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lfunc_lfunctions • Show schema
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{'Lhash': '1176716238899062242961651813393', 'a10': [-4.505797215848959, 0.0], 'a2': [-1.778955842238984, 0.0], 'a3': [-1.207794436536417, 0.0], 'a4': [1.1646838886362125, 0.0], 'a5': [2.532832523924814, 0.0], 'a6': [2.148612969100201, 0.0], 'a7': [0.0, 0.0], 'a8': [1.4859904764269591, 0.0], 'a9': [-1.5412325990716789, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.041945766075237, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [41, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 41], 'central_character': '2009.1', 'coefficient_field': 'CDF', 'conductor': 2009, 'conductor_radical': 287, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.778955842238984, 0], [2.0, 0]], [[1.0, 0], [1.207794436536417, 0], [3.0, 0]], [[1.0, 0], [-2.532832523924814, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.694424485056568, 0], [11.0, 0]], [[1.0, 0], [-2.9779892737960867, 0], [13.0, 0]], [[1.0, 0], [-7.011873207632775, 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'3.04677369887514431798764488254141', '4.35180591228141789415630654581682', '5.43790208751979290518068398078590', '6.14555107067643667636352165362855', '6.70745947515470906365086879662876', '7.75279937108280077258093824693622', '8.699305183743703792002554061270730', '9.112900033431056507069599601453342'], 'prelabel': '2-2009-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.005239788836024, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.928265437406178625050439177719', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.61083231568308690084749804186', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04677369887514431798764488254', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.041945766075237, 'bad_primes': [7, 41], 'central_character': '1.1', 'conductor': 2009, 'conductor_radical': 287, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2009/2/a/r/1/4'], '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': '2-2009-1.1-c1-0-42', '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': '2-2009-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.005239788836024, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.928265437406178625050439177719', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1176716238899062242961651813393', 'Lhash_array': ['1176716238899062242961651813393'], 'label': '2-2009-1.1-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2009/2/a/r/1/4'}