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hmf_forms • Show schema
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{'deg': 3, 'dimension': 5, 'disc': 469, 'field_bad_primes': [7, 67], 'field_label': '3.3.469.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.469.1-28.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2, 7], 'level_ideal': '[28, 14, w^2 + w - 7]', 'level_label': '28.1', 'level_norm': 28, 'parallel_weight': 2, 'short_label': '28.1-b', 'weight': '[2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[4, 2, -w^2 - w + 3]', -1], ['[7, 7, w + 1]', 1]], 'hecke_eigenvalues': ['e', 1, -1, '-e^3 + e^2 + 6*e - 4', 'e^4 - 8*e^2 - e + 10', '-e^4 - 2*e^3 + 10*e^2 + 13*e - 20', '-e^3 - e^2 + 6*e + 2', '2*e - 2', '2*e^3 - 12*e + 2', '-2*e^4 - e^3 + 15*e^2 + 6*e - 16', '2*e^4 + 2*e^3 - 18*e^2 - 16*e + 32', '2*e^4 + 2*e^3 - 16*e^2 - 14*e + 22', 'e^3 - 3*e^2 - 6*e + 12', '2*e^3 - 10*e + 6', '-e^4 - 2*e^3 + 8*e^2 + 9*e - 10', 'e^3 - e^2 - 6*e + 8', 'e^4 - 6*e^2 - e + 8', '2*e^4 + 2*e^3 - 16*e^2 - 12*e + 22', '2*e^4 + 2*e^3 - 18*e^2 - 10*e + 32', '2*e^3 - 6*e^2 - 14*e + 30', '2*e^4 + e^3 - 17*e^2 - 6*e + 20', 'e^4 - 12*e^2 + e + 22', '2*e + 4', 'e^4 - 2*e^3 - 4*e^2 + 11*e - 10', '-e^4 + 10*e^2 + 5*e - 20', '-4*e^3 + 4*e^2 + 24*e - 20', '-6*e - 2', '2*e^3 - 4*e^2 - 10*e + 24', '2*e^3 - 10*e + 6', '-2*e^4 + 14*e^2 - 10', '-4*e^4 - 3*e^3 + 31*e^2 + 18*e - 42', '-2*e^4 - 2*e^3 + 18*e^2 + 16*e - 36', '-2*e^2 - 2*e + 12', 'e^4 - 6*e^2 - 3*e - 4', 'e^3 - 3*e^2 - 6*e + 12', '-3*e^4 - 2*e^3 + 26*e^2 + 11*e - 32', '4*e^2 - 22', '-2*e^4 + e^3 + 13*e^2 - 6*e - 10', '-2*e^4 - e^3 + 13*e^2 + 2*e - 10', '-2*e^4 - 3*e^3 + 19*e^2 + 14*e - 32', '-3*e^4 + 2*e^3 + 22*e^2 - 7*e - 12', '-3*e^4 + 22*e^2 + 5*e - 16', '-e^4 - 2*e^3 + 10*e^2 + 7*e - 28', '4*e^4 + 2*e^3 - 32*e^2 - 12*e + 40', '-2*e^4 - 2*e^3 + 20*e^2 + 10*e - 42', '6*e^3 - 2*e^2 - 36*e + 12', '-2*e^4 - 4*e^3 + 16*e^2 + 28*e - 34', '-2*e^3 + 6*e^2 + 14*e - 24', '4*e^4 + 2*e^3 - 30*e^2 - 14*e + 38', '-2*e^4 - 4*e^3 + 18*e^2 + 26*e - 40', '4*e^4 + 4*e^3 - 36*e^2 - 20*e + 58', '-2*e^4 - 2*e^3 + 14*e^2 + 8*e + 2', '5*e^3 - 7*e^2 - 30*e + 30', '-2*e^2 + 8*e + 10', '4*e^4 + 4*e^3 - 32*e^2 - 24*e + 38', '5*e^3 - 5*e^2 - 30*e + 26', '6*e^4 + 4*e^3 - 50*e^2 - 26*e + 68', '2*e^4 - 10*e^2 - 10', '-6*e^2 - 8*e + 40', '-e^4 + 8*e^2 + e - 26', '-4*e^3 + 8*e^2 + 26*e - 32', 'e^4 - 4*e^3 - 8*e^2 + 25*e + 2', '2*e^4 - 14*e^2 - 10*e + 6', '4*e^4 - e^3 - 29*e^2 + 10*e + 38', '-2*e^4 + 2*e^3 + 16*e^2 - 8*e - 18', '-2*e^4 + 2*e^3 + 20*e^2 - 12*e - 32', '4*e^4 + 6*e^3 - 36*e^2 - 48*e + 68', '-4*e^4 - 7*e^3 + 39*e^2 + 42*e - 70', '7*e^3 - 