56, 14, 2*w^2 + 2*w - 18]', '[56, 28, -w^2 + 4*w - 2]', '[56, 28, -w^2 + w + 6]', '[56, 56, w^2 + 2*w - 7]', '[61, 61, 2*w^2 + 2*w - 9]', '[62, 62, -2*w^2 - w + 12]', '[62, 62, -w^2 - 2*w + 1]', '[64, 4, 4]', '[64, 8, w^2 - 2*w + 2]', '[64, 8, 2*w^2 - 12]', '[64, 8, 2*w^2 + 2*w - 8]', '[64, 16, -2*w^2 + 18]', '[64, 32, 3*w^2 + 3*w - 16]', '[64, 64, w^2 - 2*w - 3]', '[65, 65, 2*w + 5]', '[70, 70, 2*w^2 - w - 10]', '[70, 70, -w + 5]', '[71, 71, w^2 + w - 11]', '[71, 71, -w^2 - 3*w + 7]', '[71, 71, 2*w^2 + 2*w - 13]', '[76, 38, -w^2 - 2*w + 8]', '[76, 38, -w^2 - 3*w + 4]', '[76, 76, -3*w^2 - 2*w + 21]', '[79, 79, w^2 + 3*w - 1]', '[79, 79, w^2 + w - 1]', '[79, 79, -w^2 - 3*w - 1]', '[80, 20, 2*w]', '[80, 20, w^2 + 2*w - 10]', '[80, 20, 2*w^2 + 4*w - 10]', '[80, 40, -w^2 + w + 10]', '[80, 80, 3*w^2 + 4*w - 15]', '[83, 83, w^2 - w - 7]', '[86, 86, -2*w^2 + w + 12]', '[86, 86, w^2 + 2*w - 9]', '[91, 91, -w^2 + w - 1]', '[94, 94, -2*w^2 + 3*w - 1]', '[94, 94, -2*w^2 + 5*w - 2]', '[95, 95, 3*w^2 + w - 25]', '[97, 97, 4*w^2 + 4*w - 23]', '[98, 14, 2*w^2 + w - 18]', '[98, 14, -2*w^2 - w + 11]', '[98, 98, 2*w^2 + w - 6]', '[98, 98, -w^2 + 11]', '[100, 10, 3*w^2 + 2*w - 24]', '[100, 10, -w^2 + w + 8]', '[100, 20, 2*w^2 + 3*w - 11]', '[100, 50, w^2]', '[100, 50, 3*w^2 + w - 20]', '[100, 100, w + 5]', '[101, 101, -w^2 + w + 9]', '[101, 101, w^2 + 3*w - 3]', '[101, 101, 2*w - 7]', '[104, 26, -2*w^2 - 2*w + 14]', '[104, 52, -w^2 - 3*w + 2]', '[104, 52, 3*w^2 - 22]', '[104, 104, 2*w^2 - 5*w + 1]', '[107, 107, 2*w^2 + 2*w - 17]', '[107, 107, 5*w^2 + 7*w - 21]', '[107, 107, w^2 - 3*w - 1]', '[108, 6, 3*w^2 - 24]', '[108, 6, -3*w^2 - 3*w + 18]', '[108, 12, -3*w + 9]', '[109, 109, -2*w - 1]', '[109, 109, 4*w - 7]', '[109, 109, 4*w^2 + 2*w - 27]', '[112, 28, 2*w + 4]', '[112, 28, 3*w^2 + 2*w - 22]', '[112, 28, 4*w^2 + 6*w - 18]', '[112, 56, -w^2 + 3*w - 4]', '[112, 112, -3*w^2 + 19]', '[113, 113, 2*w^2 - 11]', '[122, 122, -3*w + 2]', '[122, 122, -2*w^2 - 5*w + 11]', '[124, 62, w^2 + 3*w - 8]', '[124, 62, -w^2 + 2*w + 4]', '[124, 124, -3*w^2 + 23]', '[125, 5, 5]', '[125, 125, 2*w^2 + 2*w - 15]', '[127, 127, -2*w^2 + 2*w + 7]', '[128, 8, -4*w + 8]', '[128, 8, 2*w^2 + 4*w - 4]', '[128, 8, -4*w + 4]', '[128, 16, 3*w^2 + 2*w - 18]', '[128, 16, -2*w^2 - 2*w + 16]', '[128, 32, -2*w - 2]', '[128, 64, -3*w^2 - 5*w + 14]', '[128, 128, 2*w^2 - w - 19]', '[130, 130, -2*w^2 - 3*w + 