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hmf_forms • Show schema
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{'deg': 3, 'dimension': 3, 'disc': 49, 'field_bad_primes': [7], 'field_label': '3.3.49.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.49.1-167.3-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [167], 'level_ideal': '[167,167,-2*w^2 + w - 3]', 'level_label': '167.3', 'level_norm': 167, 'parallel_weight': 2, 'short_label': '167.3-a', 'weight': '[2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[167,167,-2*w^2 + w - 3]', -1]], 'hecke_eigenvalues': ['e', '2*e^2 - 4*e - 4', '-e^2 - e + 3', '-3*e^2 + 4*e + 8', '2*e - 2', '-3*e^2 + 6*e + 6', '-e^2 + e + 3', '4*e - 2', '4*e^2 - 6*e - 12', '4*e^2 - 5*e - 8', '-2*e^2 + 4', '3*e^2 - 7*e - 11', '-6*e^2 + 10*e + 16', '-2*e^2 + 6', '4*e^2 - 4*e - 14', '3*e^2 - 5*e + 3', '-2*e^2 + 4*e + 2', '-5*e^2 + 6*e + 12', '4*e^2 + e - 14', '6*e^2 - 15*e - 14', '2*e^2 - 4*e - 12', '-2*e^2 + 8*e - 4', '-4*e^2 + 2*e + 6', '5*e^2 - 6*e - 8', '-5*e^2 + 10*e + 22', '-4*e^2 + 3*e + 14', '6*e^2 - 12*e - 8', '6*e^2 - 10*e - 12', '-4*e - 6', '-e^2 + 4*e - 6', '2*e^2', '-7*e^2 + 8*e + 26', '-5*e^2 + 5*e + 5', '2*e^2 + 2*e - 4', '-6*e^2 + 4*e + 22', '9*e^2 - 17*e - 23', 1, '-4*e^2 + 12*e + 10', '6*e^2 - 2*e - 20', 'e^2 + 5*e - 5', '4*e^2 - 7*e - 2', '6*e - 16', '-6*e^2 + 9*e + 12', '4*e^2 - 4*e - 12', '7*e - 10', '-2*e^2 - 2*e + 24', '-10*e^2 + 21*e + 32', '4*e^2 - 2*e - 16', '6*e^2 - 18*e - 16', '4*e^2 - 2*e', '10*e^2 - 26*e - 26', '-e^2 + 5*e + 15', '-11*e^2 + 23*e + 25', '-10*e', '-2*e^2 + 8*e - 16', 'e^2 + 6*e + 4', '-8*e^2 + 14*e + 18', '-4*e^2 + 2*e + 24', '-4*e - 6', '-4*e^2 + 6*e + 4', '6*e^2 - 11*e - 2', '-4*e + 8', '2*e^2 + 2*e - 2', '2*e^2 - e + 22', '-2*e^2 - 6*e + 16', '4*e^2 - 10*e - 4', 6, '2*e^2 - 14*e + 2', '-4*e^2 + 10*e + 28', '8*e^2 - 16*e - 34', '-8*e^2 + 4*e + 30', '-12*e^2 + 16*e + 24', '4*e^2 - 6*e + 6', '3*e^2 - e - 13', '8*e^2 - 12*e + 4', '2*e^2 - 4*e - 8', '-4*e^2 + 2*e - 2', 'e^2 + 6*e - 22', '-2*e^2 + 6*e + 4', '-9*e^2 + 18*e + 36', '8*e^2 - 8*e - 14', '6*e^2 - 13*e - 12', '-16*e^2 + 14*e + 34', '-6*e^2 - 4*e + 36', '-7*e^2 + 6*e + 20', '-4*e - 4', '-6*e^2 + e + 8', '-2*e^2 - 12*e + 22', '-8*e^2 + 16*e + 18', '-6*e^2 + 21*e + 16', 'e^2 + 8*e + 4', '8*e^2 + 2*e - 36', '-e^2 + 6*e + 10', '12*e^2 - 12*e - 14', '5*e^2 - 16*e - 20', 6, '2*e - 10', '-18*e^2 + 22*e + 30', '-11*e^2 + 19*e + 21', '-9*e^2 + 21*e + 43', '8*e^2 - 7*e - 34', '-9*e^2 + 18*e + 24', '16*e^2 - 30*e - 30', '12*e^2 - 19*e - 14', '-2*e^2 + 8*e + 2', '8*e^2 - 8*e - 12', '-e^2 + 13*e - 3', '2*e^2 - 22*e + 2', '-4*e^2 + 2*e + 28', '-12*e^2 + 26*e + 30', '-10*e^2 + 13*e + 6', '22*e^2 - 30*e - 38', '-7*e^2 + 21*e + 11', '-8*e^2 + 18*e + 