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hmf_forms • Show schema
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{'deg': 3, 'dimension': 2, 'disc': 1772, 'field_bad_primes': [2, 443], 'field_label': '3.3.1772.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1772.1-10.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2, 5], 'level_ideal': '[10, 10, -1/2*w^2 + 3/2*w]', 'level_label': '10.1', 'level_norm': 10, 'parallel_weight': 2, 'short_label': '10.1-b', 'weight': '[2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2, 2, -1/2*w^2 - 1/2*w + 4]', 1], ['[5, 5, -3/2*w^2 - 1/2*w + 15]', 1]], 'hecke_eigenvalues': [-1, 'e', 'e + 1', -1, '-e', -3, '-3*e', '2*e', '-e - 6', 6, '-3*e', -10, '3*e + 3', '-6*e - 2', 2, 'e', '-2*e', '6*e - 1', 'e', '9*e + 4', '-5*e - 3', '5*e + 3', '-8*e - 3', '-3*e - 1', '3*e - 3', '-9*e', '6*e + 7', '-12*e + 5', '7*e', '-6*e - 8', -17, 9, '3*e - 2', '-e - 6', '-3*e - 12', '-3*e - 21', '8*e + 3', 'e + 18', '-4*e', '6*e - 11', '3*e + 4', '9*e + 6', '-3*e - 16', '-3*e - 3', -24, '-2*e + 12', '4*e + 12', '-6*e + 8', '-14*e - 3', '-9*e - 10', '-2*e - 3', 11, '-7*e + 6', '-11*e', '-10*e', '-4*e', '-6*e - 10', '-6*e - 18', '-3*e + 15', '9*e + 7', '-6*e - 9', '3*e + 8', '-6*e + 4', 4, '6*e - 24', '-3*e - 8', '2*e - 12', '-15*e + 7', '-3*e - 7', '11*e - 15', '8*e - 24', '-3*e - 13', '12*e + 6', '3*e + 10', '6*e - 6', '13*e - 9', '-12*e - 13', '7*e - 15', '-3*e + 11', '-9*e - 7', '24*e + 7', '-3*e - 11', '9*e - 9', '10*e + 12', '8*e + 27', '5*e + 6', '3*e - 19', '-9*e - 25', '24*e', '6*e - 1', '-6*e + 12', '-14*e - 6', '15*e', '-9*e + 25', '5*e - 6', '-2*e + 30', '-3*e - 12', '-15*e - 9', '5*e', '27*e - 2', '18*e + 14', '18*e + 10', '-7*e + 27', '-19*e + 6', '12*e + 25', '-24*e + 4', '-e - 27', '-6*e + 7', '-18*e - 10', '6*e + 15', '6*e - 12', '-11*e + 15', 22, '6*e - 21', '2*e + 24', '-9*e - 5', '9*e - 6', '6*e - 37', '12*e - 16', '22*e - 12', '-12*e - 6', '3*e - 24', '15*e + 17', '18*e + 17', '3*e + 29', '8*e + 18', '3*e - 10', '30*e - 4', '-26*e - 12', -50, '4*e - 3', '6*e - 20', '-9*e + 2', '-21*e + 12', '-6*e - 33', 34, '3*e + 36', '9*e + 18', '21*e + 22', '6*e + 18', '14*e', -22, '-6*e + 30', '-21*e + 16', '18*e - 15', '3*e - 21', '9*e + 15', '-12*e + 6', '6*e - 6', '3*e - 45', '3*e + 31', '16*e + 9', '15*e - 23', '-21*e + 6', '-12*e - 14', '6*e + 9', '21*e + 21', '12*e + 7'], 'hecke_polynomial': 'x^2 - 2', 'label': '3.3.1772.1-10.1-b'}
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hmf_fields • Show schema
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{'degree': 3, 'discriminant': 1772, 'ideals': ['[1, 1, 1]', '[2, 2, -1/2*w^2 - 1/2*w + 4]', '[2, 2, -w^2 + 11]', '[3, 3, -1/2*w^2 + 1/2*w + 7]', '[4, 2, -w^2 + 4*w - 2]', '[4, 2, 1/2*w^2 - 5/2*w + 2]', '[4, 4, -w + 1]', '[5, 5, -3/2*w^2 - 1/2*w + 15]', '[6, 6, 1/2*w^2 - 3/2*w + 1]', '[6, 6, 3/2*w^2 - 13/2*w + 4]', '[8, 2, 2]', '[8, 4, w]', '[8, 4, -1/2*w^2 + 1/2*w + 6]', '[8, 8, w + 3]', '[9, 3, -1/2*w^2 + 5/2*w - 1]', '[9, 9, w^2 - 5*w + 3]', '[10, 10, -1/2*w^2 + 3/2*w]', '[10, 10, -w + 3]', '[12, 6, -1/2*w^2 + 1/2*w + 4]', '[12, 6, -w + 2]', '[12, 12, -1/2*w^2 - 1/2*w + 3]', '[15, 15, 1/2*w^2 - 5/2*w + 3]', '[16, 4, -w^2 - w + 8]', '[16, 4, -w^2 + 12]', '[16, 