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lfunc_lfunctions • Show schema
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{'Lhash': '813760711802420078614036409200', 'a10': [-36.14580082539492, 0], 'a2': [0, 2.3472707383523574], 'a3': [3.0, 0], 'a4': [2.4903200808747794, 0], 'a5': [0, 15.399076141837433], 'a6': [0, 7.041812215057072], 'a7': [0, 10.131734592999134], 'a8': [0, 24.623621361787503], 'a9': [9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.913968372910507, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.337', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '2720589801284546166973762871696', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.3472707383523574], [-8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [0, -15.399076141837433], [-125.0, 0]], [[1.0, 0], [0, -10.131734592999134], [-343.0, 0]], [[1.0, 0], [0, 15.066897200355514], [-1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [90.83522507308638, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.913968372910507, 'bad_primes': [3, 13], 'central_character': '13.12', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/4/b/k/337/12'], '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': '2-507-13.12-c3-0-21', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-507-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 0.4951473641045361, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64194401174575200849422610276', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '813760711802420078614036409200', 'Lhash_array': ['813760711802420078614036409200'], 'label': '2-507-13.12-c3-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/4/b/k/337/12'}