16', '5*e^2 - 11*e - 3', '3*e^2 - 13*e - 9', '-20*e^2 + 30*e + 40', '14*e^2 - 25*e - 36', '16*e^2 - 16*e - 56', '-4*e^2 + 10*e + 20', '-8*e^2 + 22*e + 14', '-13*e^2 + 24*e + 14', '3*e^2 - 20*e + 6', '6*e^2 - 3*e + 10', '10*e^2 - 6*e - 30', '-10*e^2 + 2*e + 24', '10*e^2 - 10*e + 2', '15*e^2 - 31*e - 51', '4*e^2 - 20*e - 16', '3*e^2 - 10*e - 32', '12*e - 2', '24*e^2 - 29*e - 48', '24*e^2 - 30*e - 40', '-13*e^2 + 30*e + 34', '-10*e^2 + 26*e + 40', '8*e^2 - 5*e - 34', '4*e^2 - 10*e - 42', -32, '-6*e^2 - 2*e + 36', '14*e^2 - 26*e - 42', '-9*e^2 + 19*e - 9', '16*e^2 - 20*e - 52', '-7*e^2 - e + 39', '-24*e^2 + 38*e + 68', '15*e^2 - 21*e - 47', '20*e^2 - 29*e - 42', '-5*e^2 + 11*e - 7', '-8*e^2 + 24', '24*e^2 - 37*e - 54', '-8*e^2 + 4*e + 6', '6*e - 24', '14*e^2 - 40*e - 26', 'e^2 + 5*e + 31', '-17*e^2 + 32*e + 54', '-9*e^2 + 12*e + 36', '-18*e^2 + 41*e + 48', 'e^2 - 10', '-6*e^2 + 18*e - 10', '6*e^2 - 15*e - 16', '14*e^2 - 32*e - 60', '19*e^2 - 21*e - 27', '4*e^2 - 18*e - 4', '-2*e^2 + 7*e + 14', '-4*e^2 + 26*e + 6', '6*e^2 - 8*e - 30', '-6*e^2 + 18*e + 32', '16*e^2 - 25*e - 22', '-10*e^2 - 12*e + 44', '2*e^2 + 8*e - 54'], 'hecke_polynomial': 'x^3 - x^2 - 4*x - 1', 'label': '3.3.49.1-167.3-a'}
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hmf_fields • Show schema
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{'degree': 3, 'discriminant': 49, 'ideals': ['[1, 1, 1]', '[7, 7, 2*w^2 - w - 3]', '[8, 2, 2]', '[13, 13, -w^2 - w + 3]', '[13, 13, -w^2 + 2*w + 2]', '[13, 13, -2*w^2 + w + 2]', '[27, 3, 3]', '[29, 29, 3*w^2 - 2*w - 4]', '[29, 29, 2*w^2 + w - 4]', '[29, 29, -w^2 + 3*w + 1]', '[41, 41, w^2 - w - 5]', '[41, 41, 2*w^2 - 3*w - 4]', '[41, 41, -3*w^2 + w + 3]', '[43, 43, w^2 + 2*w - 5]', '[43, 43, 2*w^2 + w - 5]', '[43, 43, 3*w^2 - 2*w - 3]', '[49, 7, -w^2 + 3*w + 3]', '[56, 14, 4*w^2 - 2*w - 6]', '[64, 4, 4]', '[71, 71, 4*w^2 - 3*w - 5]', '[71, 71, 3*w^2 - 4*w - 5]', '[71, 71, -4*w^2 + w + 5]', '[83, 83, w^2 + w - 7]', '[83, 83, w^2 - 2*w - 6]', '[83, 83, -3*w^2 - 2*w + 5]', '[91, 91, w^2 - w - 6]', '[91, 91, -w^2 - 3]', '[91, 91, -w + 5]', '[97, 97, 3*w^2 + w - 7]', '[97, 97, 3*w^2 - 4*w - 7]', '[97, 97, 2*w^2 - w - 8]', '[104, 26, -2*w^2 - 2*w + 6]', '[104, 26, -2*w^2 + 4*w + 4]', '[104, 26, -4*w^2 + 2*w + 4]', '[113, 113, 3*w^2 + w - 8]', '[113, 113, 2*w^2 - 4*w - 5]', '[113, 113, 2*w^2 + 2*w - 7]', '[125, 5, -5]', '[127, 127, 2*w^2 - 9]', '[127, 127, -3*w^2 - 2*w + 6]', '[127, 127, -5*w^2 + 3*w + 7]', '[139, 139, 5*w^2 - 4*w - 6]', '[139, 139, 4*w^2 - 5*w - 7]', '[139, 139, -5*w^2 + w + 6]', '[167, 167, w^2 + w - 8]', '[167, 167, 6*w^2 - 4*w - 9]', '[167, 167, -4*w^2 - 2*w + 7]', '[169, 13, -3*w^2 - 2*w + 7]', '[169, 13, -5*w^2 + 3*w + 6]', '[169, 13, -2*w^2 + 5*w + 3]', '[169, 