4, -2*w^2 + 22]', '[16, 8, 5/2*w^2 - 21/2*w + 6]', '[16, 16, -3/2*w^2 + 13/2*w - 3]', '[18, 6, -1/2*w^2 - 1/2*w + 2]', '[18, 6, -1/2*w^2 - 1/2*w + 5]', '[18, 18, w + 1]', '[18, 18, -1/2*w^2 + 3/2*w + 2]', '[20, 10, w + 2]', '[20, 10, -1/2*w^2 + 1/2*w + 8]', '[20, 20, -2*w^2 + w + 25]', '[24, 6, -w^2 + w + 14]', '[24, 12, -7/2*w^2 + 3/2*w + 44]', '[24, 12, w + 4]', '[24, 24, -4*w^2 + 17*w - 9]', '[25, 5, 7/2*w^2 - 31/2*w + 9]', '[25, 25, -1/2*w^2 + 1/2*w + 3]', '[27, 3, 3]', '[27, 27, -1/2*w^2 + 1/2*w + 1]', '[29, 29, -5/2*w^2 + 1/2*w + 29]', '[30, 30, -3/2*w^2 + 1/2*w + 17]', '[30, 30, -1/2*w^2 - 1/2*w + 6]', '[32, 4, -2*w^2 + 8*w - 4]', '[32, 4, w^2 - 5*w + 4]', '[32, 8, -3*w^2 + 2*w + 40]', '[32, 8, -2*w + 2]', '[32, 16, -1/2*w^2 + 1/2*w + 2]', '[32, 32, -1/2*w^2 - 1/2*w + 7]', '[36, 6, -2*w^2 + w + 26]', '[36, 6, -1/2*w^2 + 5/2*w + 14]', '[36, 12, -5/2*w^2 + 19/2*w - 5]', '[36, 18, -5/2*w^2 + 1/2*w + 30]', '[36, 18, -w^2 + 10]', '[36, 36, -2*w^2 - w + 19]', '[40, 10, -3*w^2 - w + 30]', '[40, 20, -4*w^2 + w + 48]', '[40, 20, -3/2*w^2 + 15/2*w - 4]', '[40, 40, w^2 - 4*w + 3]', '[41, 41, -w^2 + 3*w - 1]', '[41, 41, -1/2*w^2 - 3/2*w + 3]', '[41, 41, 2*w + 7]', '[43, 43, -7/2*w^2 - 1/2*w + 37]', '[43, 43, 1/2*w^2 - 9/2*w + 3]', '[43, 43, 1/2*w^2 - 1/2*w + 1]', '[45, 15, -w^2 - w + 7]', '[45, 45, -w^2 + w + 11]', '[47, 47, -w^2 + w + 15]', '[48, 12, w^2 - 3*w + 2]', '[48, 12, 3*w^2 - 13*w + 8]', '[48, 12, -7*w^2 + 2*w + 84]', '[48, 24, -1/2*w^2 + 5/2*w]', '[48, 48, -w + 5]', '[50, 10, 1/2*w^2 - 3/2*w + 2]', '[50, 10, -1/2*w^2 + 3/2*w + 3]', '[50, 50, -5/2*w^2 + 3/2*w + 33]', '[50, 50, -1/2*w^2 + 3/2*w + 10]', '[53, 53, -2*w^2 + 2*w + 29]', '[54, 6, -3/2*w^2 - 3/2*w + 12]', '[54, 6, -3*w^2 + 33]', '[54, 54, -3/2*w^2 + 1/2*w + 20]', '[54, 54, -1/2*w^2 + 3/2*w + 11]', '[58, 58, 1/2*w^2 - 7/2*w + 3]', '[58, 58, -3/2*w^2 + 9/2*w - 2]', '[59, 59, w^2 - w - 13]', '[60, 30, -9/2*w^2 + 5/2*w + 58]', '[60, 30, -w^2 + 2*w + 18]', '[60, 60, 5/2*w^2 - 23/2*w + 7]', '[64, 4, 4]', '[64, 8, 2*w]', '[64, 8, -w^2 + 4*w]', '[64, 8, -w^2 + w + 12]', '[64, 16, 2*w + 6]', '[64, 32, -3/2*w^2 + 3/2*w + 22]', '[64, 64, -11/2*w^2 + 5/2*w + 69]', '[67, 67, -1/2*w^2 + 1/2*w + 9]', '[71, 71, 2*w - 3]', '[72, 6, -w^2 + 5*w - 2]', '[72, 12, 2*w^2 - 7*w + 4]', '[72, 12, 1/2*w^2 - 5/2*w + 4]', '[72, 18, 2*w^2 - 10*w + 6]', '[72, 24, 1/2*w^2 + 1/2*w + 1]', '[72, 36, -3/2*w^2 + 11/2*w - 2]', '[72, 36, -2*w^2 + 3*w + 32]', '[72, 72, 1/2*w^2 - 7/2*w + 5]', '[73, 73, 3/2*w^2 - 11/2*w + 1]', '[75, 15, -w^2 + 3*w + 1]', '[75, 75, -2*w^2 + 23]', '[79, 79, -3/2*w^2 + 15/2*w - 5]', '[80, 20, w^2 - 6*w + 4]', '[80, 20, -w^2 + 3*w]', '[80, 20, -2*w + 6]', '[80, 40, -1/2*w^2 - 3/2*w + 4]', '[80, 80, -w^2 + 9]', '[81, 9, -5*w^2 + w + 59]', '[81, 9, -3/2*w^2 + 3/2*w + 21]', '[81, 81, -w^2 - w + 9]', '[82, 82, w + 5]', '[82, 82, -1/2*w^2 + 7/2*w + 17]', '[82, 82, -5/2*w^2 + 23/2*w - 6]', '[82, 82, -1/2*w^2 - 1/2*w + 10]', '[82, 82, -5/2*w^2 + 3/2*w + 32]', '[82, 82, 3/2*w^2 - 13/2*w + 5]', '[86, 86, 1/2*w^2 - 7/2*w + 4]', '[86, 86, -1/2*w^2 + 3/2*w + 4]', '[86, 86, -3/2*w^2 + 1/2*w + 16]', '[86, 86, -w^2 + 2*w + 5]', '[86, 86, -w^2 + 15]', '[86, 86, -3/2*w^2 - 3/2*w + 11]', '[87, 87, 2*w^2 - 8*w + 5]', '[90, 30, -17/2*w^2 + 