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lfunc_lfunctions • Show schema
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{'Lhash': '1679257922834953455507344771651', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9482235240027046, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [19, [1, -1]]], 'bad_primes': [2, 5, 19], 'central_character': '1900.1101', 'coefficient_field': '1.1.1.1', 'conductor': 1900, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[1], [1, 0, -1], [1], [1, -1, 1], [1, 1, 1], [1, 0, -1], [1, -1, 1], [1, -1], [1, 2, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, -1, 1], [1, -1, 1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, -1, 1], [1, 0, -1], [1, 2, 1], [1, 0, -1], [1, 0, -1], [1, -2, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1]], 'euler_factors_factorization': [[1], [[[1, -1], 1], [[1, 1], 1]], [1], [[[1, -1, 1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1, 1], 1]], 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'spectral_label': 'c0-0', 'trace_hash': 1182071415764080923, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32470092510713737382210346631', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37941265958342105230705797667', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65343682061870927329442026144', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9482235240027046, 'bad_primes': [2, 5, 19], 'central_character': '19.18', 'conductor': 1900, 'conductor_radical': 190, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], 'euler11': [1, 1, 1], 'euler13': [1, 0, -1], 'euler17': [1, -1, 1], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 2, 1], 'euler29': [1, 0, -1], 'euler3': [1, 0, -1], 'euler31': [1, 0, -1], 'euler37': [1, 0, -1], 'euler41': [1, 0, -1], 'euler43': [1, -1, 1], 'euler47': [1, -1, 1], 'euler5': [1, 0, 0], 'euler53': [1, 0, -1], 'euler59': [1, 0, -1], 'euler61': [1, 1, 1], 'euler67': [1, 0, -1], 'euler7': [1, -1, 1], 'euler71': [1, 0, -1], 'euler73': [1, -1, 1], 'euler79': [1, 0, -1], 'euler83': [1, 2, 1], 'euler89': [1, 0, -1], 'euler97': [1, 0, -1], 'euler_factors': [[1, 0, 0], [1, 0, -1], [1, 0, 0], [1, -1, 1], [1, 1, 1], [1, 0, -1], [1, -1, 1], [1, -1, 0], [1, 2, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, -1, 1], [1, -1, 1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, -1, 1], [1, 0, -1], [1, 2, 1], [1, 0, -1], [1, 0, -1]], 'index': 1, 'instance_types': ['CMF', 'CMF', 'Artin', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1900/1/e/a/1101/1', 'ModularForm/GL2/Q/holomorphic/1900/1/e/a', 'ArtinRepresentation/2.1900.6t3.a.a', 'ArtinRepresentation/2.1900.6t3.a'], 'is_instance_Artin': True, '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': '2-1900-19.18-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1900-19.18-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9737676950909311, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'trace_hash': 1182071415764080923, 'z1': {'__RealLiteral__': 0, 'data': '1.32470092510713737382210346631', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24605412
{'Lhash': '1679257922834953455507344771651', 'Lhash_array': ['1679257922834953455507344771651'], 'factors': ['2-1900-19.18-c0-0-1'], 'label': '2-1900-19.18-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1900.6t3.a'}
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id: 24599110
{'Lhash': '1679257922834953455507344771651', 'Lhash_array': ['1679257922834953455507344771651'], 'factors': ['2-1900-19.18-c0-0-1'], 'label': '2-1900-19.18-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1900.6t3.a.a'}
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id: 19813546
{'Lhash': '1679257922834953455507344771651', 'Lhash_array': ['1679257922834953455507344771651'], 'factors': ['2-1900-19.18-c0-0-1'], 'label': '2-1900-19.18-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1900/1/e/a'}
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id: 24546929
{'Lhash': '1679257922834953455507344771651', 'Lhash_array': ['1679257922834953455507344771651'], 'factors': ['2-1900-19.18-c0-0-1'], 'label': '2-1900-19.18-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1900/1/e/a/1101/1'}