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lfunc_lfunctions • Show schema
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{'Lhash': '1015640431076019705746386964517', 'a10': [0.8320301716942639, 2.508072530876792e-61], 'a2': [0.4030317167626848, -0.4030317167626848], 'a3': [0.0, 0.0], 'a4': [0.0, 1.6751308705666461], 'a5': [1.0322142614202545, 1.0322142614202545], 'a6': [0.0, 0.0], 'a7': [-0.45074729728889706, 2.607072471947559], 'a8': [1.4811943040920157, 1.4811943040920157], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.45074729728889706, -2.607072471947559]]], [13, [[1.0, 0], [-3.593338407458737, -0.2965115334719825]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.811', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '2666336020494147357726028261279', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.4030317167626848, 0.4030317167626848], [0, -2.0]], [[1.0, 0], [0, 0]], [[1.0, 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{'__RealLiteral__': 0, 'data': '-0.256440882993', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.801199029837687554194185906222', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.06396097415801544588797427015', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94512128294279010809082144159', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '91.83', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/y/h/811/4'], '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': '2-819-91.83-c1-0-9', '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': '2-819-91.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': -0.2564408829928051, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.801199029837687554194185906222', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1015640431076019705746386964517', 'Lhash_array': ['1015640431076019705746386964517'], 'label': '2-819-91.83-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/y/h/811/4'}