7/2*w + 106]', '[90, 30, -7/2*w^2 + 29/2*w - 7]', '[90, 90, -10*w^2 + 3*w + 121]', '[90, 90, -7/2*w^2 + 1/2*w + 40]', '[94, 94, -9/2*w^2 + 39/2*w - 10]', '[94, 94, -w^2 + 6*w - 3]', '[96, 12, -w^2 + w + 8]', '[96, 12, -2*w + 4]', '[96, 24, -w^2 + 2*w]', '[96, 24, -w^2 - w + 6]', '[96, 48, -3/2*w^2 - 1/2*w + 16]', '[96, 96, -4*w^2 + w + 47]', '[97, 97, 3*w^2 - w - 35]', '[100, 10, -3/2*w^2 - 1/2*w + 14]', '[100, 10, -w^2 - 2*w + 6]', '[100, 20, -7/2*w^2 + 1/2*w + 41]', '[100, 50, 3/2*w^2 - 7/2*w + 2]', '[100, 50, 4*w^2 - 17*w + 10]', '[100, 100, -1/2*w^2 + 7/2*w - 1]', '[101, 101, 2*w - 5]', '[103, 103, 5/2*w^2 + 3/2*w - 23]', '[106, 106, 1/2*w^2 - 7/2*w + 7]', '[106, 106, -3/2*w^2 + 13/2*w - 2]', '[107, 107, 1/2*w^2 - 5/2*w - 1]', '[108, 6, -3*w^2 + 12*w - 6]', '[108, 6, 3/2*w^2 - 15/2*w + 6]', '[108, 12, -3*w + 3]', '[108, 54, -6*w^2 + w + 70]', '[108, 54, -7/2*w^2 + 31/2*w - 8]', '[108, 108, 2*w^2 - 9*w + 7]', '[109, 109, -2*w - 1]', '[109, 109, -4*w^2 + 16*w - 9]', '[109, 109, 5*w^2 - 21*w + 11]', '[116, 58, 1/2*w^2 + 3/2*w + 2]', '[116, 58, -w + 6]', '[116, 116, -1/2*w^2 + 3/2*w + 9]', '[118, 118, 9/2*w^2 + 1/2*w - 48]', '[118, 118, 12*w^2 - 3*w - 143]', '[120, 30, w^2 - 5*w + 6]', '[120, 60, 1/2*w^2 - 1/2*w + 2]', '[120, 60, -2*w^2 + 9*w - 4]', '[120, 120, -1/2*w^2 + 3/2*w + 5]', '[123, 123, -1/2*w^2 - 3/2*w + 5]', '[123, 123, -2*w^2 - 2*w + 15]', '[123, 123, 4*w^2 - 18*w + 11]', '[125, 5, 5]', '[125, 125, -3*w^2 + 3*w + 43]', '[128, 8, -2*w^2 - 2*w + 16]', '[128, 8, -2*w^2 + 24]', '[128, 8, -4*w^2 + 44]', '[128, 16, -w^2 + 8]', '[128, 16, 5*w^2 - 21*w + 12]', '[128, 32, -3*w^2 + 13*w - 6]', '[128, 64, -1/2*w^2 + 9/2*w - 2]', '[128, 128, 1/2*w^2 - 3/2*w + 3]', '[129, 129, w^2 - w + 1]', '[129, 129, -w^2 - w + 3]', '[129, 129, 2*w + 5]', '[131, 131, w^2 + w - 5]', '[134, 134, -7/2*w^2 - 3/2*w + 34]', '[134, 134, -7/2*w^2 + 33/2*w - 9]', '[135, 15, -9/2*w^2 - 3/2*w + 45]', '[135, 135, 4*w + 13]', '[137, 137, 7*w^2 - 31*w + 17]', '[137, 137, 3*w^2 + 3*w - 23]', '[137, 137, 2*w^2 - 25]', '[139, 139, 2*w^2 - 21]', '[141, 141, -7/2*w^2 + 27/2*w - 7]', '[142, 142, -1/2*w^2 - 5/2*w - 4]', '[142, 142, w^2 - 2*w - 17]', '[144, 12, -w^2 - w + 4]', '[144, 12, -w^2 + 2*w + 4]', '[144, 12, -w^2 - w + 10]', '[144, 24, -5/2*w^2 + 1/2*w + 28]', '[144, 36, 2*w + 2]', '[144, 36, -w^2 + 3*w + 4]', '[144, 36, w^2 - 4*w + 4]', '[144, 48, -5/2*w^2 - 5/2*w + 19]', '[144, 72, -1/2*w^2 + 1/2*w + 10]', '[144, 144, -5/2*w^2 + 3/2*w + 31]', '[145, 145, -w^2 + w + 1]', '[146, 146, 1/2*w^2 - 3/2*w - 6]', '[146, 146, 3/2*w^2 - 1/2*w - 21]', '[150, 30, -2*w^2 + w + 27]', '[150, 30, -1/2*w^2 + 3/2*w + 8]', '[150, 150, -2*w^2 + 7*w - 3]', '[150, 150, 5/2*w^2 - 27/2*w + 8]', '[151, 151, w^2 - w - 7]', '[157, 157, 14*w^2 - 60*w + 33]', '[158, 158, -1/2*w^2 - 1/2*w - 2]', '[158, 158, 1/2*w^2 - 3/2*w - 7]', '[159, 159, 2*w^2 - 10*w + 9]', '[160, 20, 2*w + 4]', '[160, 20, -w^2 + w + 16]', '[160, 40, -4*w^2 + 2*w + 50]', '[160, 40, -w^2 + 2*w + 8]', '[160, 80, -3/2*w^2 + 7/2*w + 28]', '[160, 160, 4*w^2 - 19*w + 11]', '[162, 18, 1/2*w^2 - 11/2*w + 4]', '[162, 18, 3/2*w^2 - 9/2*w + 3]', '[162, 18, -w^2 + 2*w + 1]', '[162, 18, 9/2*w^2 - 39/2*w + 12]', '[162, 162, -23/2*w^2 + 9/2*w + 142]', '[162, 162, -3*w^2 + 10*w - 5]', '[163, 163, -2*w - 3]', '[164, 82, -17/2*w^2 + 5/2*w + 102]', '[164, 82, 3/2*w^2 - 11/2*w + 4]', '[164, 82, -w^2 + 2]', '[164, 82, -3*w^2 + 34]', '[164, 82, -1/2*w^2 - 3/2*w + 6]', '[164, 82, -2*w^2 + 11*w - 6]', '[164, 164, -w^2 + 4*w + 1]', '[164, 164, -3*w^2 + 16*w - 9]', '[164, 164, -3/2*w^2 + 1/2*w + 15]', '[167, 167, 3/2*w^2 + 1/2*w - 17]', '[172, 86, w + 6]', '[172, 86, -3/2*w^2 + 3/2*w + 20]', '[172, 86, -2*w^2 - w + 18]', '[172, 86, -9/2*w^2 + 1/2*w + 52]', '[172, 86, -4*w^2 + 3*w + 54]', '[172, 86, 9/2*w^2 - 41/2*w + 12]', '[172, 172, -13*w^2 + 4*w + 157]', '[172, 172, -3*w^2 + 12*w - 5]', '[172, 172, -5*w^2 + 2*w + 63]', '[173, 173, -1/2*w^2 + 5/2*w - 5]', '[174, 174, -1/2*w^2 - 5/2*w + 4]', '[174, 174, -w^2 + 7]', '[177, 177, 15/2*w^2 - 7/2*w - 95]', '[180, 30, w^2 - 2*w + 2]', '[180, 30, -1/2*w^2 + 5/2*w + 2]', '[180, 60, -1/2*w^2 - 1/2*w + 11]', '[180, 90, 1/2*w^2 - 9/2*w + 4]', '[180, 90, -2*w^2 + 5*w - 2]', '[180, 180, -w^2 + 2*w + 3]', '[181, 181, -5/2*w^2 + 21/2*w - 7]', '[181, 181, w^2 + 3*w + 1]', '[181, 181, w^2 + 5*w + 5]', '[188, 94, -w^2 + 2*w + 2]', '[188, 94, -1/2*w^2 - 3/2*w + 10]', '[188, 188, -w^2 - 2*w + 7]', '[191, 191, 1/2*w^2 - 5/2*w - 13]', '[192, 12, -2*w^2 + 2*w + 28]', '[192, 24, -7*w^2 + 3*w + 88]', '[192, 24, 2*w + 8]', '[192, 24, -w^2 + 16]', '[192, 48, -8*w^2 + 34*w - 18]', '[192, 96, -5/2*w^2 + 17/2*w - 4]', '[192, 192, w^2 - 6*w + 5]', '[193, 193, -w^2 + 3*w - 3]', '[194, 194, -3*w^2 + 14*w - 9]', '[194, 194, 19/2*w^2 - 9/2*w - 120]', '[197, 197, 1/2*w^2 + 3/2*w - 7]', '[197, 197, -2*w^2 + 10*w - 5]', '[197, 197, -9/2*w^2 + 1/2*w + 51]', '[199, 199, 2*w - 9]', '[199, 199, 3/2*w^2 - 3/2*w - 13]', '[199, 199, w^2 + w - 11]', '[200, 10, 7*w^2 - 31*w + 18]', '[200, 20, -6*w^2 + 3*w + 76]', '[200, 20, 3/2*w^2 - 19/2*w + 6]', '[200, 40, -3/2*w^2 + 9/2*w - 1]', '[200, 50, -w^2 + w + 6]', '[200, 100, -3/2*w^2 - 1/2*w + 20]', '[200, 100, -3*w + 4]', '[200, 200, -3/2*w^2 - 3/2*w + 13]', '[201, 201, -5*w^2 + 3*w + 65]', '[202, 202, 1/2*w^2 - 3/2*w - 12]', '[202, 202, 3*w^2 - 2*w - 39]', '[205, 205, -21/2*w^2 + 9/2*w + 131]', '[205, 205, 1/2*w^2 + 7/2*w + 5]', '[205, 205, -w^2 + 5*w - 1]', '[206, 206, -w^2 + 6*w - 7]', '[206, 206, 5/2*w^2 - 19/2*w + 4]', '[212, 106, -3/2*w^2 - 1/2*w + 18]', '[212, 106, -w^2 + 6]', '[212, 212, -9/2*w^2 + 3/2*w + 53]', '[213, 213, 3/2*w^2 + 1/2*w - 13]', '[214, 214, 5/2*w^2 + 1/2*w - 27]', '[214, 214, 3/2*w^2 + 3/2*w - 10]', '[215, 215, -3/2*w^2 + 3/2*w + 19]', '[215, 215, -11/2*w^2 + 3/2*w + 65]', '[215, 215, -1/2*w^2 - 3/2*w + 9]', '[216, 6, 6]', '[216, 12, 3*w]', '[216, 12, -3/2*w^2 + 3/2*w + 18]', '[216, 24, 3*w + 9]', '[216, 54, -w^2 + w + 2]', '[216, 108, -2*w^2 + 7*w]', '[216, 108, -1/2*w^2 - 3/2*w + 8]', '[216, 216, -2*w^2 + w + 21]', '[218, 218, 3*w^2 + 2*w - 27]', '[218, 218, 1/2*w^2 + 9/2*w - 4]', '[218, 218, 1/2*w^2 - 7/2*w]', '[218, 218, 5/2*w^2 + 9/2*w - 12]', '[218, 218, w^2 - 3]', '[218, 218, w - 7]', '[219, 219, w^2 + w - 15]', '[225, 15, 1/2*w^2 + 7/2*w + 7]', '[225, 45, -3/2*w^2 - 1/2*w + 19]', '[225, 75, 2*w^2 - 10*w + 7]', '[225, 225, -9/2*w^2 + 41/2*w - 11]', '[227, 227, -1/2*w^2 - 3/2*w - 3]', '[232, 58, -5*w^2 + w + 58]', '[232, 116, -9/2*w^2 - 