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lfunc_lfunctions • Show schema
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{'Lhash': '1335221055966635299640549897497', 'a10': [0.5525655866882957, 0.0], 'a2': [-2.5414434836240796, 0.0], 'a3': [0.6265453599177796, 0.0], 'a4': [4.458934980455298, 0.0], 'a5': [-0.21742194553952512, 0.0], 'a6': [-1.5923296221579444, 0.0], 'a7': [-0.8030242474619721, 0.0], 'a8': [-6.24924428273342, 0.0], 'a9': [-2.6074409119655, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 73.86960690988651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 29], 'central_character': '9251.1', 'coefficient_field': 'CDF', 'conductor': 9251, 'conductor_radical': 319, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.5414434836240796, 0], [2.0, 0]], [[1.0, 0], [-0.6265453599177796, 0], [3.0, 0]], [[1.0, 0], [0.21742194553952512, 0], [5.0, 0]], [[1.0, 0], [0.8030242474619721, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.17033947178713732, 0], [13.0, 0]], [[1.0, 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'3.18232823966526188512853014909289', '4.61956414954577095059665490282944', '5.61950909721077731162038702225385', '6.27720740752709194505319069680313', '7.03572409758881373600283944415123', '7.57090853064315416154226785780924'], 'prelabel': '2-9251-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.594742981025465, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05330369087999518848233110390', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.90308226164946797323111370163', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04095409083034315576582125243', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 73.86960690988651, 'bad_primes': [11, 29], 'central_character': '1.1', 'conductor': 9251, 'conductor_radical': 319, 'degree': 2, 'index': 420, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/2'], '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': '2-9251-1.1-c1-0-420', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-9251-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.594742981025465, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05330369087999518848233110390', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1335221055966635299640549897497', 'Lhash_array': ['1335221055966635299640549897497'], 'label': '2-9251-1.1-c1-0-420', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/2'}