5]', '[130, 130, -2*w^2 - w + 10]', '[131, 131, -2*w - 3]', '[133, 133, -3*w^2 - 5*w + 9]', '[135, 15, -3*w^2 - 3*w + 15]', '[137, 137, 2*w + 7]', '[139, 139, -5*w^2 - 3*w + 33]', '[140, 70, w^2 + 2*w]', '[140, 70, 5*w^2 + 7*w - 20]', '[140, 140, w^2 - 6*w + 5]', '[142, 142, 5*w - 12]', '[142, 142, -3*w - 8]', '[142, 142, -2*w^2 - w + 7]', '[142, 142, -w^2 + 4*w - 1]', '[142, 142, 2*w^2 - w - 9]', '[142, 142, w - 6]', '[149, 149, -w^2 - 3*w + 13]', '[152, 38, 2*w^2 - 2*w - 2]', '[152, 76, w^2 - 4*w + 6]', '[152, 76, -w^2 - w + 12]', '[152, 152, 2*w^2 + w - 9]', '[155, 155, 5*w^2 + w - 35]', '[157, 157, w^2 - 5*w + 3]', '[158, 158, 4*w^2 + w - 33]', '[158, 158, -5*w + 8]', '[158, 158, -6*w^2 - w + 47]', '[158, 158, -2*w^2 - w + 8]', '[158, 158, -w^2 - 6*w + 9]', '[158, 158, 2*w^2 + 3*w - 12]', '[160, 20, -2*w^2 + 4*w]', '[160, 20, 2*w^2 + 2*w - 20]', '[160, 40, 3*w^2 + 6*w - 10]', '[160, 40, -2*w^2 + 10]', '[160, 80, -w^2 - w]', '[160, 160, -5*w^2 - 2*w + 35]', '[163, 163, -4*w^2 + 33]', '[163, 163, 7*w^2 + 3*w - 53]', '[163, 163, -8*w^2 - 4*w + 57]', '[166, 166, w^2 - 2*w + 3]', '[166, 166, 2*w^2 - 3*w - 4]', '[169, 13, w^2 + 3*w - 9]', '[169, 169, -2*w^2 + 19]', '[172, 86, 3*w^2 + 4*w - 16]', '[172, 86, -w^2 + 5*w - 8]', '[172, 172, -2*w^2 + 3*w + 1]', '[173, 173, 3*w^2 + w - 19]', '[175, 35, -w^2 + w + 13]', '[175, 175, 5*w^2 + 3*w - 35]', '[179, 179, 6*w^2 + 2*w - 43]', '[182, 182, -2*w^2 + 3*w + 7]', '[182, 182, -4*w^2 - 3*w + 24]', '[188, 94, -3*w^2 - 3*w + 14]', '[188, 94, w^2 - 12]', '[188, 188, -2*w^2 + 7*w - 3]', '[189, 21, 3*w^2 + 3*w - 27]', '[190, 190, 2*w^2 + 3*w - 20]', '[190, 190, -w^2 + 2*w + 5]', '[193, 193, -6*w + 7]', '[194, 194, -w - 6]', '[194, 194, -4*w^2 - 5*w + 17]', '[196, 14, -5*w^2 - 6*w + 24]', '[196, 14, -w^2 + 3*w + 2]', '[196, 28, w^2 + 4*w - 9]', '[196, 98, 3*w^2 - 2*w - 16]', '[196, 98, -w^2 - 3*w + 12]', '[196, 196, -3*w + 1]', '[197, 197, -5*w^2 - w + 41]', '[197, 197, 4*w^2 + 4*w - 21]', '[197, 197, 3*w^2 + 3*w - 19]', '[199, 199, 2*w^2 - 9]', '[200, 10, -2*w^2 + 2*w + 6]', '[200, 20, w^2 + 4*w + 2]', '[200, 20, -w^2 + w - 2]', '[200, 40, -4*w^2 - w + 27]', '[200, 50, 2*w^2 - 2*w - 10]', '[200, 100, -w^2 - 3*w + 10]', '[200, 100, 5*w^2 + 4*w - 30]', '[200, 200, -w^2 - 4*w + 5]', '[202, 202, -2*w^2 + w + 8]', '[202, 202, -3*w^2 - 2*w + 7]', '[202, 202, 2*w^2 - w - 21]', '[202, 202, -w^2 - 1]', '[202, 202, -2*w^2 + w + 