169, -w^2 + w + 7]', '[169, 169, w^2 + 4]', '[169, 169, -w + 6]', '[181, 181, 4*w^2 + w - 9]', '[181, 181, 4*w^2 - 5*w - 9]', '[181, 181, 2*w^2 - w - 9]', '[189, 21, 6*w^2 - 3*w - 9]', '[197, 197, 2*w - 7]', '[197, 197, 3*w^2 - 5*w - 6]', '[197, 197, 2*w^2 - 2*w - 9]', '[203, 203, 5*w^2 - 3*w - 5]', '[203, 203, 3*w^2 + 2*w - 8]', '[203, 203, -2*w^2 + 5*w + 4]', '[211, 211, 3*w^2 - 5*w - 7]', '[211, 211, 2*w^2 + 3*w - 8]', '[211, 211, 4*w^2 + w - 10]', '[216, 6, 6]', '[223, 223, 3*w^2 + 2*w - 9]', '[223, 223, 4*w^2 + w - 11]', '[223, 223, 3*w^2 + 2*w - 10]', '[232, 58, 6*w^2 - 4*w - 8]', '[232, 58, 4*w^2 + 2*w - 8]', '[232, 58, -2*w^2 + 6*w + 2]', '[239, 239, 6*w^2 - 5*w - 7]', '[239, 239, -5*w^2 + 6*w + 9]', '[239, 239, -6*w^2 + w + 7]', '[251, 251, w^2 - 3*w - 8]', '[251, 251, -3*w^2 + 2*w - 3]', '[251, 251, 2*w^2 + w - 11]', '[281, 281, -7*w^2 + 6*w + 9]', '[281, 281, 6*w^2 + w - 11]', '[281, 281, w^2 - 7*w]', '[287, 287, -7*w^2 + w + 16]', '[287, 287, w^2 - 2*w - 8]', '[287, 287, -9*w^2 + 4*w + 16]', '[293, 293, -7*w^2 + 2*w + 10]', '[293, 293, 5*w^2 - 7*w - 7]', '[293, 293, 2*w^2 + 5*w - 6]', '[301, 301, -6*w^2 + 7*w + 10]', '[301, 301, -w^2 - w - 5]', '[301, 301, -2*w^2 + w + 10]', '[307, 307, -3*w^2 + w - 3]', '[307, 307, 2*w^2 - 3*w - 10]', '[307, 307, w^2 + 2*w - 10]', '[328, 82, 2*w^2 - 2*w - 10]', '[328, 82, 4*w^2 - 6*w - 8]', '[328, 82, -6*w^2 + 2*w + 6]', '[337, 337, 7*w^2 - 3*w - 10]', '[337, 337, 7*w^2 - 4*w - 10]', '[337, 337, -4*w^2 - 3*w + 8]', '[343, 7, 7]', '[344, 86, 2*w^2 + 4*w - 10]', '[344, 86, 4*w^2 + 2*w - 10]', '[344, 86, 6*w^2 - 4*w - 6]', '[349, 349, 5*w^2 + w - 15]', '[349, 349, 7*w^2 - 8*w - 11]', '[349, 349, -6*w^2 + 5*w + 2]', '[351, 39, -3*w^2 - 3*w + 9]', '[351, 39, -3*w^2 + 6*w + 6]', '[351, 39, -6*w^2 + 3*w + 6]', '[377, 377, -w - 7]', '[377, 377, -3*w^2 - 3*w + 10]', '[377, 377, w^2 - w + 6]', '[377, 377, 3*w^2 - 6*w - 7]', '[377, 377, 6*w^2 - 3*w - 5]', '[377, 377, -7*w^2 + 5*w + 9]', '[377, 377, -2*w^2 + 7*w + 2]', '[377, 377, -5*w^2 - 2*w + 10]', '[377, 377, w^2 - 9]', '[379, 379, 3*w^2 + 3*w - 11]', '[379, 379, 4*w^2 + 2*w - 11]', '[379, 379, 5*w^2 + w - 14]', '[392, 14, -2*w^2 + 6*w + 6]', '[419, 419, -5*w^2 - 3*w + 9]', '[419, 419, 2*w^2 + w - 12]', '[419, 419, w^2 - 3*w - 9]', '[421, 421, 9*w^2 - 5*w - 15]', '[421, 421, 3*w^2 + 5*w - 7]', '[421, 421, 4*w^2 - w - 15]', '[433, 433, -8*w^2 + 7*w + 10]', '[433, 433, 7*w^2 + w - 13]', '[433, 433, w^2 - 8*w]', '[448, 28, 8*w^2 - 4*w - 12]', '[449, 449, -7*w^2 + 2*w + 8]', '[449, 449, 8*w^2 - 6*w - 11]', '[449, 449, -6*w^2 - 2*w + 11]', '[461, 461, 2*w^2 + 6*w - 7]', '[461, 461, -8*w^2 + 2*w + 11]', '[461, 461, 6*w^2 - 8*w - 9]', '[463, 463, -7*w^2 + 8*w + 12]', '[463, 463, w^2 + 7*w - 7]', '[463, 