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w + 118]', '[1944, 972, -6*w^2 - 7*w + 44]', '[1944, 972, 17/2*w^2 - 69/2*w + 20]', '[1944, 1944, -5*w^2 + 22*w - 9]', '[1949, 1949, w^2 + w - 23]', '[1949, 1949, 3*w^2 - 9*w + 1]', '[1949, 1949, 4*w^2 + 4*w - 29]', '[1954, 1954, -29/2*w^2 + 127/2*w - 34]', '[1954, 1954, -3*w^2 + 20*w - 11]', '[1956, 978, 3/2*w^2 + 5/2*w - 20]', '[1956, 978, 2*w^2 - w - 6]', '[1956, 1956, 7/2*w^2 + 15/2*w - 17]', '[1959, 1959, 3/2*w^2 + 5/2*w - 23]', '[1962, 654, 5/2*w^2 + 5/2*w - 13]', '[1962, 654, 17/2*w^2 - 55/2*w + 14]', '[1962, 654, -19/2*w^2 + 77/2*w - 22]', '[1962, 654, 5/2*w^2 + 17/2*w - 10]', '[1962, 654, -7/2*w^2 + 41/2*w - 13]', '[1962, 654, 11/2*w^2 - 49/2*w + 11]', '[1962, 1962, -2*w^2 - 3*w - 1]', '[1962, 1962, 15/2*w^2 + 19/2*w - 52]', '[1962, 1962, -11*w^2 + 50*w - 29]', '[1962, 1962, -3/2*w^2 + 13/2*w - 10]', '[1962, 1962, 8*w^2 - 41*w + 23]', '[1962, 1962, 15/2*w^2 - 13/2*w - 104]', '[1964, 982, w^2 - 4*w - 10]', '[1964, 982, 5/2*w^2 - 1/2*w - 38]', '[1964, 1964, -5*w - 19]', '[1965, 1965, 5/2*w^2 - 13/2*w - 3]', '[1968, 492, -11*w^2 + 5*w + 136]', '[1968, 492, -3*w^2 + 2*w + 44]', '[1968, 492, 7*w^2 - 33*w + 20]', '[1968, 492, -11*w^2 + 8*w + 148]', '[1968, 492, -w^2 + 10*w - 4]', '[1968, 492, w^2 - 3*w + 8]', '[1968, 492, -5*w^2 + 7*w + 78]', '[1968, 492, -5*w^2 + 19*w - 6]', '[1968, 492, -2*w^2 + 4*w + 18]', '[1968, 984, -5/2*w^2 + 5/2*w + 2]', '[1968, 984, 21/2*w^2 - 97/2*w + 28]', '[1968, 984, 1/2*w^2 + 11/2*w + 8]', '[1968, 1968, -2*w^2 + 3*w + 35]', '[1968, 1968, -1/2*w^2 - 9/2*w + 11]', '[1968, 1968, -7*w^2 + 28*w - 13]', '[1970, 1970, w^2 + 8*w + 17]', '[1970, 1970, -27/2*w^2 + 13/2*w + 172]', '[1970, 1970, 5/2*w^2 - 23/2*w + 2]', '[1970, 1970, -5/2*w^2 + 3/2*w + 38]', '[1970, 1970, -9/2*w^2 + 27/2*w + 95]', '[1970, 1970, -1/2*w^2 + 11/2*w - 17]', '[1971, 219, 9/2*w^2 - 33/2*w + 3]', '[1971, 1971, -8*w^2 + 34*w - 21]', '[1975, 395, 7/2*w^2 + 9/2*w - 21]', '[1975, 1975, -11/2*w^2 + 15/2*w - 3]', '[1982, 1982, 13*w^2 - 6*w - 165]', '[1982, 1982, 7/2*w^2 - 9/2*w - 52]', '[1983, 1983, 5/2*w^2 + 3/2*w - 31]', '[1985, 1985, 7*w^2 - w - 85]', '[1986, 1986, -11/2*w^2 + 21/2*w - 5]', '[1986, 1986, -27/2*w^2 + 113/2*w - 32]', '[1987, 1987, 17/2*w^2 - 9/2*w - 107]', '[1990, 1990, 9/2*w^2 - 19/2*w - 27]', '[1990, 1990, 13/2*w^2 - 51/2*w + 8]', '[1990, 1990, 3/2*w^2 - 13/2*w - 4]', '[1990, 1990, -5/2*w^2 + 27/2*w - 18]', '[1990, 1990, -2*w^2 + 15*w - 27]', '[1990, 1990, w^2 + 2*w - 25]', '[1993, 1993, -5/2*w^2 - 3/2*w + 33]', '[1993, 1993, 2*w^2 + 2*w - 37]', '[1993, 1993, 2*w^2 - 2*w - 9]', '[1996, 998, 3/2*w^2 - 7/2*w + 6]', '[1996, 998, 4*w^2 - 19*w + 18]', '[1996, 1996, -3/2*w^2 + 9/2*w + 11]', '[1999, 1999, 6*w^2 - 26*w + 11]', '[2000, 20, -5*w^2 - 5*w + 40]', '[2000, 20, -5*w^2 + 60]', '[2000, 20, -10*w^2 + 110]', '[2000, 40, 25/2*w^2 - 105/2*w + 30]', '[2000, 80, -15/2*w^2 + 65/2*w - 15]', '[2000, 500, 2*w^2 + 2]', '[2000, 500, -5*w^2 + 24*w - 12]', '[2000, 500, 3*w^2 - 13*w + 12]', '[2000, 1000, -1/2*w^2 + 9/2*w + 6]', '[2000, 2000, -3/2*w^2 + 1/2*w + 27]', '[2003, 2003, -1/2*w^2 + 1/2*w - 9]', '[2004, 1002, 11/2*w^2 - 7/2*w - 66]', '[2004, 1002, w^2 - 22]', '[2004, 2004, 2*w^2 - 5*w - 37]', '[2005, 2005, 3/2*w^2 + 5/2*w - 21]', '[2008, 