3*e^2 - 38*e + 14', '2*e^4 - 10*e^2 - 2*e - 8', '6*e^4 + 2*e^3 - 50*e^2 - 22*e + 66', '4*e^3 - 4*e^2 - 20*e + 26', '-2*e^4 - e^3 + 13*e^2 - 2*e - 10', '-2*e^4 - 3*e^3 + 21*e^2 + 18*e - 38', '2*e^4 - 2*e^3 - 18*e^2 + 10*e + 22', '4*e^4 + 6*e^3 - 36*e^2 - 32*e + 60', '-6*e^3 + 2*e^2 + 34*e - 8', '-2*e^4 - 4*e^3 + 18*e^2 + 32*e - 34', '2*e^4 - 16*e^2 - 6*e + 12', '4*e^3 - 36*e', '3*e^4 + 2*e^3 - 28*e^2 - 13*e + 38', '-2*e^4 + 14*e^2 + 8*e - 4', 'e^4 - 6*e^2 - 3*e - 12', '2*e^4 + 4*e^3 - 14*e^2 - 24*e + 2', '-5*e^4 - 2*e^3 + 44*e^2 + 13*e - 66', '-2*e^4 + 2*e^3 + 14*e^2 - 14*e', '8*e^2 + 8*e - 36', '8*e^2 + 8*e - 34', '5*e^3 - 7*e^2 - 38*e + 30', '2*e^4 - e^3 - 19*e^2 + 6*e + 34', '-4*e^4 - 2*e^3 + 36*e^2 + 22*e - 52', '4*e^4 + 4*e^3 - 34*e^2 - 26*e + 56', '-3*e^4 + 30*e^2 + 7*e - 48', '-2*e^4 - 6*e^3 + 28*e^2 + 38*e - 78', '-2*e^4 - 4*e^3 + 16*e^2 + 20*e - 2', '5*e^3 - 7*e^2 - 26*e + 46', '6*e^4 + 8*e^3 - 48*e^2 - 48*e + 74', '-e^4 + 2*e^3 + 14*e^2 - 9*e - 20', '-4*e^2 + 36', '-4*e^4 + 3*e^3 + 25*e^2 - 18*e - 14', '4*e^4 + 4*e^3 - 30*e^2 - 14*e + 28', '-5*e^4 + 38*e^2 - e - 36', '-3*e^4 - 2*e^3 + 24*e^2 + 21*e - 38', '4*e^4 + 4*e^3 - 30*e^2 - 20*e + 36', '4*e^4 + 2*e^3 - 22*e^2 - 14*e + 8', '2*e^4 + 2*e^3 - 22*e^2 - 14*e + 58', '-4*e^3 + 4*e^2 + 28*e - 36', '-2*e^4 + 14*e^2 + 2*e - 8', '-3*e^4 - 4*e^3 + 24*e^2 + 27*e - 30', '-3*e^4 - 6*e^3 + 34*e^2 + 33*e - 80', '-3*e^3 + e^2 + 14*e - 22', '-2*e^4 - 6*e^3 + 12*e^2 + 42*e - 12', '-2*e^4 + 2*e^3 + 10*e^2 - 16*e + 14', '-4*e^4 + 5*e^3 + 31*e^2 - 22*e - 38', '2*e^4 + e^3 - 21*e^2 - 10*e + 12', '6*e^4 + 7*e^3 - 53*e^2 - 42*e + 72', '-2*e^4 - e^3 + 15*e^2 + 6*e - 44', '-4*e^4 + 6*e^3 + 30*e^2 - 28*e - 18', '2*e^4 - e^3 - 15*e^2 - 6*e - 2', '-8*e^4 - 2*e^3 + 60*e^2 + 16*e - 66', '4*e^4 - 32*e^2 + 6*e + 50', '-4*e^4 - 4*e^3 + 32*e^2 + 30*e - 66', '-2*e^4 + 7*e^3 + 11*e^2 - 42*e + 4', '-2*e^4 - 2*e^3 + 10*e^2 + 24*e + 4', '-2*e^4 - 4*e^3 + 22*e^2 + 22*e - 24', '-4*e - 34', '2*e^4 + 4*e^3 - 28*e^2 - 38*e + 74', '8*e^3 - 12*e^2 - 52*e + 58', '-e^4 - 6*e^3 + 14*e^2 + 33*e - 20', '2*e^4 + 5*e^3 - 17*e^2 - 42*e + 22', '-4*e^4 + 4*e^3 + 24*e^2 - 24*e + 4', '2*e^4 + 2*e^3 - 20*e^2 - 12*e + 44', '-6*e^4 - 2*e^3 + 46*e^2 + 14*e - 30', '4*e^4 + 2*e^3 - 30*e^2 - 18*e + 36', '4*e^3 - 8*e^2 - 14*e + 50', '-2*e^4 - 9*e^3 + 33*e^2 + 58*e - 90', '-2*e^4 + 4*e^3 + 12*e^2 - 26*e - 4', '2*e^4 + 2*e^3 - 12*e^2 - 4*e + 6', '6*e^3 - 8*e^2 - 38*e + 24', '-2*e^3 - 8*e^2 + 6*e + 26', '5*e^4 - 2*e^3 - 30*e^2 + 15*e + 8', '-5*e^4 - 8*e^3 + 48*e^2 + 55*e - 98', '4*e^4 + 2*e^3 - 26*e^2 - 2*e + 16', '-3*e^4 + 2*e^3 + 22*e^2 - 3*e - 16', '-4*e^4 + 2*e^3 + 28*e^2 - 6*e - 34', '-e^4 - 6*e^3 + 16*e^2 + 43*e - 30', '-e^4 - 2*e^3 + 8*e^2 + 7*e - 2', '4*e^4 - 32*e^2 - 16*e + 36', '4*e^3 - 8*e^2 - 20*e + 38', '9*e^3 - 7*e^2 - 62*e + 24', '-6*e^4 - 8*e^3 + 58*e^2 + 62*e - 112', '-e^4 - 2*e^3 + 16*e^2 + 11*e - 66', '6*e^4 + 15*e^3 - 59*e^2 - 90*e + 122', '7*e^4 - 46*e^2 - 3*e + 36', '6*e^3 + 4*e^2 - 34*e - 24', '-2*e^4 + 2*e^3 + 14*e^2 - 8*e - 18', '-4*e^4 + 36*e^2 + 12*e - 46'], 'hecke_polynomial': 'x^5 - 10*x^3 + 2*x^2 + 22*x - 13', 'label': '3.3.469.1-28.1-b'}
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hmf_fields • Show schema
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{'degree': 3, 'discriminant': 469, 'ideals': ['[1, 1, 1]', '[2, 2, -w + 2]', '[4, 2, -w^2 - w + 3]', '[4, 4, -w]', '[7, 7, w + 1]', '[7, 7, -w + 3]', '[8, 2, 2]', '[8, 8, -w^2 + w + 4]', '[11, 11, -w^2 + 3]', '[14, 14, w^2 - 2]', '[14, 14, -w^2 + w + 2]', '[16, 4, -2*w + 4]', '[16, 4, w^2 - w - 5]', '[16, 16, w^2 + w - 4]', '[17, 17, w + 3]', '[19, 19, w^2 - 7]', '[22, 22, -w^2 + 2*w + 2]', '[27, 3, 3]', '[28, 14, w^2 + w - 7]', '[28, 14, -w^2 - w + 5]', '[28, 28, -2*w^2 + w + 8]', '[28, 28, -w^2 - w]', '[32, 4, -2*w^2 - 2*w + 6]', '[32, 8, -2*w]', '[32, 32, w - 4]', '[34, 34, -w^2 - w + 6]', '[38, 38, -2*w^2 - w + 6]', '[43, 43, -2*w - 5]', '[44, 22, w^2 + w - 9]', '[44, 44, w^2 + 2*w - 4]', '[47, 47, 2*w + 3]', '[49, 7, w^2 + 2*w + 1]', '[49, 7, -w^2 + 2*w + 3]', '[49, 49, -2*w - 1]', '[53, 53, 3*w^2 + 2*w - 9]', '[54, 6, -3*w + 6]', '[56, 14, 2*w + 2]', '[56, 14, -2*w + 6]', '[56, 56, -w - 4]', '[56, 56, -w^2 + 8]', '[59, 59, 2*w^2 + w - 5]', '[61, 61, 3*w - 1]', '[61, 61, 2*w^2 + w - 9]', '[61, 61, 2*w^2 - w - 7]', '[64, 4, 4]', '[64, 8, w^2 + 3*w - 1]', '[64, 16, -2*w^2 + 2*w + 8]', '[64, 64, -2*w^2 - w + 4]', '[67, 67, -2*w^2 + 13]', '[67, 67, -3*w - 7]', '[68, 34, -w^2 + 3*w + 1]', '[68, 68, -w^2 - 3*w]', '[73, 73, w^2 + 2*w - 5]', '[76, 38, w^2 + w + 1]', '[76, 76, -w^2 + 2*w + 4]', '[77, 77, -2*w^2 + 2*w + 5]', '[77, 77, -2*w^2 - 2*w + 7]', '[79, 79, w - 5]', '[83, 83, -2*w^2 + 4*w + 3]', '[86, 86, 2*w^2 + w - 10]', '[88, 22, -2*w^2 + 6]', '[88, 88, -2*w^2 - w + 12]', '[89, 89, w^2 + 2*w - 9]', '[94, 94, -2*w^2 + w + 6]', '[97, 97, -w^2 + 2*w - 3]', '[97, 97, w^2 - 2*w - 7]', '[97, 97, w^2 - 2*w - 5]', '[98, 14, 2*w^2 + 3*w - 6]', '[98, 14, -w^2 - 2*w + 6]', '[98, 98, 2*w^2 - 3*w - 2]', '[103, 103, 2*w^2 - 2*w - 9]', '[106, 106, w^2 - 2*w - 6]', '[107, 107, 3*w^2 + 2*w - 11]', '[107, 107, 3*w^2 + 4*w - 3]', '[107, 107, 2*w^2 - 5]', '[108, 6, -3*w^2 - 3*w + 9]', '[108, 12, -3*w]', '[109, 109, -3*w^2 + 2*w + 11]', '[112, 28, -w^2 - 3*w + 5]', '[112, 