4]', '[202, 202, -4*w^2 - 5*w + 16]', '[208, 52, 2*w^2 - 6]', '[208, 52, 3*w^2 - 2*w - 14]', '[208, 52, -2*w + 8]', '[208, 104, -3*w^2 - w + 26]', '[208, 208, 3*w^2 + 2*w - 17]', '[211, 211, w^2 + 3*w - 11]', '[214, 214, 5*w - 14]', '[214, 214, -2*w^2 - 5*w + 8]', '[214, 214, w^2 - 2*w - 13]', '[214, 214, -2*w^2 + 3*w + 3]', '[214, 214, -7*w^2 - 12*w + 29]', '[214, 214, -6*w^2 - 3*w + 44]', '[215, 215, 2*w^2 - 8*w + 5]', '[216, 6, 6]', '[216, 12, 3*w^2 - 18]', '[216, 12, 3*w^2 + 3*w - 12]', '[216, 24, -3*w^2 + 27]', '[217, 217, 3*w^2 + 3*w - 13]', '[218, 218, 2*w^2 - w - 1]', '[218, 218, 6*w^2 + 11*w - 24]', '[218, 218, 2*w^2 - w - 14]', '[218, 218, 2*w^2 - 3*w - 2]', '[218, 218, 4*w^2 + 5*w - 21]', '[218, 218, -2*w^2 - 3*w + 13]', '[223, 223, w^2 + 5*w - 7]', '[223, 223, 5*w^2 + 5*w - 27]', '[224, 28, -2*w^2 + 8]', '[224, 28, -2*w^2 - 2*w + 4]', '[224, 56, w^2 + 2*w - 14]', '[224, 56, -4*w^2 - 2*w + 26]', '[224, 112, -w^2 - 3*w - 2]', '[224, 224, 5*w - 11]', '[226, 226, 2*w^2 - 5*w - 2]', '[226, 226, -5*w + 9]', '[227, 227, -2*w^2 + 2*w + 3]', '[229, 229, 2*w^2 - 7]', '[233, 233, -4*w - 11]', '[235, 235, -3*w^2 - 5*w + 15]', '[239, 239, 4*w^2 + 6*w - 19]', '[244, 122, -3*w^2 - 7*w + 6]', '[244, 122, -5*w^2 - 4*w + 32]', '[244, 244, 2*w^2 - w - 7]', '[245, 35, w^2 - 3*w + 5]', '[245, 245, -2*w^2 + 2*w + 5]', '[247, 247, -4*w + 3]', '[248, 62, -2*w^2 + 2*w + 22]', '[248, 124, 9*w^2 + 4*w - 66]', '[248, 124, -3*w^2 + w + 16]', '[248, 248, w - 7]', '[250, 10, -5*w + 10]', '[250, 10, -5*w + 5]', '[250, 250, 3*w - 10]', '[250, 250, -2*w^2 + w + 5]', '[251, 251, 5*w^2 + 5*w - 29]', '[254, 254, -4*w^2 + 13*w - 6]', '[254, 254, -2*w^2 + 11*w - 13]', '[256, 8, 4*w^2 - 32]', '[256, 8, -4*w^2 - 4*w + 24]', '[256, 16, -2*w^2 - 4*w + 12]', '[256, 16, w^2 - 2*w - 6]', '[256, 16, -4*w + 12]', '[256, 32, 2*w^2 - 2*w - 4]', '[256, 64, 2*w^2 - 2]', '[256, 128, 3*w^2 + w - 18]', '[256, 256, w^2 + 2*w + 1]', '[260, 130, -w^2 + 4*w]', '[260, 130, w^2 + 5*w - 10]', '[260, 260, -2*w^2 + w + 15]', '[262, 262, 2*w^2 + w - 3]', '[262, 262, 2*w^2 - w - 6]', '[266, 266, -2*w^2 + w + 17]', '[266, 266, 2*w^2 + 5*w - 12]', '[269, 269, w^2 + w - 13]', '[270, 30, 3*w]', '[270, 30, 3*w^2 + 6*w - 15]', '[274, 274, -2*w^2 - 3*w + 14]', '[274, 274, -2*w^2 - 5*w + 7]', '[277, 277, -w^2 - w - 1]', '[278, 278, 3*w^2 + 4*w - 17]', '[278, 278, -2*w^2 + w + 16]', '[280, 70, 4*w^2 - 30]', '[280, 