463, -8*w^2 + w + 10]', '[491, 491, w^2 + 2*w - 11]', '[491, 491, 4*w^2 - 7*w - 7]', '[491, 491, 2*w^2 - 3*w - 11]', '[497, 497, -8*w^2 + w + 20]', '[497, 497, -5*w^2 + 2*w + 17]', '[497, 497, 3*w^2 - 4*w - 13]', '[503, 503, 5*w^2 - 7*w - 10]', '[503, 503, 2*w^2 - 2*w - 11]', '[503, 503, -7*w^2 + 2*w + 7]', '[512, 8, 8]', '[533, 533, 3*w^2 - 2*w - 13]', '[533, 533, 6*w^2 + w - 14]', '[533, 533, 5*w^2 + 2*w - 12]', '[533, 533, -5*w^2 - 3*w + 10]', '[533, 533, 2*w^2 + w + 5]', '[533, 533, 8*w^2 - 5*w - 11]', '[533, 533, 5*w^2 - 7*w - 12]', '[533, 533, 8*w^2 - 3*w - 11]', '[533, 533, -2*w^2 + 7*w + 4]', '[547, 547, 4*w^2 + 3*w - 15]', '[547, 547, -3*w^2 + 10*w]', '[547, 547, -7*w^2 + 4*w + 3]', '[559, 559, 8*w^2 - 7*w - 9]', '[559, 559, -w^2 + w - 7]', '[559, 559, 4*w^2 + 3]', '[559, 559, 4*w - 11]', '[559, 559, 5*w^2 - 9*w - 5]', '[559, 559, 4*w^2 + 3*w - 11]', '[559, 559, -4*w^2 - 5*w + 8]', '[559, 559, 4*w^2 - 8*w - 5]', '[559, 559, -w^2 + 8*w + 1]', '[568, 142, 8*w^2 - 6*w - 10]', '[568, 142, 6*w^2 - 8*w - 10]', '[568, 142, -8*w^2 + 2*w + 10]', '[581, 581, -11*w^2 + 8*w + 18]', '[581, 581, -12*w^2 + 4*w + 21]', '[581, 581, 2*w^2 - 7*w - 8]', '[587, 587, 6*w^2 + w - 17]', '[587, 587, 5*w^2 - 3*w - 17]', '[587, 587, w^2 - 7*w - 6]', '[601, 601, 4*w^2 + 3*w - 14]', '[601, 601, 4*w^2 + 3*w - 12]', '[601, 601, 6*w^2 + w - 16]', '[617, 617, 5*w^2 + 2*w - 14]', '[617, 617, 4*w^2 + 3*w - 13]', '[617, 617, 5*w^2 + 2*w - 15]', '[631, 631, -9*w^2 + 8*w + 11]', '[631, 631, 8*w^2 + w - 15]', '[631, 631, w^2 - 9*w]', '[637, 91, -8*w^2 + 3*w + 10]', '[637, 91, 3*w^2 + 5*w - 9]', '[637, 91, 5*w^2 - 8*w - 8]', '[643, 643, 6*w^2 - 9*w - 8]', '[643, 643, 3*w^2 + 6*w - 8]', '[643, 643, 4*w^2 - w - 16]', '[659, 659, -8*w^2 + 2*w + 9]', '[659, 659, 9*w^2 - 7*w - 12]', '[659, 659, 7*w^2 + 2*w - 13]', '[664, 166, 2*w^2 + 2*w - 14]', '[664, 166, 2*w^2 - 4*w - 12]', '[664, 166, -6*w^2 - 4*w + 10]', '[673, 673, -8*w^2 + 9*w + 14]', '[673, 673, w^2 + 8*w - 8]', '[673, 673, -9*w^2 + w + 11]', '[679, 679, -12*w^2 + 3*w + 26]', '[679, 679, -7*w^2 + 8*w + 16]', '[679, 679, -13*w^2 + 7*w + 24]', '[701, 701, 9*w^2 - 4*w - 13]', '[701, 701, -5*w^2 - 4*w + 10]', '[701, 701, -4*w^2 - 5*w + 9]', '[727, 727, -7*w^2 - 3*w + 12]', '[727, 727, w^2 + 2*w - 12]', '[727, 727, 10*w^2 - 7*w - 15]', '[728, 182, 2*w^2 - 2*w - 12]', '[728, 182, -2*w^2 - 6]', '[728, 182, -2*w + 10]', '[729, 9, 9]', '[743, 743, 5*w^2 - 2*w - 18]', '[743, 743, 4*w^2 - 5*w - 16]', '[743, 743, w^2 + 4*w - 14]', '[757, 757, 11*w^2 - 7*w - 18]', '[757, 757, w^2 + 3*w - 13]', '[757, 757, 3*w^2 + 5*w - 15]', '[769, 769, 2*w^2 - 11*w + 1]', '[769, 769, -10*w^2 + w + 13]', '[769, 769, 9*w^2 + 2*w - 15]', '[776, 194, 6*w^2 + 2*w - 14]', '[776, 194, 6*w^2 - 8*w - 