28, 2*w^2 - 4]', '[112, 28, w^2 + 3*w + 3]', '[112, 28, -2*w^2 + 2*w + 4]', '[112, 112, w^2 + 2*w - 8]', '[112, 112, 3*w^2 + 2*w - 8]', '[113, 113, w^2 + 2*w - 7]', '[118, 118, w^2 - 3*w - 2]', '[119, 119, 2*w^2 + w - 15]', '[119, 119, -w^2 + 9]', '[121, 11, 2*w^2 - w - 5]', '[121, 121, w + 5]', '[122, 122, -3*w^2 + 7*w - 2]', '[122, 122, w^2 + w - 10]', '[122, 122, 3*w^2 - 5*w - 6]', '[125, 5, -5]', '[128, 8, -4*w + 8]', '[128, 8, 2*w^2 - 2*w - 10]', '[128, 32, 2*w^2 + 2*w - 8]', '[128, 128, 3*w^2 - w - 12]', '[131, 131, 2*w^2 - 2*w - 3]', '[133, 133, -2*w^2 + w + 3]', '[133, 133, 3*w + 5]', '[134, 134, 3*w^2 + w - 10]', '[134, 134, 3*w^2 + w - 14]', '[136, 34, 2*w + 6]', '[136, 136, 2*w^2 - w - 4]', '[137, 137, 4*w^2 + 7*w - 5]', '[146, 146, -w^2 + 4*w - 6]', '[149, 149, -3*w - 1]', '[149, 149, 5*w - 11]', '[149, 149, 4*w^2 + 3*w - 11]', '[152, 38, 2*w^2 - 14]', '[152, 152, 3*w^2 + 4*w - 8]', '[154, 154, -w^2 - w - 2]', '[154, 154, -w + 6]', '[157, 157, -2*w^2 - 6*w - 3]', '[158, 158, -w^2 + 7*w - 10]', '[166, 166, w^2 + 3*w - 6]', '[167, 167, 2*w^2 + 3*w - 7]', '[172, 86, -5*w^2 + w + 23]', '[172, 172, w^2 + 2*w - 12]', '[173, 173, 3*w^2 - 11]', '[176, 44, w^2 - w + 3]', '[176, 44, -2*w^2 + 4*w + 4]', '[176, 176, -3*w - 4]', '[178, 178, -w^2 + 8*w - 14]', '[179, 179, 2*w^2 + 2*w - 9]', '[181, 181, 3*w^2 - 6*w - 1]', '[187, 187, -2*w^2 - 5*w + 3]', '[188, 94, 3*w^2 + w - 17]', '[188, 188, -3*w^2 + 6*w + 4]', '[189, 21, 3*w + 3]', '[189, 21, -3*w + 9]', '[191, 191, 4*w^2 + w - 15]', '[194, 194, -3*w^2 + 12*w - 10]', '[194, 194, 3*w^2 - 2*w - 10]', '[194, 194, 3*w^2 - 4*w - 6]', '[196, 14, 3*w^2 - w - 11]', '[196, 14, -3*w^2 - w + 9]', '[196, 28, -3*w^2 - w + 16]', '[196, 28, w^2 - 5*w + 8]', '[196, 98, -w^2 - 3*w + 11]', '[196, 196, 3*w^2 + 2*w - 12]', '[197, 197, 2*w^2 - 3*w - 7]', '[199, 199, -3*w^2 + 4*w + 9]', '[206, 206, -3*w^2 - 3*w + 10]', '[209, 209, -w^2 + 4*w + 1]', '[212, 106, -3*w^2 + w + 19]', '[212, 212, 3*w^2 - 3*w - 8]', '[214, 214, w^2 - 10]', '[214, 214, -w^2 - 4*w + 6]', '[214, 214, 2*w^2 - 5*w - 2]', '[216, 6, 6]', '[216, 24, -3*w^2 + 3*w + 12]', '[218, 218, -5*w^2 + 8*w + 10]', '[223, 223, -2*w^2 - 5*w + 1]', '[224, 28, 2*w^2 + 2*w - 14]', '[224, 28, -2*w^2 - 2*w + 10]', '[224, 56, -4*w^2 + 2*w + 16]', '[224, 56, -2*w^2 - 2*w]', '[224, 224, w^2 + 4*w]', '[224, 224, w^2 - 3*w - 4]', '[226, 226, -w^2 + 6*w - 10]', '[227, 227, 5*w - 13]', '[233, 233, -w^2 - 2*w - 3]', '[236, 118, -5*w^2 - 9*w + 5]', '[236, 236, -3*w^2 - 5*w + 8]', '[238, 238, 4*w^2 + 3*w - 10]', '[238, 238, -3*w^2 + 10]', '[239, 239, -2*w^2 - 4*w + 7]', '[241, 241, -w^2 - 3]', '[242, 22, 