140, -w^2 - 4*w + 10]', '[280, 140, -3*w^2 - 3*w + 20]', '[280, 280, -2*w^2 - 5*w + 5]', '[283, 283, 2*w^2 + 4*w - 3]', '[284, 142, -9*w^2 - 2*w + 68]', '[284, 142, 5*w^2 + 3*w - 36]', '[284, 142, 3*w^2 + 2*w - 16]', '[284, 142, 3*w^2 + 5*w - 8]', '[284, 142, w^2 - 3*w - 18]', '[284, 142, -9*w^2 - 4*w + 64]', '[284, 284, 2*w^2 + 3*w - 19]', '[284, 284, w^2 + 6*w - 23]', '[284, 284, 7*w^2 + 4*w - 47]', '[293, 293, -4*w^2 + 31]', '[298, 298, 3*w^2 - 8*w + 3]', '[298, 298, 2*w^2 - 11*w + 16]', '[301, 301, w^2 - 3*w - 3]', '[304, 76, 2*w + 8]', '[304, 76, 5*w^2 + 2*w - 34]', '[304, 76, -6*w + 14]', '[304, 152, w^2 - 5*w + 2]', '[304, 304, -4*w^2 - 3*w + 33]', '[305, 305, -5*w^2 - 9*w + 15]', '[310, 310, -w^2 - 4*w + 15]', '[310, 310, 3*w + 10]', '[313, 313, 3*w^2 - w - 27]', '[314, 314, -w^2 - 4*w - 1]', '[314, 314, -4*w^2 - 3*w + 28]', '[316, 158, 3*w^2 + 3*w - 26]', '[316, 158, -w^2 + 6*w - 4]', '[316, 158, w^2 - 2*w - 12]', '[316, 158, -5*w^2 - 7*w + 24]', '[316, 158, -5*w^2 - w + 34]', '[316, 158, -w^2 + 2*w - 4]', '[316, 316, -w^2 + 2*w + 7]', '[316, 316, w^2 - 4*w + 7]', '[316, 316, w^2 - 13]', '[320, 20, -4*w^2 - 4*w + 20]', '[320, 40, -3*w^2 - 2*w + 10]', '[320, 40, 2*w^2 - 20]', '[320, 40, -2*w^2 + 6*w]', '[320, 80, 6*w - 10]', '[320, 160, -3*w^2 + w + 20]', '[320, 320, 2*w^2 + 3*w - 15]', '[325, 65, -2*w^2 + 2*w + 11]', '[325, 325, 4*w^2 - 25]', '[326, 326, -w - 7]', '[326, 326, 4*w^2 + 3*w - 36]', '[326, 326, 4*w^2 + 3*w - 23]', '[326, 326, -4*w^2 - w + 26]', '[326, 326, -3*w^2 + 17]', '[326, 326, -4*w^2 - w + 34]', '[329, 329, 3*w^2 - 3*w - 11]', '[332, 166, 5*w^2 + 3*w - 32]', '[332, 166, -7*w^2 - 2*w + 56]', '[332, 332, 3*w^2 - 4*w - 11]', '[337, 337, 2*w^2 + 2*w - 21]', '[338, 26, -2*w^2 + 7*w - 8]', '[338, 26, -3*w^2 + 4*w + 1]', '[338, 338, -3*w - 1]', '[338, 338, -2*w^2 - 3*w + 18]', '[343, 7, 7]', '[343, 343, -3*w^2 - w + 17]', '[344, 86, -6*w^2 - 2*w + 42]', '[344, 172, -w^2 - 2]', '[344, 172, w^2 - w - 14]', '[344, 344, 7*w - 17]', '[346, 346, 2*w^2 - 3*w - 8]', '[346, 346, -w^2 - 4*w + 11]', '[347, 347, -2*w^2 - 6*w + 13]', '[350, 70, -2*w^2 - 3*w + 16]', '[350, 70, -w^2 - 4*w + 3]', '[350, 350, 2*w^2 + w - 20]', '[350, 350, -3*w^2 - 2*w + 15]', '[351, 39, -3*w^2 - 3*w + 21]', '[353, 353, -5*w^2 - 3*w + 37]', '[353, 353, 2*w^2 + 4*w - 13]', '[353, 353, -w^2 + w - 3]', '[355, 355, 4*w^2 + 8*w - 15]', '[355, 355, -w^2 - 5*w - 5]', '[355, 