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lfunc_lfunctions • Show schema
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{'Lhash': '1775323362691372642490010004528', 'a10': [1.2586823067487243, 0], 'a2': [0, 1.0], 'a3': [0, -1.0273828103117846], 'a4': [-1.0, 0], 'a5': [0, -1.2586823067487243], 'a6': [1.0273828103117846, 0], 'a7': [0, 0], 'a8': [0, -1.0], 'a9': [1.9444845610758599, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [3.3082449366810582, -0.23561714480092535]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.1077', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '922081372295440490828494976823', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 1.0273828103117846], [-3.0, 0]], [[1.0, 0], [0, 1.2586823067487243], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.3082449366810582, -0.23561714480092535]], [[1.0, 0], [-4.083383559520024, 0], 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['1.40048319495272688002495201230928', '2.84915042545349786407406957318322', '3.61187301580099564916197658359151', '4.61677311155788298639113143262689', '5.48984717975362770059939438758138', '6.60844971072376704654884117866392', '7.61459893678164963772703803383011', '8.481105315842264297864494417822557', '9.460353918626363037445127202301834', '10.06486111737702448578787092778946'], 'prelabel': '2-1078-77.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.25018228026897077, 'root_number': '0.7067017403199876729471021089868481231246093924508179169 + 0.7075115901726986616341133610788863737780298752459883850*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.12509114013448538', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40048319495272688002495201231', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84915042545349786407406957318', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.61187301580099564916197658359', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '77.76', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/c/b/1077/12'], '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': '2-1078-77.76-c1-0-29', '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': '2-1078-77.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.12509114013448538, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40048319495272688002495201231', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1775323362691372642490010004528', 'Lhash_array': ['1775323362691372642490010004528'], 'label': '2-1078-77.76-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/c/b/1077/12'}