3*w^2 - 7*w - 2]', '[242, 242, -w^2 - 3*w + 10]', '[244, 122, -5*w^2 - 5*w + 9]', '[244, 122, -w^2 - 5*w - 7]', '[244, 122, w^2 - 3*w - 9]', '[244, 244, -3*w^2 + w]', '[244, 244, -w^2 - 3*w + 8]', '[244, 244, -3*w^2 - w + 8]', '[250, 10, 5*w - 10]', '[256, 8, -4*w^2 - 4*w + 12]', '[256, 16, -4*w]', '[256, 16, w^2 + 3*w - 9]', '[256, 64, 2*w - 8]', '[256, 256, w^2 + 3*w + 4]', '[257, 257, 2*w^2 + 2*w - 11]', '[262, 262, 4*w^2 - 11*w + 2]', '[263, 263, 2*w^2 + 2*w - 13]', '[263, 263, 4*w^2 - 7*w - 5]', '[263, 263, w - 7]', '[266, 266, 4*w^2 - 3*w - 14]', '[266, 266, -3*w^2 + w + 10]', '[268, 134, -w^2 - w - 3]', '[268, 134, -7*w^2 + w + 33]', '[268, 268, 2*w^2 - 3*w - 8]', '[268, 268, 2*w^2 + w - 16]', '[269, 269, -2*w^2 - 5*w + 7]', '[272, 68, -3*w^2 - w + 7]', '[272, 68, -2*w^2 - 2*w + 12]', '[272, 272, -5*w^2 + 3*w + 20]', '[274, 274, -3*w^2 - w + 6]', '[277, 277, 5*w - 7]', '[277, 277, -4*w - 7]', '[277, 277, 3*w^2 - 2*w - 9]', '[281, 281, 2*w^2 - 4*w - 5]', '[283, 283, 3*w^2 + 2*w - 13]', '[289, 17, w^2 - 4*w + 7]', '[289, 289, -3*w^2 + 4*w + 5]', '[292, 146, -3*w^2 - 5*w + 1]', '[292, 292, -3*w^2 + 4]', '[293, 293, 6*w - 13]', '[297, 33, -3*w^2 + 9]', '[298, 298, 3*w^2 - 5*w - 2]', '[298, 298, w^2 - 3*w - 6]', '[298, 298, -w^2 + 4*w + 2]', '[301, 301, 2*w^2 - w - 15]', '[301, 301, -4*w^2 + 25]', '[304, 76, -4*w^2 - 2*w + 12]', '[304, 76, 3*w^2 - 3*w - 7]', '[304, 304, -w^2 + w - 4]', '[307, 307, 2*w^2 + 3*w - 17]', '[308, 154, -w^2 + 3*w + 7]', '[308, 154, 3*w^2 - 3*w - 13]', '[308, 308, 5*w - 8]', '[308, 308, 4*w^2 + 3*w - 8]', '[314, 314, 4*w^2 + w - 14]', '[316, 158, 3*w^2 + 3*w - 11]', '[316, 316, -w^2 + 5*w]', '[323, 323, -2*w^2 - 3*w + 9]', '[329, 329, -2*w^2 + 3*w + 9]', '[329, 329, 4*w^2 - 4*w - 15]', '[331, 331, -4*w - 1]', '[332, 166, -3*w^2 + w + 9]', '[332, 332, -3*w^2 - 2*w + 20]', '[334, 334, -w^2 + 3*w - 6]', '[337, 337, 4*w^2 + w - 21]', '[343, 7, 7]', '[343, 49, w^2 + 2*w - 13]', '[343, 49, -2*w^2 - 3*w - 1]', '[343, 343, 2*w^2 - 5*w - 3]', '[344, 86, -4*w - 10]', '[344, 344, -3*w^2 + 8]', '[346, 346, 3*w^2 - 4*w - 10]', '[347, 347, w^2 - 11]', '[349, 349, 4*w^2 + 5*w - 11]', '[352, 44, 2*w^2 + 2*w - 18]', '[352, 88, 2*w^2 + 4*w - 8]', '[352, 352, 3*w^2 - 2*w - 8]', '[353, 353, -w - 7]', '[353, 353, 4*w^2 - 2*w - 15]', '[353, 353, 2*w^2 - 3*w - 13]', '[356, 178, w^2 - w - 11]', '[356, 356, -3*w^2 + 4*w + 4]', '[358, 358, 3*w - 10]', '[361, 19, 4*w^2 + 2*w - 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61]', '[9884, 4942, -9*w^2 - 5*w + 53]', '[9884, 4942, -19*w^2 + 13*w + 81]', '[9884, 4942, 9*w^2 + 7*w - 39]', '[9884, 4942, 11*w^2 - 9*w - 51]', '[9884, 