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lfunc_lfunctions • Show schema
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{'Lhash': '834000372551164577779189016054', 'a10': [0.0, -3.289945082937479], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [-1.6449725414687395, 0.5422779156612186], 'a4': [0.0, -1.0], 'a5': [-2.32634247787643, 2.32634247787643], 'a6': [0.7797228474864606, -1.5466196303899695], 'a7': [-1.766896782903509, 1.766896782903509], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [2.4118693243722484, -1.7840645622152114], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [1.6449725414687395, -0.5422779156612186]]], [13, [[1.0, 0], [-0.7668967829035088, -3.5230483000339703]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.47', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '4620007166600850592782508414263', 'degree': 2, 'euler_factors': [[[1.0, 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-0.8260040627844897, 'root_number': '-0.8542840663775727 - 0.5198064389110614*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.413002031392', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65791028884537277568242105239', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.85016665786878510166097608901', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.38877139318244346406308799767', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'bad_primes': [2, 3, 13], 'central_character': '39.8', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/2/g/a/47/1'], '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': '2-78-39.8-c1-0-0', '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': '2-78-39.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': -0.41300203139224484, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.65791028884537277568242105239', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '834000372551164577779189016054', 'Lhash_array': ['834000372551164577779189016054'], 'label': '2-78-39.8-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/g/a/47/1'}