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lfunc_lfunctions • Show schema
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{'Lhash': '896186567429575732139043894942', 'a10': [247.47359318619675, 0.0], 'a2': [-6.38986691902975, 0.0], 'a3': [0.0, 0.0], 'a4': [8.83039924291075, 0.0], 'a5': [-38.72906843320825, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [148.05066540485126, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 70.72926453752447, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [6.38986691902975, 0], [32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [38.72906843320825, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-576.3898669190297, 0], [161051.0, 0]], [[1.0, 0], [-391.49119772873223, 0], [371293.0, 0]], [[1.0, 0], [-1329.700304016403, 0], [1419857.0, 0]], [[1.0, 0], [-942.4735931861967, 0], [2476099.0, 0]], 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['0.70696654682940644707459410537640', '1.54558195139549606126964651958760', '3.43162232135470607513512599127089', '4.30506551096447963731067089021625', '5.71055750718579183677579920586698', '7.02596325487524799379895398118873', '7.67117074420058788260545161248697', '8.684850933300064792974571476858321', '9.235606943084840546019348601941584', '10.15670163445372126028916953912728'], 'prelabel': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70696654682940644707459410538', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.54558195139549606126964651959', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43162232135470607513512599127', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 70.72926453752447, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/6/a/t/1/1'], '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': '2-21e2-1.1-c5-0-22', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70696654682940644707459410538', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '896186567429575732139043894942', 'Lhash_array': ['896186567429575732139043894942'], 'label': '2-21e2-1.1-c5-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/a/t/1/1'}