355, 4*w^2 + 2*w - 25]', '[358, 358, 4*w^2 - w - 26]', '[358, 358, -2*w^2 - 3*w + 17]', '[359, 359, 2*w - 9]', '[361, 19, -7*w^2 - 3*w + 49]', '[361, 361, -4*w^2 - 8*w + 13]', '[364, 182, -w^2 + 2*w + 8]', '[364, 182, 3*w^2 + 5*w - 16]', '[364, 364, -5*w^2 + 41]', '[367, 367, w^2 - 5*w + 9]', '[373, 373, 3*w^2 + w - 27]', '[376, 94, 4*w - 2]', '[376, 188, 3*w^2 + 7*w - 16]', '[376, 188, w^2 + 4*w - 14]', '[376, 376, -w^2 + 2*w + 11]', '[378, 42, 3*w + 6]', '[378, 42, 6*w^2 + 9*w - 27]', '[379, 379, -w^2 - 5*w - 7]', '[380, 190, w^2 + 4*w]', '[380, 190, 7*w^2 + 11*w - 30]', '[380, 380, -2*w^2 + 5*w - 5]', '[386, 386, -6*w^2 - 11*w + 21]', '[386, 386, -4*w^2 - 5*w + 22]', '[388, 194, w^2 + 4*w - 12]', '[388, 194, w^2 + 5*w - 6]', '[388, 388, 4*w^2 + 3*w - 29]', '[392, 14, 8*w^2 + 4*w - 58]', '[392, 28, w^2 + 4*w - 2]', '[392, 28, -w^2 + 3*w + 16]', '[392, 56, -3*w^2 + 2*w + 13]', '[392, 98, -4*w^2 - 8*w + 14]', '[392, 196, -3*w^2 - 4*w + 18]', '[392, 196, 3*w^2 - 7*w + 2]', '[392, 392, -2*w^2 - 3*w + 23]', '[394, 394, -4*w^2 - 3*w + 32]', '[394, 394, -3*w - 2]', '[394, 394, -3*w^2 - 2*w + 11]', '[394, 394, w^2 - 2*w - 9]', '[394, 394, -4*w^2 - 7*w + 19]', '[394, 394, w - 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96]', '[1916, 1916, w^2 - 18*w + 41]', '[1917, 213, 3*w^2 + 3*w - 33]', '[1917, 213, -3*w^2 - 9*w + 21]', '[1917, 213, 6*w^2 + 6*w - 39]', '[1918, 1918, 6*w^2 + 5*w - 56]', '[1918, 1918, -5*w^2 + 27]', '[1919, 1919, 4*w^2 + 14*w - 27]', '[1919, 1919, 9*w^2 + 7*w - 59]', '[1919, 1919, 2*w^2 + 8*w - 19]', '[1922, 62, -6*w^2 - 5*w + 44]', '[1922, 62, -w^2 - 6*w - 3]', '[1922, 1922, 4*w^2 - w - 3]', '[1922, 1922, 4*w^2 - 5*w - 6]', '[1930, 1930, 2*w^2 + 5*w - 30]', '[1930, 1930, -4*w^2 + w + 15]', '[1933, 1933, 4*w^2 - 2*w - 29]', '[1934, 1934, 9*w - 26]', '[1934, 1934, w^2 + 8*w - 19]', '[1934, 1934, -6*w^2 + w + 34]', '[1934, 1934, -4*w^2 + 5*w + 7]', '[1934, 1934, -4*w^2 + 7*w + 12]', '[1934, 1934, w - 13]', '[1937, 1937, -4*w^2 - 4*w + 41]', '[1939, 1939, -4*w^2 - 6*w + 39]', '[1940, 970, -w^2 - 6*w]', '[1940, 970, -9*w^2 - 15*w + 40]', '[1940, 1940, 3*w^2 - 4*w - 35]', '[1946, 1946, 4*w^2 - 3*w - 8]', '[1946, 1946, -6*w^2 - 3*w + 53]', '[1948, 974, 3*w^2 + 2*w - 32]', '[1948, 974, -5*w^2 - 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61]', '[9874, 9874, 14*w^2 + 29*w - 59]', '[9874, 9874, -8*w^2 + 5*w + 48]', '[9874, 9874, -10*w^2 - 3*w + 88]', '[9874, 9874, 6*w^2 + 15*w - 38]', '[9874, 9874, 5*w^2 + 10*w - 41]', '[9875, 395, 5*w^2 + 15*w - 5]', '[9875, 395, 5*w^2 + 5*w - 5]', '[9875, 395, -5*w^2 - 15*w - 5]', '[9875, 9875, -19*w^2 - 17*w + 115]', '[9875, 9875, 15*w^2 + 13*w - 85]', '[9875, 9875, 7*w^2 + 11*w - 45]', '[9880, 2470, 10*w^2 + 18*w - 50]', '[9880, 4940, -9*w^2 + 3*w + 80]', '[9880, 4940, -w^2 + 8*w + 10]', '[9880, 9880, 16*w^2 + 19*w - 85]', '[9884, 4942, -9*w^2 + 2*w + 68]', '[9884, 4942, 9*w^2 + 11*w - 56]', '[9884, 4942, -w^2 - 12*w + 8]', '[9884, 4942, -11*w^2 - 23*w + 54]', '[9884, 4942, 7*w^2 - 6*w - 12]', '[9884, 4942, 9*w^2 + 3*w - 16]', '[9884, 9884, 9*w^2 + 4*w - 49]', '[9884, 9884, 10*w^2 + 21*w - 33]', '[9884, 9884, 2*w^2 - 7*w - 29]', '[9886, 9886, 19*w^2 + 2*w - 159]', '[9886, 9886, -12*w^2 - 13*w + 54]', '[9892, 4946, -w^2 - 16]', '[9892, 4946, -11*w^2 - 11*w + 42]', '[9892, 9892, 8*w^2 - w - 77]', '[9893, 9893, 10*w^2 + 4*w - 59]', '[9896, 2474, 6*w^2 - 6*w - 34]', '[9896, 4948, -11*w^2 - 12*w + 102]', '[9896, 4948, -5*w^2 - 11*w + 38]', '[9896, 9896, 20*w^2 + 3*w - 153]', '[9898, 1414, -20*w^2 - 3*w + 152]', '[9898, 1414, -11*w^2 - 16*w + 57]', '[9898, 1414, 8*w^2 - 3*w - 37]', '[9898, 1414, 13*w^2 + 10*w - 89]', '[9898, 1414, 4*w^2 - 5*w - 36]', '[9898, 1414, -2*w^2 - 15*w - 24]', '[9898, 9898, 8*w^2 + 15*w - 44]', '[9898, 9898, 5*w^2 + 6*w - 57]', '[9898, 9898, 2*w^2 + 11*w + 7]', '[9898, 9898, 17*w^2 + 32*w - 67]', '[9898, 9898, -8*w^2 + 13*w + 2]', '[9898, 9898, 16*w^2 + 31*w - 72]', '[9899, 9899, 6*w^2 + 4*w - 61]', '[9905, 9905, 8*w^2 - 4*w - 75]', '[9908, 4954, 21*w^2 + 11*w - 152]', '[9908, 4954, -39*w^2 - 10*w + 296]', '[9908, 9908, 7*w^2 + 16*w - 91]', '[9909, 1101, 3*w^2 - 15*w + 27]', '[9910, 9910, 14*w^2 + 17*w - 60]', '[9910, 9910, 4*w^2 - 5*w - 35]', '[9910, 9910, -7*w^2 + 4*w + 25]', '[9910, 9910, 6*w^2 - 25*w + 15]', '[9910, 9910, -14*w^2 - 9*w + 110]', '[9910, 9910, 8*w^2 + 21*w - 10]', '[9914, 9914, 6*w^2 + 11*w - 41]', '[9914, 9914, -6*w^2 + 5*w + 38]', '[9917, 9917, -7*w^2 + 9*w + 9]', '[9919, 9919, -9*w^2 - 5*w + 47]', '[9919, 9919, w^2 + 17*w - 19]', '[9919, 9919, 15*w^2 + 15*w - 79]', '[9920, 620, 20*w^2 + 4*w - 140]', '[9920, 1240, -6*w^2 - 2*w + 60]', '[9920, 1240, -19*w^2 - 26*w + 90]', '[9920, 1240, 2*w^2 - 8*w + 20]', '[9920, 2480, 10*w^2 + 8*w - 50]', '[9920, 4960, -29*w^2 - 7*w + 230]', '[9920, 9920, 21*w^2 + 