502, 2*w^2 - 2*w - 6]', '[2008, 502, 9*w^2 - 37*w + 18]', '[2008, 502, -9*w^2 + 9*w + 130]', '[2008, 1004, 3/2*w^2 + 5/2*w - 22]', '[2008, 1004, 20*w^2 - 9*w - 252]', '[2008, 1004, -13/2*w^2 + 49/2*w - 12]', '[2008, 1004, -9/2*w^2 + 45/2*w - 20]', '[2008, 1004, 9*w - 8]', '[2008, 1004, -18*w^2 + 7*w + 224]', '[2008, 2008, 3*w^2 + 6*w - 17]', '[2008, 2008, 3*w^2 - 16*w + 13]', '[2008, 2008, -1/2*w^2 + 15/2*w - 9]', '[2010, 2010, -11/2*w^2 - 15/2*w + 37]', '[2010, 2010, -9/2*w^2 - 1/2*w + 52]', '[2017, 2017, -5/2*w^2 + 29/2*w - 17]', '[2019, 2019, -3/2*w^2 + 7/2*w + 17]', '[2020, 1010, 2*w^2 - w - 10]', '[2020, 1010, 5/2*w^2 + 3/2*w - 32]', '[2020, 2020, 8*w^2 - 3*w - 93]', '[2021, 2021, -3/2*w^2 - 13/2*w + 9]', '[2021, 2021, 1/2*w^2 + 7/2*w + 11]', '[2021, 2021, -1/2*w^2 + 21/2*w - 5]', '[2022, 2022, 13/2*w^2 + 1/2*w - 72]', '[2022, 2022, 18*w^2 - 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39]', '[9963, 1107, -9/2*w^2 + 21/2*w + 15]', '[9963, 9963, 5*w^2 - 21*w + 19]', '[9963, 9963, -85/2*w^2 + 33/2*w + 527]', '[9963, 9963, 1/2*w^2 + 15/2*w + 25]', '[9964, 4982, -9*w^2 - 2*w + 90]', '[9964, 4982, -45/2*w^2 + 9/2*w + 266]', '[9964, 9964, -133/2*w^2 + 43/2*w + 807]', '[9965, 9965, 15/2*w^2 - 27/2*w - 127]', '[9965, 9965, -34*w^2 + 18*w + 437]', '[9965, 9965, 83/2*w^2 - 23/2*w - 499]', '[9967, 9967, 14*w - 5]', '[9972, 1662, 5*w^2 + 2*w - 62]', '[9972, 1662, 13/2*w^2 + 19/2*w - 44]', '[9972, 3324, 11*w^2 + 2*w - 113]', '[9972, 4986, 2*w^2 - 7*w - 18]', '[9972, 4986, 9/2*w^2 - 1/2*w - 68]', '[9972, 9972, 1/2*w^2 - 15/2*w - 35]', '[9973, 9973, -15*w^2 + 69*w - 41]', '[9973, 9973, -33*w^2 + 143*w - 83]', '[9973, 9973, 5/2*w^2 - 17/2*w - 15]', '[9974, 9974, 7/2*w^2 - 17/2*w - 64]', '[9974, 9974, 16*w^2 - 9*w - 209]', '[9976, 2494, -6*w^2 - 2*w + 54]', '[9976, 2494, 8*w + 10]', '[9976, 2494, -12*w + 14]', '[9976, 4988, -5/2*w^2 + 5/2*w + 46]', '[9976, 4988, -4*w^2 + 11*w + 20]', '[9976, 4988, -4*w^2 - 9*w + 24]', '[9976, 4988, -27/2*w^2 + 3/2*w + 158]', '[9976, 4988, 6*w^2 - 31*w + 28]', '[9976, 4988, -7/2*w^2 + 7/2*w + 18]', '[9976, 9976, -13*w^2 - 12*w + 105]', '[9976, 9976, -9/2*w^2 - 5/2*w + 61]', '[9976, 9976, -23/2*w^2 + 13/2*w + 143]', '[9980, 4990, -53/2*w^2 + 17/2*w + 318]', '[9980, 4990, -9*w^2 + 106]', '[9980, 9980, -18*w^2 - w + 195]', '[9981, 3327, 38*w^2 - 16*w - 473]', '[9981, 9981, 31/2*w^2 - 3/2*w - 179]', '[9986, 9986, 14*w^2 - 9*w - 183]', '[9986, 9986, 3/2*w^2 - 17/2*w - 9]', '[9986, 9986, -13/2*w^2 - 17/2*w + 6]', '[9986, 9986, 5/2*w^2 - 15/2*w - 56]', '[9986, 9986, -7/2*w^2 + 9/2*w - 6]', '[9986, 9986, -3/2*w^2 - 23/2*w + 1]', '[9987, 9987, 31/2*w^2 - 15/2*w - 191]', '[9991, 9991, 27/2*w^2 - 107/2*w + 27]', '[9993, 9993, 7/2*w^2 - 51/2*w + 13]', '[9993, 9993, 43/2*w^2 - 15/2*w - 269]', '[9993, 9993, 5*w^2 - 9*w - 29]', '[9995, 9995, 11/2*w^2 + 1/2*w - 51]', '[9998, 9998, 4*w^2 - 13*w - 13]', '[9998, 9998, -9/2*w^2 + 35/2*w - 16]', '[10000, 100, -23*w^2 + 9*w + 288]', '[10000, 100, -7*w^2 + 6*w + 92]', '[10000, 100, 5*w^2 - 30*w + 20]', '[10000, 100, -5*w^2 + 15*w]', '[10000, 100, -11*w^2 + 13*w + 166]', '[10000, 100, -10*w + 30]', '[10000, 200, -5/2*w^2 - 15/2*w + 20]', '[10000, 200, -31/2*w^2 + 123/2*w - 32]', '[10000, 400, -5*w^2 + 45]', '[10000, 