9884, 23*w^2 - w - 120]', '[9884, 9884, 9*w^2 + 12*w - 4]', '[9884, 9884, -9*w^2 + w + 24]', '[9884, 9884, 15*w^2 - 5*w - 64]', '[9884, 9884, 20*w^2 + w - 120]', '[9884, 9884, 5*w^2 + 16*w + 4]', '[9886, 9886, -5*w^2 + 30*w - 46]', '[9887, 9887, 12*w - 35]', '[9887, 9887, -8*w^2 - w + 57]', '[9887, 9887, 16*w^2 - 6*w - 69]', '[9892, 4946, 15*w^2 + 19*w - 37]', '[9892, 9892, 2*w^2 + 17*w - 8]', '[9902, 9902, 9*w^2 - 26*w + 22]', '[9902, 9902, 9*w^2 - 7*w - 22]', '[9902, 9902, -5*w^2 - 16*w + 22]', '[9904, 2476, 10*w^2 - 18*w - 4]', '[9904, 2476, -w^2 + w + 25]', '[9904, 9904, -11*w^2 - 6*w + 24]', '[9907, 9907, 10*w^2 - 4*w - 33]', '[9908, 4954, 17*w^2 + 3*w - 79]', '[9908, 9908, -7*w^2 + 10*w + 28]', '[9911, 9911, 9*w^2 - 4*w - 25]', '[9914, 9914, -12*w^2 + w + 46]', '[9923, 9923, -2*w^2 + 13*w + 33]', '[9928, 2482, 12*w^2 + 12*w - 38]', '[9928, 9928, -w^2 + 14*w]', '[9931, 9931, -12*w^2 - 8*w + 23]', '[9934, 9934, 9*w^2 - 11*w - 14]', '[9934, 9934, 7*w^2 + 9*w - 30]', '[9934, 9934, w^2 + 14*w - 26]', '[9937, 9937, -6*w^2 - 8*w - 3]', '[9941, 9941, 16*w^2 + 3*w - 63]', '[9941, 9941, 16*w^2 + 8*w - 53]', '[9941, 9941, 11*w^2 + 6*w - 23]', '[9944, 2486, 4*w^2 - 10*w - 18]', '[9944, 9944, 7*w^2 + 4*w - 56]', '[9946, 9946, 5*w^2 - 17*w - 2]', '[9956, 4978, 9*w^2 - 3*w - 11]', '[9956, 9956, w^2 + 14*w - 28]', '[9961, 9961, -6*w^2 - 4*w + 51]', '[9961, 9961, -9*w^2 - 6*w + 59]', '[9961, 9961, 9*w^2 - 10*w - 37]', '[9961, 9961, -w^2 - 10*w - 23]', '[9961, 9961, 2*w^2 - w - 29]', '[9961, 9961, 8*w^2 + 6*w - 41]', '[9962, 9962, w^2 + 12*w + 10]', '[9964, 4982, 11*w^2 + 5*w - 29]', '[9964, 9964, 5*w^2 - 8*w + 12]', '[9968, 2492, -6*w^2 + 14*w + 12]', '[9968, 2492, 11*w^2 + 5*w - 51]', '[9968, 2492, -3*w^2 + 11*w - 21]', '[9968, 2492, 12*w^2 - 22*w - 20]', '[9968, 9968, -3*w^2 - 13*w + 52]', '[9968, 9968, -5*w^2 + 9*w + 28]', '[9974, 9974, 2*w^2 - 11*w - 10]', '[9983, 9983, 8*w^2 - 9*w - 37]', '[9983, 9983, 13*w^2 - 51]', '[9983, 9983, -w^2 - 12*w - 7]', '[9983, 9983, -w^2 + 18*w - 27]', '[9983, 9983, -2*w^2 + 4*w - 17]', '[9983, 9983, w^2 - 2*w - 25]', '[9988, 4994, 7*w^2 - 9*w - 33]', '[9988, 9988, 13*w^2 + 2*w - 84]', '[9991, 9991, 23*w^2 + 18*w - 71]', '[9991, 9991, 4*w^2 + 10*w - 27]', '[9991, 9991, 14*w^2 + 30*w - 3]', '[9994, 9994, 6*w^2 - 9*w - 38]', '[9994, 9994, 3*w^2 + 5*w - 38]', '[9994, 9994, 11*w^2 + 3*w - 34]', '[9998, 9998, 3*w^2 + 12*w - 50]'], 'label': '3.3.469.1', 'narrow_class_no': 1, 'primes': ['[2, 2, -w + 2]', '[4, 2, -w^2 - w + 3]', '[7, 7, w + 1]', '[7, 7, -w + 3]', '[11, 11, -w^2 + 3]', '[17, 17, w + 3]', '[19, 19, w^2 - 7]', '[27, 3, 3]', '[43, 43, -2*w - 5]', '[47, 47, 2*w + 3]', '[53, 53, 3*w^2 + 2*w - 9]', '[59, 59, 2*w^2 + w - 5]', '[61, 61, 3*w - 1]', '[61, 61, 2*w^2 + w - 9]', '[61, 61, 2*w^2 - w - 7]', '[67, 67, -2*w^2 + 13]', '[67, 67, -3*w - 7]', '[73, 73, w^2 + 2*w - 5]', '[79, 79, w - 5]', '[83, 83, -2*w^2 + 4*w + 3]', '[89, 89, w^2 + 2*w - 9]', '[97, 97, -w^2 + 2*w - 3]', '[97, 97, w^2 - 2*w - 7]', '[97, 97, w^2 - 2*w - 5]', '[103, 103, 2*w^2 - 2*w - 9]', '[107, 107, 3*w^2 + 2*w - 11]', '[107, 107, 3*w^2 + 4*w - 3]', '[107, 107, 2*w^2 - 5]', '[109, 109, -3*w^2 + 2*w + 11]', '[113, 113, w^2 + 2*w - 7]', '[121, 11, 2*w^2 - w - 5]', '[125, 5, -5]', '[131, 131, 2*w^2 - 2*w - 3]', '[137, 137, 4*w^2 + 7*w - 5]', '[149, 149, -3*w - 1]', '[149, 149, 5*w - 11]', '[149, 149, 4*w^2 + 3*w - 11]', '[157, 157, -2*w^2 - 6*w - 3]', '[167, 167, 2*w^2 + 3*w - 7]', '[173, 173, 3*w^2 - 11]', '[179, 179, 2*w^2 + 2*w - 9]', '[181, 181, 3*w^2 - 6*w - 1]', '[191, 191, 4*w^2 + w - 15]', '[197, 197, 2*w^2 - 3*w - 7]', '[199, 199, -3*w^2 + 4*w + 9]', '[223, 223, -2*w^2 - 5*w + 1]', '[227, 227, 5*w - 13]', '[233, 233, -w^2 - 2*w - 3]', '[239, 239, -2*w^2 - 4*w + 7]', '[241, 241, -w^2 - 3]', '[257, 257, 2*w^2 + 2*w - 11]', '[263, 263, 2*w^2 + 2*w - 13]', '[263, 263, 4*w^2 - 7*w - 5]', '[263, 263, w - 7]', '[269, 269, -2*w^2 - 5*w + 7]', '[277, 277, 5*w - 7]', '[277, 277, -4*w - 7]', '[277, 277, 3*w^2 - 2*w - 9]', '[281, 281, 2*w^2 - 4*w - 5]', '[283, 283, 3*w^2 + 2*w - 13]', '[289, 17, w^2 - 4*w + 7]', '[293, 293, 6*w - 13]', '[307, 307, 2*w^2 + 3*w - 17]', '[331, 331, -4*w - 1]', '[337, 337, 4*w^2 + w - 21]', '[347, 347, w^2 - 11]', '[349, 349, 4*w^2 + 5*w - 11]', '[353, 353, -w - 7]', '[353, 353, 4*w^2 - 2*w - 15]', '[353, 353, 2*w^2 - 3*w - 13]', '[361, 19, 4*w^2 + 2*w - 17]', '[373, 373, 3*w^2 - 7]', '[379, 379, 7*w^2 + 4*w - 25]', '[389, 389, w^2 - 4*w - 3]', '[389, 389, -5*w^2 - 10*w + 1]', '[389, 389, 5*w^2 + 2*w - 21]', '[397, 397, 2*w^2 - 3*w - 11]', '[401, 401, 4*w^2 + 2*w - 11]', '[419, 419, 2*w - 9]', '[431, 431, 4*w^2 + w - 13]', '[431, 431, -4*w - 5]', '[431, 431, -w^2 - 6*w - 7]', '[433, 433, 4*w^2 - w - 15]', '[433, 433, -4*w - 3]', '[433, 433, w^2 + 4*w - 9]', '[439, 439, -6*w^2 - 3*w + 23]', '[443, 443, -4*w^2 + 4*w + 11]', '[461, 461, 5*w^2 - 4*w - 21]', '[463, 463, 2*w^2 + 3*w - 11]', '[467, 467, 5*w^2 + 10*w - 3]', '[479, 479, -2*w^2 - 6*w - 1]', '[487, 487, -3*w^2 + 8*w + 1]', '[491, 491, 3*w^2 + 2*w - 17]', '[491, 491, 5*w + 9]', '[491, 491, -6*w^2 - 10*w + 5]', '[499, 499, 4*w^2 - 5*w - 13]', '[503, 503, 2*w^2 - 4*w - 7]', '[503, 503, 2*w^2 + 3*w - 15]', '[503, 503, 7*w - 15]', '[509, 509, 4*w^2 - 10*w - 1]', '[523, 