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lfunc_lfunctions • Show schema
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{'Lhash': '1877420850421568925794758825071', 'a10': [-128.7877107121804, 0.0], 'a2': [4.0, 0.0], 'a3': [9.426130962698156, 0.0], 'a4': [16.0, 0.0], 'a5': [-32.1969276780451, 0.0], 'a6': [37.704523850792626, 0.0], 'a7': [-9.662854370967517, 0.0], 'a8': [64.0, 0.0], 'a9': [-154.1480550740631, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 138.25085267878933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-4.0, 0]]], [431, [[1.0, 0], [-185761.0, 0]]]], 'bad_primes': [2, 431], 'central_character': '862.1', 'coefficient_field': 'CDF', 'conductor': 862, 'conductor_radical': 862, 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.0, 0]], [[1.0, 0], [-9.426130962698156, 0], [243.0, 0]], [[1.0, 0], [32.1969276780451, 0], [3125.0, 0]], [[1.0, 0], [9.662854370967517, 0], [16807.0, 0]], [[1.0, 0], [114.01232751577376, 0], [161051.0, 0]], [[1.0, 0], [-37.251202144790746, 0], [371293.0, 0]], [[1.0, 0], [-946.6667805080174, 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103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 138.25085267878933, 'bad_primes': [2, 431], 'central_character': '1.1', 'conductor': 862, 'conductor_radical': 862, 'degree': 2, 'index': 149, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/862/6/a/b/1/31'], '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': '2-862-1.1-c5-0-149', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-862-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.75801227583937, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48102391154436066599162504340', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1877420850421568925794758825071', 'Lhash_array': ['1877420850421568925794758825071'], 'label': '2-862-1.1-c5-0-149', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/862/6/a/b/1/31'}