400, 8*w^2 - 39*w + 27]', '[10000, 2500, -18*w^2 + 4*w + 210]', '[10000, 2500, -5*w^2 - 6*w + 28]', '[10000, 2500, -7*w^2 - 3*w + 72]', '[10000, 5000, -31/2*w^2 - 21/2*w + 136]', '[10000, 10000, 13*w^2 - 48*w + 27]'], 'label': '3.3.1772.1', 'narrow_class_no': 1, 'primes': ['[2, 2, -1/2*w^2 - 1/2*w + 4]', '[2, 2, -w^2 + 11]', '[3, 3, -1/2*w^2 + 1/2*w + 7]', '[5, 5, -3/2*w^2 - 1/2*w + 15]', '[9, 3, -1/2*w^2 + 5/2*w - 1]', '[25, 5, 7/2*w^2 - 31/2*w + 9]', '[29, 29, -5/2*w^2 + 1/2*w + 29]', '[41, 41, -w^2 + 3*w - 1]', '[41, 41, -1/2*w^2 - 3/2*w + 3]', '[41, 41, 2*w + 7]', '[43, 43, -7/2*w^2 - 1/2*w + 37]', '[43, 43, 1/2*w^2 - 9/2*w + 3]', '[43, 43, 1/2*w^2 - 1/2*w + 1]', '[47, 47, -w^2 + w + 15]', '[53, 53, -2*w^2 + 2*w + 29]', '[59, 59, w^2 - w - 13]', '[67, 67, -1/2*w^2 + 1/2*w + 9]', '[71, 71, 2*w - 3]', '[73, 73, 3/2*w^2 - 11/2*w + 1]', '[79, 79, -3/2*w^2 + 15/2*w - 5]', '[97, 97, 3*w^2 - w - 35]', '[101, 101, 2*w - 5]', '[103, 103, 5/2*w^2 + 3/2*w - 23]', '[107, 107, 1/2*w^2 - 5/2*w - 1]', '[109, 109, -2*w - 1]', '[109, 109, -4*w^2 + 16*w - 9]', '[109, 109, 5*w^2 - 21*w + 11]', '[131, 131, w^2 + w - 5]', '[137, 137, 7*w^2 - 31*w + 17]', '[137, 137, 3*w^2 + 3*w - 23]', '[137, 137, 2*w^2 - 25]', '[139, 139, 2*w^2 - 21]', '[151, 151, w^2 - w - 7]', '[157, 157, 14*w^2 - 60*w + 33]', '[163, 163, -2*w - 3]', '[167, 167, 3/2*w^2 + 1/2*w - 17]', '[173, 173, -1/2*w^2 + 5/2*w - 5]', '[181, 181, -5/2*w^2 + 21/2*w - 7]', '[181, 181, w^2 + 3*w + 1]', '[181, 181, w^2 + 5*w + 5]', '[191, 191, 1/2*w^2 - 5/2*w - 13]', '[193, 193, -w^2 + 3*w - 3]', '[197, 197, 1/2*w^2 + 3/2*w - 7]', '[197, 197, -2*w^2 + 10*w - 5]', '[197, 197, -9/2*w^2 + 1/2*w + 51]', '[199, 199, 2*w - 9]', '[199, 199, 3/2*w^2 - 3/2*w - 13]', '[199, 199, w^2 + w - 11]', '[227, 227, -1/2*w^2 - 3/2*w - 3]', '[233, 233, -1/2*w^2 + 1/2*w - 3]', '[233, 233, -10*w^2 + 44*w - 25]', '[233, 233, 5*w^2 - 21*w + 9]', '[241, 241, 7/2*w^2 - 27/2*w + 3]', '[251, 251, w^2 - w - 3]', '[251, 251, 9/2*w^2 - 37/2*w + 9]', '[251, 251, -9/2*w^2 + 9/2*w + 65]', '[257, 257, 1/2*w^2 - 1/2*w - 11]', '[263, 263, -3*w^2 + 13*w - 9]', '[269, 269, 3/2*w^2 - 3/2*w - 23]', '[271, 271, 4*w^2 - 45]', '[277, 277, -1/2*w^2 + 9/2*w - 5]', '[307, 307, -w^2 + 5*w - 7]', '[311, 311, 13/2*w^2 - 57/2*w + 15]', '[313, 313, -9/2*w^2 + 41/2*w - 13]', '[317, 317, 4*w - 1]', '[331, 331, -w^2 - w - 1]', '[337, 337, 5/2*w^2 - 21/2*w + 3]', '[343, 7, -7]', '[347, 347, 3*w^2 - 11*w + 5]', '[353, 353, -21/2*w^2 + 89/2*w - 25]', '[359, 359, 9/2*w^2 - 5/2*w - 57]', '[367, 367, 9/2*w^2 - 5/2*w - 59]', '[379, 379, 4*w^2 - 18*w + 9]', '[379, 379, -9/2*w^2 + 37/2*w - 11]', '[379, 379, -3/2*w^2 + 3/2*w + 1]', '[383, 383, 5*w^2 - w - 61]', '[397, 397, -5/2*w^2 + 25/2*w - 13]', '[401, 401, -9*w^2 + 39*w - 23]', '[419, 419, 11*w^2 - 7*w - 145]', '[421, 421, -3*w^2 - w + 31]', '[433, 433, 7/2*w^2 - 31/2*w + 7]', '[439, 439, 3*w^2 - w - 33]', '[439, 439, -3/2*w^2 + 7/2*w - 3]', '[439, 439, 3/2*w^2 + 1/2*w - 11]', '[443, 443, -2*w^2 + 10*w - 11]', '[443, 443, 13*w^2 - 57*w + 33]', '[449, 449, 3/2*w^2 - 3/2*w - 11]', '[457, 457, 2*w^2 - 19]', '[457, 457, 5/2*w^2 - 17/2*w - 1]', '[457, 457, 3/2*w^2 + 9/2*w + 1]', '[461, 461, 3/2*w^2 - 7/2*w - 1]', '[463, 463, 2*w^2 - 6*w - 3]', '[463, 