14]', '[776, 194, 4*w^2 - 2*w - 16]', '[783, 87, 9*w^2 - 6*w - 12]', '[783, 87, 6*w^2 + 3*w - 12]', '[783, 87, -3*w^2 + 9*w + 3]', '[791, 791, -9*w^2 + 9*w + 19]', '[791, 791, -8*w^2 + 9*w + 15]', '[791, 791, -10*w^2 + w + 21]', '[797, 797, -8*w^2 + 5*w + 3]', '[797, 797, -3*w^2 + 11*w]', '[797, 797, 5*w^2 + 3*w - 18]', '[811, 811, -9*w^2 + 2*w + 11]', '[811, 811, 7*w^2 - 9*w - 12]', '[811, 811, 9*w^2 - 7*w - 11]', '[827, 827, 3*w^2 + 5*w - 14]', '[827, 827, 5*w^2 + 3*w - 13]', '[827, 827, 8*w^2 - 21]', '[832, 52, -4*w^2 - 4*w + 12]', '[832, 52, -4*w^2 + 8*w + 8]', '[832, 52, -8*w^2 + 4*w + 8]', '[839, 839, -6*w^2 - 4*w + 11]', '[839, 839, w^2 - 4*w - 11]', '[839, 839, 3*w^2 + w - 16]', '[841, 29, 8*w^2 - 3*w - 7]', '[841, 29, -5*w^2 + 8*w + 11]', '[841, 29, 3*w^2 + 5*w - 12]', '[841, 841, -4*w^2 + 9*w + 5]', '[841, 841, 5*w^2 + 4*w - 11]', '[841, 841, 9*w^2 - 5*w - 12]', '[853, 853, -8*w^2 + 7*w + 3]', '[853, 853, 7*w^2 + w - 20]', '[853, 853, w^2 - 8*w - 7]', '[875, 35, -10*w^2 + 5*w + 15]', '[881, 881, -10*w^2 + 9*w + 12]', '[881, 881, 9*w^2 + w - 17]', '[881, 881, w^2 - 10*w]', '[883, 883, 7*w^2 + w - 18]', '[883, 883, -8*w^2 + 5*w + 4]', '[883, 883, 5*w^2 + 3*w - 17]', '[889, 889, 4*w^2 - 8*w - 11]', '[889, 889, -14*w^2 + 9*w + 25]', '[889, 889, -3*w^2 + 8*w + 7]', '[904, 226, 6*w^2 + 2*w - 16]', '[904, 226, 4*w^2 - 8*w - 10]', '[904, 226, 4*w^2 + 4*w - 14]', '[911, 911, 10*w^2 - 7*w - 14]', '[911, 911, 2*w^2 + w - 14]', '[911, 911, -7*w^2 - 3*w + 13]', '[923, 923, w^2 + w - 12]', '[923, 923, 10*w^2 - 8*w - 13]', '[923, 923, 6*w^2 + 2*w - 17]', '[923, 923, w^2 + 3*w + 8]', '[923, 923, 7*w^2 - 10*w - 10]', '[923, 923, 5*w^2 + 3*w - 15]', '[923, 923, -8*w^2 - 2*w + 15]', '[923, 923, 4*w^2 - w - 17]', '[923, 923, -3*w^2 + 8*w + 8]', '[937, 937, -9*w^2 + 10*w + 16]', '[937, 937, w^2 + 9*w - 9]', '[937, 937, -10*w^2 + w + 12]', '[953, 953, 9*w^2 - 7*w - 10]', '[953, 953, -10*w^2 + 2*w + 13]', '[953, 953, 8*w^2 - 10*w - 13]', '[967, 967, 2*w^2 + 2*w - 15]', '[967, 967, 11*w^2 - 7*w - 17]', '[967, 967, -7*w^2 - 4*w + 12]', '[973, 973, -11*w^2 + 2*w + 27]', '[973, 973, -6*w^2 + 2*w + 21]', '[973, 973, 3*w^2 - 5*w - 15]', '[1000, 10, -10]', '[1009, 1009, 2*w^2 - 11*w]', '[1009, 1009, 9*w^2 + 2*w - 16]', '[1009, 1009, -11*w^2 + 9*w + 15]', '[1016, 254, 4*w^2 - 18]', '[1016, 254, -6*w^2 - 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44]', '[9799, 9799, 21*w^2 - 25*w - 31]', '[9799, 9799, 3*w^2 + 6*w - 31]', '[9799, 9799, -16*w^2 - 9*w + 26]', '[9799, 9799, 19*w^2 + 3*w - 36]', '[9799, 9799, 25*w^2 - 16*w - 40]', '[9799, 9799, 22*w^2 - 19*w - 27]', '[9799, 9799, -18*w^2 + 15*w + 7]', '[9829, 9829, 9*w^2 + 9*w - 35]', '[9829, 9829, 17*w^2 + w - 44]', '[9829, 9829, 11*w^2 - 10*w - 