523, 6*w^2 + 6*w - 17]', '[541, 541, 6*w^2 + 5*w - 19]', '[547, 547, -4*w^2 - 6*w + 11]', '[593, 593, 2*w^2 + 5*w - 9]', '[593, 593, 4*w^2 + 2*w - 25]', '[593, 593, -w^2 - 2*w - 5]', '[599, 599, 4*w^2 + 2*w - 19]', '[601, 601, 4*w^2 - 13]', '[607, 607, w - 9]', '[619, 619, -5*w - 1]', '[631, 631, 2*w^2 + 2*w - 19]', '[641, 641, w^2 - 4*w - 9]', '[643, 643, 2*w^2 - 5*w - 5]', '[653, 653, w^2 - 4*w - 7]', '[673, 673, 4*w^2 - w - 13]', '[683, 683, -2*w^2 - 8*w - 9]', '[691, 691, 2*w^2 + 4*w - 11]', '[701, 701, 2*w^2 - 4*w - 9]', '[719, 719, 4*w^2 + w - 9]', '[739, 739, 5*w^2 - 2*w - 19]', '[751, 751, 3*w^2 - 4*w - 13]', '[751, 751, w^2 + 6*w - 1]', '[751, 751, w^2 - 13]', '[757, 757, -3*w^2 - 8*w - 1]', '[761, 761, -w - 9]', '[769, 769, 6*w^2 + 3*w - 19]', '[769, 769, -w^2 + 2*w - 7]', '[769, 769, 4*w^2 - 4*w - 9]', '[773, 773, 6*w^2 - 2*w - 25]', '[787, 787, 5*w^2 + 2*w - 15]', '[787, 787, 6*w + 11]', '[787, 787, -5*w - 7]', '[797, 797, 6*w^2 + 2*w - 21]', '[809, 809, w^2 - 6*w - 1]', '[827, 827, 3*w^2 - 6*w - 7]', '[827, 827, 2*w^2 - 4*w - 11]', '[827, 827, -2*w^2 - 3*w - 3]', '[829, 829, 2*w^2 + 4*w - 17]', '[839, 839, 6*w^2 + 13*w - 1]', '[853, 853, -2*w^2 - w - 3]', '[857, 857, 2*w^2 + 4*w - 13]', '[857, 857, 7*w^2 + 6*w - 17]', '[857, 857, 4*w^2 - 7*w - 9]', '[859, 859, 4*w^2 - 7]', '[881, 881, 4*w^2 - w - 11]', '[883, 883, -2*w^2 + 9*w - 13]', '[887, 887, -2*w^2 - 2*w - 3]', '[919, 919, 2*w^2 + 4*w - 15]', '[941, 941, 6*w^2 - 9*w - 11]', '[941, 941, 6*w^2 - 4*w - 29]', '[941, 941, 4*w^2 - 5*w - 3]', '[971, 971, 4*w^2 - 3*w - 9]', '[983, 983, 6*w - 17]', '[983, 983, 3*w^2 - 4*w - 17]', '[983, 983, -2*w^2 + 10*w - 15]', '[991, 991, 4*w^2 - 4*w - 7]', '[997, 997, 5*w^2 - 6*w - 17]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [4, -5, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 469, 'disc_rad': 469, 'disc_sign': 1, 'frobs': [[2, [[2, 1], [1, 1]]], [3, [[3, 1]]], [5, [[3, 1]]], [7, [0]], [11, [[2, 1], [1, 1]]], [13, [[3, 1]]], [17, [[2, 1], [1, 1]]], [19, [[2, 1], [1, 1]]], [23, [[3, 1]]], [29, [[3, 1]]], [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, [[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': 21.656407827707714, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.469.1', 'local_algs': ['7.1.0.1', '7.2.1.1', '67.1.0.1', '67.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [7, 67], 'rd': 7.76946201167, 'regulator': {'__RealLiteral__': 0, 'data': '3.85282661562', 'prec': 44}, 'res': {'gal': ['-28,56,39,-42,-25,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a^{2} - 2 a - 1 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}