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lfunc_lfunctions • Show schema
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{'Lhash': '4893854072880353467316653766922', 'a10': -4, 'a2': 1, 'a3': -1, 'a4': 1, 'a5': -4, 'a6': -1, 'a7': 3, 'a8': 1, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3034315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [19, [1, 1]]], 'bad_primes': [2, 19], 'central_character': '38.1', 'coefficient_field': '1.1.1.1', 'conductor': 38, 'conductor_radical': 38, 'degree': 2, 'euler_factors': [[1, -1], [1, 1, 3], [1, 4, 5], [1, -3, 7], [1, -2, 11], [1, 1, 13], [1, -3, 17], [1, 1], [1, 1, 23], [1, 5, 29], [1, 8, 31], [1, 2, 37], [1, 8, 41], [1, -4, 43], [1, -8, 47], [1, 1, 53], [1, -15, 59], [1, -2, 61], [1, -3, 67], [1, -2, 71], [1, -9, 73], [1, 10, 79], [1, 6, 83], [1, 0, 89], [1, 2, 97], [1, -2, 101], [1, 6, 103], [1, 7, 107], [1, 15, 109], [1, -14, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 1, 3], 1]], [[[1, 4, 5], 1]], [[[1, -3, 7], 1]], [[[1, -2, 11], 1]], [[[1, 1, 13], 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0.9347987110759756, 0.7912683011679235, 0.4626122191876038, 0.03584370683033081, -0.3758839216394919, -0.6562462943736924, -0.7097386959503011, -0.48209093647192264, 0.026884100914950467], 'positive_zeros': ['3.86057015395193111701613139712576', '5.28069074518443602737935578595782', '7.25038064772684706053554512262789', '8.408486909011940238981299566497374', '10.98850264170077345648603277340860', '11.61515083240032291487198991803438', '12.38825742592724708014161209088465', '14.37348632970750952303967845812089', '15.00174295764739089605520124900834', '16.27742004806018738020850312916682'], 'prelabel': '2-38-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.5508461923993535, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 51301870551309226, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.86057015395193111701613139713', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.28069074518443602737935578596', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.25038064772684706053554512263', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3034315276808656, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 38, 'conductor_radical': 38, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, -4, -1, 3, 1, -2, -4, 2, -1, -1, 3, 4, 1, 3, -2, -1, -4, -3, 2, -1, -1, 11, -1, 5, 3, -5, 4, -8, 1, -2, 3, -12, -2, -2, -1, 1, -4, -8, -3, 4, 2, 8, -1, 8, -1, 2, 11, -3, -1, -1, 5, -8, 3, 1, -5, 15, 4, 2, -8, -6, 1, 4, -2, 3, 3, 1, -12, 2, -2, 9, -2, -11, -1, 6, 1, -10, -4, 1, -8, -6, -3, -12, 4, 5, 2, 0, 8, -3, -1, 8, 8, 4, -1, -2, 2, -4, 11], 'euler11': [1, -2, 11], 'euler13': [1, 1, 13], 'euler17': [1, -3, 17], 'euler19': [1, 1, 0], 'euler2': [1, -1, 0], 'euler23': [1, 1, 23], 'euler29': [1, 5, 29], 'euler3': [1, 1, 3], 'euler31': [1, 8, 31], 'euler37': [1, 2, 37], 'euler41': [1, 8, 41], 'euler43': [1, -4, 43], 'euler47': [1, -8, 47], 'euler5': [1, 4, 5], 'euler53': [1, 1, 53], 'euler59': [1, -15, 59], 'euler61': [1, -2, 61], 'euler67': [1, -3, 67], 'euler7': [1, -3, 7], 'euler71': [1, -2, 71], 'euler73': [1, -9, 73], 'euler79': [1, 10, 79], 'euler83': [1, 6, 83], 'euler89': [1, 0, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -1, 0], [1, 1, 3], [1, 4, 5], [1, -3, 7], [1, -2, 11], [1, 1, 13], [1, -3, 17], [1, 1, 0], [1, 1, 23], [1, 5, 29], [1, 8, 31], [1, 2, 37], [1, 8, 41], [1, -4, 43], [1, -8, 47], [1, 1, 53], [1, -15, 59], [1, -2, 61], [1, -3, 67], [1, -2, 71], [1, -9, 73], [1, 10, 79], [1, 6, 83], [1, 0, 89], [1, 2, 97]], 'index': 1, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/38/b', 'ModularForm/GL2/Q/holomorphic/38/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/38/2/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-38-1.1-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-38-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.5508461923993535, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 51301870551309226, 'z1': {'__RealLiteral__': 0, 'data': '3.86057015395193111701613139713', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9955883
{'Lhash': '4893854072880353467316653766922', 'Lhash_array': ['4893854072880353467316653766922'], 'factors': ['2-38-1.1-c1-0-1'], 'label': '2-38-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/38/2/a/b'}
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id: 24546006
{'Lhash': '4893854072880353467316653766922', 'Lhash_array': ['4893854072880353467316653766922'], 'factors': ['2-38-1.1-c1-0-1'], 'label': '2-38-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/38/2/a/b/1/1'}
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id: 22094
{'Lhash': '51301870551309226', 'Lhash_array': ['51301870551309226'], 'factors': ['2-38-1.1-c1-0-1'], 'label': '2-38-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/38/b'}