40]', '[9841, 9841, 17*w^2 - 23*w - 24]', '[9841, 9841, 2*w^2 + 11*w - 34]', '[9841, 9841, 16*w^2 - 25*w - 17]', '[9841, 9841, 6*w^2 + 13*w - 34]', '[9841, 9841, 22*w^2 - 3*w - 54]', '[9841, 9841, 20*w^2 - 19*w - 19]', '[9841, 9841, 21*w^2 - 22*w - 39]', '[9841, 9841, 10*w^2 - 4*w - 39]', '[9841, 9841, 23*w^2 - 21*w - 28]', '[9848, 2462, 12*w^2 + 6*w - 40]', '[9848, 2462, 16*w^2 + 2*w - 40]', '[9848, 2462, -18*w^2 + 12*w + 8]', '[9857, 9857, -13*w^2 - 9*w + 25]', '[9857, 9857, 8*w^2 + w - 38]', '[9857, 9857, w^2 - 9*w - 23]', '[9869, 9869, -12*w^2 - 9*w + 25]', '[9869, 9869, -23*w^2 + 2*w + 29]', '[9869, 9869, -5*w^2 + 24*w]', '[9869, 9869, -12*w^2 + 25*w + 8]', '[9869, 9869, 21*w^2 + 4*w - 36]', '[9869, 9869, -21*w^2 + 23*w + 36]', '[9869, 9869, 10*w^2 - w - 41]', '[9869, 9869, -24*w^2 + 19*w + 34]', '[9869, 9869, 19*w^2 + 5*w - 33]', '[9871, 9871, 24*w^2 - 17*w - 36]', '[9871, 9871, -17*w^2 - 7*w + 29]', '[9871, 9871, 21*w^2 - 2*w - 49]', '[9883, 9883, 9*w^2 - 2*w - 38]', '[9883, 9883, 7*w^2 + 15*w - 20]', '[9883, 9883, 15*w^2 - 22*w - 21]', '[9941, 9941, 18*w^2 + 6*w - 31]', '[9941, 9941, -19*w^2 + 6*w + 20]', '[9941, 9941, 24*w^2 - 18*w - 35]', '[9947, 203, 21*w^2 - 14*w - 28]', '[9947, 203, 14*w^2 + 7*w - 28]', '[9947, 203, -7*w^2 + 21*w + 7]', '[9967, 9967, -21*w^2 + 2*w + 23]', '[9967, 9967, 19*w^2 + 2*w - 38]', '[9967, 9967, 21*w^2 - 19*w - 23]', '[9976, 2494, -2*w^2 - 2*w + 26]', '[9976, 2494, 4*w^2 + 16*w - 22]', '[9976, 2494, -4*w^2 - 2*w + 30]', '[9976, 2494, 20*w^2 - 24*w - 10]', '[9976, 2494, -20*w^2 + 26*w + 26]', '[9976, 2494, -4*w^2 - 20*w - 2]', '[9976, 2494, -6*w^2 - 20*w + 18]', '[9976, 2494, -4*w^2 + 2*w - 16]', '[9976, 2494, -6*w^2 + 18*w + 14]', '[9989, 9989, 13*w^2 - 14*w - 45]', '[9989, 9989, -5*w^2 + 19*w + 9]', '[9989, 9989, -20*w^2 + w + 54]', '[9997, 9997, 26*w^2 - 3*w - 37]', '[9997, 9997, w^2 - 19*w - 17]', '[9997, 9997, 19*w^2 - 18*w - 4]', '[9997, 9997, -22*w^2 - 4*w + 37]', '[9997, 9997, 2*w^2 - 10*w - 25]', '[9997, 9997, 3*w^2 + 11*w + 18]', '[9997, 9997, -10*w^2 + 8*w - 11]', '[9997, 9997, 3*w^2 + 23*w - 18]', '[9997, 9997, -5*w^2 + 18*w + 20]'], 'label': '3.3.49.1', 'narrow_class_no': 1, 'primes': ['[7, 7, 2*w^2 - w - 3]', '[8, 2, 2]', '[13, 13, -w^2 - w + 3]', '[13, 13, -w^2 + 2*w + 2]', '[13, 13, -2*w^2 + w + 2]', '[27, 3, 3]', '[29, 29, 3*w^2 - 2*w - 4]', '[29, 29, 2*w^2 + w - 4]', '[29, 29, -w^2 + 3*w + 1]', '[41, 41, w^2 - w - 5]', '[41, 41, 2*w^2 - 3*w - 4]', '[41, 41, -3*w^2 + w + 3]', '[43, 43, w^2 + 2*w - 5]', '[43, 43, 2*w^2 + w - 5]', '[43, 43, 3*w^2 - 2*w - 3]', '[71, 71, 4*w^2 - 3*w - 5]', '[71, 71, 3*w^2 - 4*w - 5]', '[71, 71, -4*w^2 + w + 5]', '[83, 83, w^2 + w - 7]', '[83, 83, w^2 - 2*w - 6]', '[83, 83, -3*w^2 - 2*w + 5]', '[97, 97, 3*w^2 + w - 7]', '[97, 97, 3*w^2 - 4*w - 7]', '[97, 97, 2*w^2 - w - 8]', '[113, 113, 3*w^2 + w - 8]', '[113, 113, 2*w^2 - 4*w - 5]', '[113, 113, 2*w^2 + 2*w - 7]', '[125, 5, -5]', '[127, 127, 2*w^2 - 9]', '[127, 127, -3*w^2 - 2*w + 6]', '[127, 127, -5*w^2 + 3*w + 7]', '[139, 139, 5*w^2 - 4*w - 6]', '[139, 139, 4*w^2 - 5*w - 7]', '[139, 139, -5*w^2 + w + 6]', '[167, 167, w^2 + w - 8]', '[167, 167, 6*w^2 - 4*w - 9]', '[167, 167, -4*w^2 - 2*w + 7]', '[181, 181, 4*w^2 + w - 9]', '[181, 181, 4*w^2 - 5*w - 9]', '[181, 181, 2*w^2 - w - 9]', '[197, 197, 2*w - 7]', '[197, 197, 3*w^2 - 5*w - 6]', '[197, 197, 2*w^2 - 2*w - 9]', '[211, 211, 3*w^2 - 5*w - 7]', '[211, 211, 2*w^2 + 3*w - 8]', '[211, 211, 4*w^2 + w - 10]', '[223, 223, 3*w^2 + 2*w - 9]', '[223, 223, 4*w^2 + w - 11]', '[223, 223, 3*w^2 + 2*w - 10]', '[239, 239, 6*w^2 - 5*w - 7]', '[239, 239, -5*w^2 + 6*w + 9]', '[239, 239, -6*w^2 + w + 7]', '[251, 251, w^2 - 3*w - 8]', '[251, 251, -3*w^2 + 2*w - 3]', '[251, 251, 2*w^2 + w - 11]', '[281, 281, -7*w^2 + 6*w + 9]', '[281, 281, 6*w^2 + w - 11]', '[281, 281, w^2 - 7*w]', '[293, 293, -7*w^2 + 2*w + 10]', '[293, 293, 5*w^2 - 7*w - 7]', '[293, 293, 2*w^2 + 5*w - 6]', '[307, 307, -3*w^2 + w - 3]', '[307, 307, 2*w^2 - 3*w - 10]', '[307, 307, w^2 + 2*w - 10]', '[337, 337, 7*w^2 - 3*w - 10]', '[337, 337, 7*w^2 - 4*w - 10]', '[337, 337, -4*w^2 - 3*w + 8]', '[349, 349, 5*w^2 + w - 15]', '[349, 349, 7*w^2 - 8*w - 11]', '[349, 349, -6*w^2 + 5*w + 2]', '[379, 379, 3*w^2 + 3*w - 11]', '[379, 379, 4*w^2 + 2*w - 11]', '[379, 379, 5*w^2 + w - 14]', '[419, 419, -5*w^2 - 3*w + 9]', '[419, 419, 2*w^2 + w - 12]', '[419, 419, w^2 - 3*w - 9]', '[421, 421, 9*w^2 - 5*w - 15]', '[421, 421, 3*w^2 + 5*w - 7]', '[421, 421, 4*w^2 - w - 15]', '[433, 433, -8*w^2 + 7*w + 10]', '[433, 433, 7*w^2 + w - 13]', '[433, 433, w^2 - 8*w]', '[449, 449, -7*w^2 + 2*w + 8]', '[449, 449, 8*w^2 - 6*w - 11]', '[449, 449, -6*w^2 - 2*w + 11]', '[461, 461, 2*w^2 + 6*w - 7]', '[461, 461, -8*w^2 + 2*w + 11]', '[461, 461, 6*w^2 - 8*w - 9]', '[463, 463, -7*w^2 + 8*w + 12]', '[463, 463, w^2 + 7*w - 7]', '[463, 463, -8*w^2 + w + 10]', '[491, 491, w^2 + 2*w - 11]', '[491, 491, 4*w^2 - 7*w - 7]', '[491, 491, 2*w^2 - 3*w - 11]', '[503, 503, 5*w^2 - 7*w - 10]', '[503, 503, 2*w^2 - 2*w - 11]', '[503, 503, -7*w^2 + 2*w + 7]', '[547, 547, 4*w^2 + 3*w - 15]', '[547, 547, -3*w^2 + 10*w]', '[547, 547, -7*w^2 + 4*w + 3]', '[587, 587, 6*w^2 + w - 17]', '[587, 587, 5*w^2 - 3*w - 17]', '[587, 587, w^2 - 7*w - 6]', '[601, 601, 4*w^2 + 3*w - 14]', '[601, 601, 4*w^2 + 3*w - 12]', '[601, 601, 6*w^2 + w - 16]', '[617, 617, 5*w^2 + 2*w - 14]', '[617, 617, 4*w^2 + 3*w - 13]', '[617, 617, 5*w^2 + 2*w - 15]', '[631, 631, -9*w^2 + 8*w + 11]', '[631, 631, 8*w^2 + w - 15]', '[631, 