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lfunc_lfunctions • Show schema
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{'Lhash': '1208263479074859339529683146427', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.4700132061808067, 0], 'a4': [0, 0], 'a5': [0, -1.224036134229167], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [0, 0], 'a9': [-0.8390611736540254, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.97210096932068, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -1.0]]], [11, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [3.2939163630374404, 1.466327041731892]]]], 'bad_primes': [2, 7, 11, 13], 'central_character': '4004.2157', 'coefficient_field': 'CDF', 'conductor': 4004, 'conductor_radical': 2002, 'conjugate': '1032212172198651869354041812855', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.4700132061808067, 0], [3.0, 0]], [[1.0, 0], [0, 1.224036134229167], [-5.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [3.2939163630374404, 1.466327041731892]], [[1.0, 0], [-5.5011021163048905, 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'2.90394573837199581761383483688', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.97210096932068, 'bad_primes': [2, 7, 11, 13], 'central_character': '13.12', 'conductor': 4004, 'conductor_radical': 2002, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4004/2/m/c/2157/27'], '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': '2-4004-13.12-c1-0-41', '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': '2-4004-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.654387762554022, 'root_angle': 0.06665783499813528, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.953151821848482594252479102727', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1208263479074859339529683146427', 'Lhash_array': ['1208263479074859339529683146427'], 'label': '2-4004-13.12-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4004/2/m/c/2157/27'}