14*w - 135]', '[9925, 1985, 12*w^2 - 2*w - 111]', '[9925, 9925, 8*w^2 - 16*w - 5]', '[9926, 9926, 14*w^2 + 27*w - 37]', '[9926, 9926, 16*w^2 + 13*w - 94]', '[9929, 9929, -18*w^2 - 10*w + 131]', '[9931, 9931, 2*w^2 + 12*w - 9]', '[9935, 9935, -8*w^2 - 4*w + 35]', '[9937, 9937, -7*w^2 + w + 21]', '[9937, 9937, 9*w^2 + 5*w - 29]', '[9937, 9937, -12*w^2 + 26*w + 11]', '[9940, 4970, 23*w^2 + 41*w - 80]', '[9940, 4970, 15*w^2 + 18*w - 80]', '[9940, 4970, 3*w^2 - 40]', '[9940, 4970, -11*w^2 - 11*w + 50]', '[9940, 4970, 3*w^2 - 7*w - 40]', '[9940, 4970, -19*w^2 - 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40]', '[9980, 9980, -10*w^2 - 9*w + 45]', '[9986, 9986, 2*w^2 - 15*w + 8]', '[9986, 9986, -5*w^2 - 20*w + 39]', '[9989, 9989, 3*w^2 + 3*w - 41]', '[9992, 2498, -16*w^2 - 12*w + 106]', '[9992, 4996, -9*w^2 - 20*w + 34]', '[9992, 4996, -7*w^2 - 19*w + 8]', '[9992, 9992, 7*w^2 - 6*w - 21]', '[9998, 9998, 8*w^2 - 5*w - 79]', '[9998, 9998, -2*w^2 - 23*w + 37]', '[9998, 9998, -10*w^2 - 9*w + 39]', '[9998, 9998, -30*w^2 - 13*w + 222]', '[9998, 9998, 4*w^2 - 21*w + 14]', '[9998, 9998, w - 22]', '[10000, 100, 10*w]', '[10000, 100, w^2 - 6*w + 22]', '[10000, 100, 8*w^2 + 2*w - 24]', '[10000, 100, 5*w^2 + 10*w - 50]', '[10000, 100, -8*w^2 - 2*w + 74]', '[10000, 100, 10*w^2 + 20*w - 50]', '[10000, 200, -5*w^2 + 5*w + 50]', '[10000, 200, 11*w^2 + 9*w - 58]', '[10000, 400, 13*w^2 + 22*w - 39]', '[10000, 400, 15*w^2 + 20*w - 75]', '[10000, 2500, 8*w^2 + 2*w - 40]', '[10000, 2500, -7*w^2 - 6*w + 70]', '[10000, 2500, 6*w^2 + 8*w - 10]', '[10000, 5000, 19*w^2 + 9*w - 130]', '[10000, 10000, w^2 + 10*w + 25]'], 'label': '3.3.892.1', 'narrow_class_no': 2, 'primes': ['[2, 2, -w + 2]', '[2, 2, -w + 1]', '[5, 5, -w^2 - w + 5]', '[7, 7, w^2 + w - 9]', '[13, 13, -w^2 - w + 7]', '[19, 19, w^2 - w - 1]', '[25, 5, -w^2 + w + 3]', '[27, 3, 3]', '[31, 31, -w^2 + w + 11]', '[43, 43, -3*w^2 - w + 21]', '[47, 47, 2*w - 1]', '[49, 7, 4*w^2 + 2*w - 29]', '[61, 61, 2*w^2 + 2*w - 9]', '[71, 71, w^2 + w - 11]', '[71, 71, -w^2 - 3*w + 7]', '[71, 71, 2*w^2 + 2*w - 13]', '[79, 79, w^2 + 3*w - 1]', '[79, 79, w^2 + w - 1]', '[79, 79, -w^2 - 3*w - 1]', '[83, 83, w^2 - w - 7]', '[97, 97, 4*w^2 + 4*w - 23]', '[101, 101, -w^2 + w + 9]', '[101, 101, w^2 + 3*w - 3]', '[101, 101, 2*w - 7]', '[107, 107, 2*w^2 + 2*w - 17]', '[107, 107, 5*w^2 + 7*w - 21]', '[107, 107, w^2 - 3*w - 1]', '[109, 109, -2*w - 