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{'Lhash': '181537080727377592420834537846,1101786880932201114159606355535,1621737218104497282000394585567,1839689402373175549707794601173', 'a10': 0, 'a2': 2, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': -2, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 58782.34041762576, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 3, -2, 1]], [3, [1, 0, -1, 0, 1]], [5, [1]], [13, [1, -10, 51, -130, 169]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.1', 'coefficient_field': '1.1.1.1', 'conductor': 14459006250000, 'conductor_radical': 390, 'degree': 8, 'euler_factors': [[1, -2, 3, -2, 1], [1, 0, -1, 0, 1], [1], [1, -2, -8, 4, 67, 28, -392, -686, 2401], [1, 6, 28, 96, 267, 1056, 3388, 7986, 14641], [1, -10, 51, -130, 169], [1, -6, 33, -126, 356, -2142, 9537, -29478, 83521], [1, 6, 44, 192, 891, 3648, 15884, 41154, 130321], [1, 18, 180, 1296, 7139, 29808, 95220, 219006, 279841], [1, 2, -43, -22, 1252, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 58782.34041762576, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 14459006250000, 'conductor_radical': 390, 'degree': 8, 'dirichlet_coefficients': [1, 2, 0, 1, 0, 0, 2, -2, 1, 0, -6, 0, 10, 4, 0, -4, 6, 2, -6, 0, 0, -12, -18, 0, 0, 20, 0, 2, -2, 0, 0, -2, 0, 12, 0, 1, -14, -12, 0, 0, 36, 0, -30, -6, 0, -36, -12, 0, 12, 0, 0, 10, 0, 0, 0, -4, 0, -4, 0, 0, 8, 0, 2, 3, 0, 0, 2, 6, 0, 0, 6, -2, 32, -28, 0, -6, -12, 0, 24, 0, 0, 72, 20, 0, 0, -60, 0, 12, 12, 0, 20, -18, 0, -24, 0, 0, -12, 24, -6, 0], 'euler11': [1, 6, 28, 96, 267, 1056, 3388, 7986, 14641], 'euler13': [1, -10, 51, -130, 169, 0, 0, 0, 0], 'euler17': [1, -6, 33, -126, 356, -2142, 9537, -29478, 83521], 'euler19': [1, 6, 44, 192, 891, 3648, 15884, 41154, 130321], 'euler2': [1, -2, 3, -2, 1, 0, 0, 0, 0], 'euler23': [1, 18, 180, 1296, 7139, 29808, 95220, 219006, 279841], 'euler29': [1, 2, -43, -22, 1252, -638, -36163, 48778, 707281], 'euler3': [1, 0, -1, 0, 1, 0, 0, 0, 0], 'euler31': [1, 0, -92, 0, 3846, 0, -88412, 0, 923521], 'euler37': [1, 14, 85, 518, 3700, 19166, 116365, 709142, 1874161], 'euler41': [1, -36, 621, -6804, 51752, -278964, 1043901, -2481156, 2825761], 'euler43': [1, 30, 460, 4800, 36651, 206400, 850540, 2385210, 3418801], 'euler47': [1, 12, 188, 1476, 13578, 69372, 415292, 1245876, 4879681], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -170, 0, 12411, 0, -477530, 0, 7890481], 'euler59': [1, 0, 54, 0, -565, 0, 187974, 0, 12117361], 'euler61': [1, -8, -47, 88, 4696, 5368, -174887, -1815848, 13845841], 'euler67': [1, -2, 16, 292, -4613, 19564, 71824, -601526, 20151121], 'euler7': [1, -2, -8, 4, 67, 28, -392, -686, 2401], 'euler71': [1, -6, 148, -816, 14307, -57936, 746068, -2147466, 25411681], 'euler73': [1, -32, 670, -8960, 90883, -654080, 3570430, -12448544, 28398241], 'euler79': [1, -24, 508, -6264, 68358, -494856, 3170428, -11832936, 38950081], 'euler83': [1, -20, 428, -4940, 57274, -410020, 2948492, -11435740, 47458321], 'euler89': [1, -12, 202, -1848, 20067, -164472, 1600042, -8459628, 62742241], 'euler97': [1, 12, -86, 432, 29523, 41904, -809174, 10952076, 88529281], 'euler_factors': [[1, -2, 3, -2, 1, 0, 0, 0, 0], [1, 0, -1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -8, 4, 67, 28, -392, -686, 2401], [1, 6, 28, 96, 267, 1056, 3388, 7986, 14641], [1, -10, 51, -130, 169, 0, 0, 0, 0], [1, -6, 33, -126, 356, -2142, 9537, -29478, 83521], [1, 6, 44, 192, 891, 3648, 15884, 41154, 130321], [1, 18, 180, 1296, 7139, 29808, 95220, 219006, 279841], [1, 2, -43, -22, 1252, -638, -36163, 48778, 707281], [1, 0, -92, 0, 3846, 0, -88412, 0, 923521], [1, 14, 85, 518, 3700, 19166, 116365, 709142, 1874161], [1, -36, 621, -6804, 51752, -278964, 1043901, -2481156, 2825761], [1, 30, 460, 4800, 36651, 206400, 850540, 2385210, 3418801], [1, 12, 188, 1476, 13578, 69372, 415292, 1245876, 4879681], [1, 0, -170, 0, 12411, 0, -477530, 0, 7890481], [1, 0, 54, 0, -565, 0, 187974, 0, 12117361], [1, -8, -47, 88, 4696, 5368, -174887, -1815848, 13845841], [1, -2, 16, 292, -4613, 19564, 71824, -601526, 20151121], [1, -6, 148, -816, 14307, -57936, 746068, -2147466, 25411681], [1, -32, 670, -8960, 90883, -654080, 3570430, -12448544, 28398241], [1, -24, 508, -6264, 68358, -494856, 3170428, -11832936, 38950081], [1, -20, 428, -4940, 57274, -410020, 2948492, -11435740, 47458321], [1, -12, 202, -1848, 20067, -164472, 1600042, -8459628, 62742241], [1, 12, -86, 432, 29523, 41904, -809174, 10952076, 88529281]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1950/2/y/g'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '8-1950e4-1.1-c1e4-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-1950e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 934372980338124148, 'z1': {'__RealLiteral__': 0, 'data': '0.14320750583377898379455311079', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '181537080727377592420834537846,1101786880932201114159606355535,1621737218104497282000394585567,1839689402373175549707794601173', 'Lhash_array': ['181537080727377592420834537846', '1101786880932201114159606355535', '1621737218104497282000394585567', '1839689402373175549707794601173'], 'label': '8-1950e4-1.1-c1e4-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/y/g'}