463, 5/2*w^2 - 5/2*w - 37]', '[463, 463, 3/2*w^2 + 1/2*w - 3]', '[479, 479, -11/2*w^2 + 51/2*w - 15]', '[491, 491, 6*w^2 - 67]', '[499, 499, -7/2*w^2 + 3/2*w + 39]', '[521, 521, 7*w^2 - 29*w + 13]', '[541, 541, 5*w^2 + 3*w - 45]', '[547, 547, 7/2*w^2 - 27/2*w + 5]', '[547, 547, 15/2*w^2 - 3/2*w - 89]', '[547, 547, 1/2*w^2 + 3/2*w - 15]', '[563, 563, 3/2*w^2 - 11/2*w - 3]', '[577, 577, 2*w^2 + 2*w - 13]', '[587, 587, 5/2*w^2 + 3/2*w - 21]', '[593, 593, -1/2*w^2 - 3/2*w - 5]', '[599, 599, 5/2*w^2 - 1/2*w - 35]', '[601, 601, 24*w^2 - 104*w + 57]', '[607, 607, w^2 + 3*w + 3]', '[619, 619, -w^2 + w - 3]', '[619, 619, 10*w^2 - 111]', '[619, 619, -5*w^2 + 23*w - 15]', '[631, 631, 4*w^2 - 4*w - 57]', '[647, 647, -7*w^2 + 33*w - 19]', '[653, 653, 3*w^2 - 11*w + 3]', '[661, 661, 2*w^2 - 6*w - 1]', '[673, 673, 2*w^2 - 8*w + 7]', '[677, 677, -w^2 + 7*w - 9]', '[683, 683, 9/2*w^2 + 11/2*w - 31]', '[683, 683, -4*w^2 + 2*w + 53]', '[683, 683, 8*w + 27]', '[691, 691, 15/2*w^2 + 1/2*w - 81]', '[709, 709, 3/2*w^2 - 7/2*w - 27]', '[727, 727, 9/2*w^2 - 1/2*w - 55]', '[733, 733, -15/2*w^2 + 7/2*w + 93]', '[743, 743, 1/2*w^2 + 7/2*w - 7]', '[751, 751, 3*w^2 - w - 41]', '[769, 769, 17/2*w^2 - 77/2*w + 21]', '[773, 773, 33/2*w^2 - 13/2*w - 205]', '[787, 787, 13*w^2 - 57*w + 31]', '[797, 797, -5*w^2 + 19*w - 11]', '[809, 809, -4*w - 11]', '[811, 811, w^2 + 3*w - 9]', '[811, 811, w^2 - w - 19]', '[811, 811, 4*w - 9]', '[823, 823, 19/2*w^2 - 79/2*w + 21]', '[829, 829, 3/2*w^2 - 3/2*w - 7]', '[829, 829, w^2 - 3*w - 9]', '[829, 829, 3/2*w^2 + 5/2*w - 13]', '[841, 29, -7/2*w^2 + 23/2*w - 5]', '[853, 853, 4*w^2 - 47]', '[853, 853, 5/2*w^2 - 5/2*w - 33]', '[853, 853, -8*w^2 + 36*w - 23]', '[863, 863, 3/2*w^2 - 3/2*w - 5]', '[877, 877, -3/2*w^2 + 15/2*w - 1]', '[883, 883, 3/2*w^2 - 3/2*w - 25]', '[883, 883, 15/2*w^2 - 7/2*w - 91]', '[883, 883, -11/2*w^2 + 47/2*w - 15]', '[887, 887, 1/2*w^2 + 23/2*w + 33]', '[911, 911, -6*w - 19]', '[929, 929, 9/2*w^2 - 33/2*w + 1]', '[947, 947, 1/2*w^2 - 9/2*w - 19]', '[967, 967, 8*w^2 + 4*w - 75]', '[971, 971, 9/2*w^2 + 7/2*w - 39]', '[971, 971, -5*w^2 + 3*w + 63]', '[971, 971, 37/2*w^2 - 157/2*w + 43]', '[977, 977, -w^2 + 3*w + 23]', '[991, 991, 2*w^2 - 2*w - 15]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [8, -12, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1772, 'disc_rad': 886, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 1], [1, 1]]], [5, [[2, 1], [1, 1]]], [7, [[3, 1]]], [11, [[3, 1]]], [13, [[3, 1]]], [17, [[3, 1]]], [19, [[3, 1]]], [23, [[3, 1]]], [29, [[2, 1], [1, 1]]], [31, [[3, 1]]], [37, [[3, 1]]], [41, [[1, 3]]], [43, [[1, 3]]], [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': [6, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 42.09513035969837, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1772.1', 'local_algs': ['2.1.0.1', '2.2.2.2', 'm443.1.1.0', 'm443.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 443], 'rd': 12.1009993938, 'regulator': {'__RealLiteral__': 0, 'data': '15.3713537184', 'prec': 44}, 'res': {'gal': ['-8,-8,82,-42,-41,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{2} - \\frac{1}{2} a - 5 \\)', '\\( 27 a^{2} - 9 a - 329 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2 - 1/2*a']}