1]', '[109, 109, 4*w - 7]', '[109, 109, 4*w^2 + 2*w - 27]', '[113, 113, 2*w^2 - 11]', '[127, 127, -2*w^2 + 2*w + 7]', '[131, 131, -2*w - 3]', '[137, 137, 2*w + 7]', '[139, 139, -5*w^2 - 3*w + 33]', '[149, 149, -w^2 - 3*w + 13]', '[157, 157, w^2 - 5*w + 3]', '[163, 163, -4*w^2 + 33]', '[163, 163, 7*w^2 + 3*w - 53]', '[163, 163, -8*w^2 - 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3]', '[857, 857, 4*w^2 - 2*w - 19]', '[857, 857, 3*w^2 - w - 9]', '[859, 859, 2*w^2 + 2*w - 23]', '[859, 859, -10*w^2 - 6*w + 69]', '[859, 859, -3*w^2 - 5*w + 31]', '[877, 877, -10*w^2 - 2*w + 81]', '[883, 883, 7*w^2 + 7*w - 41]', '[883, 883, 3*w^2 + w - 29]', '[883, 883, 8*w^2 + 6*w - 49]', '[887, 887, 16*w^2 + 6*w - 117]', '[907, 907, 5*w^2 + 5*w - 23]', '[911, 911, w^2 - 3*w - 13]', '[919, 919, 5*w^2 + 5*w - 19]', '[919, 919, 3*w^2 + 3*w - 31]', '[919, 919, 4*w^2 + 2*w - 21]', '[937, 937, w^2 - 5*w - 1]', '[947, 947, -7*w^2 - 3*w + 47]', '[953, 953, 7*w^2 + 7*w - 37]', '[961, 31, -5*w^2 + w + 47]', '[967, 967, 4*w^2 + 4*w - 33]', '[967, 967, -5*w^2 - w + 31]', '[967, 967, -6*w^2 + 47]', '[977, 977, -7*w^2 - w + 59]', '[983, 983, -w^2 - 5*w - 1]', '[983, 983, 8*w - 17]', '[983, 983, 5*w^2 + 3*w - 29]', '[991, 991, 6*w^2 + 8*w - 31]', '[991, 991, -11*w^2 - 3*w + 79]', '[991, 991, w^2 + 7*w + 13]', '[997, 997, -4*w - 7]', '[997, 997, w^2 - 3*w - 11]', '[997, 997, -w^2 + 5*w - 11]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [10, -8, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 892, 'disc_rad': 446, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 1]]], [5, [[2, 1], [1, 1]]], [7, [[2, 1], [1, 1]]], [11, [[3, 1]]], [13, [[2, 1], [1, 1]]], [17, [[3, 1]]], [19, [[2, 1], [1, 1]]], [23, [[3, 1]]], [29, [[3, 1]]], [31, [[2, 1], [1, 1]]], [37, [[3, 1]]], [41, [[3, 1]]], [43, [[2, 1], [1, 1]]], [47, [[2, 1], [1, 1]]], [53, [[3, 1]]], [59, [[3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 29.866369046136157, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.892.1', 'local_algs': ['2.1.0.1', '2.2.2.1', 'm223.1.1.0', 'm223.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 223], 'rd': 9.62620157035, 'regulator': {'__RealLiteral__': 0, 'data': '8.32319936299', 'prec': 44}, 'res': {'gal': ['8,-8,-58,90,-29,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} + a - 3 \\)', '\\( 3 a^{2} + 5 a - 11 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}