631, w^2 - 9*w]', '[643, 643, 6*w^2 - 9*w - 8]', '[643, 643, 3*w^2 + 6*w - 8]', '[643, 643, 4*w^2 - w - 16]', '[659, 659, -8*w^2 + 2*w + 9]', '[659, 659, 9*w^2 - 7*w - 12]', '[659, 659, 7*w^2 + 2*w - 13]', '[673, 673, -8*w^2 + 9*w + 14]', '[673, 673, w^2 + 8*w - 8]', '[673, 673, -9*w^2 + w + 11]', '[701, 701, 9*w^2 - 4*w - 13]', '[701, 701, -5*w^2 - 4*w + 10]', '[701, 701, -4*w^2 - 5*w + 9]', '[727, 727, -7*w^2 - 3*w + 12]', '[727, 727, w^2 + 2*w - 12]', '[727, 727, 10*w^2 - 7*w - 15]', '[743, 743, 5*w^2 - 2*w - 18]', '[743, 743, 4*w^2 - 5*w - 16]', '[743, 743, w^2 + 4*w - 14]', '[757, 757, 11*w^2 - 7*w - 18]', '[757, 757, w^2 + 3*w - 13]', '[757, 757, 3*w^2 + 5*w - 15]', '[769, 769, 2*w^2 - 11*w + 1]', '[769, 769, -10*w^2 + w + 13]', '[769, 769, 9*w^2 + 2*w - 15]', '[797, 797, -8*w^2 + 5*w + 3]', '[797, 797, -3*w^2 + 11*w]', '[797, 797, 5*w^2 + 3*w - 18]', '[811, 811, -9*w^2 + 2*w + 11]', '[811, 811, 7*w^2 - 9*w - 12]', '[811, 811, 9*w^2 - 7*w - 11]', '[827, 827, 3*w^2 + 5*w - 14]', '[827, 827, 5*w^2 + 3*w - 13]', '[827, 827, 8*w^2 - 21]', '[839, 839, -6*w^2 - 4*w + 11]', '[839, 839, w^2 - 4*w - 11]', '[839, 839, 3*w^2 + w - 16]', '[853, 853, -8*w^2 + 7*w + 3]', '[853, 853, 7*w^2 + w - 20]', '[853, 853, w^2 - 8*w - 7]', '[881, 881, -10*w^2 + 9*w + 12]', '[881, 881, 9*w^2 + w - 17]', '[881, 881, w^2 - 10*w]', '[883, 883, 7*w^2 + w - 18]', '[883, 883, -8*w^2 + 5*w + 4]', '[883, 883, 5*w^2 + 3*w - 17]', '[911, 911, 10*w^2 - 7*w - 14]', '[911, 911, 2*w^2 + w - 14]', '[911, 911, -7*w^2 - 3*w + 13]', '[937, 937, -9*w^2 + 10*w + 16]', '[937, 937, w^2 + 9*w - 9]', '[937, 937, -10*w^2 + w + 12]', '[953, 953, 9*w^2 - 7*w - 10]', '[953, 953, -10*w^2 + 2*w + 13]', '[953, 953, 8*w^2 - 10*w - 13]', '[967, 967, 2*w^2 + 2*w - 15]', '[967, 967, 11*w^2 - 7*w - 17]', '[967, 967, -7*w^2 - 4*w + 12]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -2, -1, 1], 'conductor': 7, 'degree': 3, 'dirichlet_group': [1, 2, 4], 'disc_abs': 49, 'disc_rad': 7, 'disc_sign': 1, 'frobs': [[2, [[3, 1]]], [3, [[3, 1]]], [5, [[3, 1]]], [7, [0]], [11, [[3, 1]]], [13, [[1, 3]]], [17, [[3, 1]]], [19, [[3, 1]]], [23, [[3, 1]]], [29, [[1, 3]]], [31, [[3, 1]]], [37, [[3, 1]]], [41, [[1, 3]]], [43, [[1, 3]]], [47, [[3, 1]]], [53, [[3, 1]]], [59, [[3, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2], 'galois_label': '3T1', 'galt': 1, 'grd': 3.6593057100229713, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.49.1', 'local_algs': ['7.3.2.2'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [7], 'rd': 3.65930571002, 'regulator': {'__RealLiteral__': 0, 'data': '0.525454682123', 'prec': 47}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - 2 \\)', '\\( a^{2} - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}