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lfunc_lfunctions • Show schema
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{'Lhash': '1035804416907585325155875220676', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-2.224744871391589, -0.22474487139158905], 'a6': [0, 0], 'a7': [0, -1.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.24460261872533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.224744871391589, 0.22474487139158905]]], [7, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '5040.1009', 'coefficient_field': 'CDF', 'conductor': 5040, 'conductor_radical': 210, 'conjugate': '272318925457794472352261096631', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.224744871391589, 0.22474487139158905]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [4.898979485566356, 0], [11.0, 0]], [[1.0, 0], [0, -4.449489742783178], [-13.0, 0]], [[1.0, 0], [0, -2.0], [-17.0, 0]], [[1.0, 0], 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'3.85827042592478622963160508210611', '5.01021407039934160574169127587831', '5.24091583399066390131621550158954', '6.28292480726181280911809778455398', '7.18903919514920674350944881304152', '7.81508886386271855235692694180802', '8.226267554384505922750137649956077'], 'prelabel': '2-5040-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.343863382728645, 'root_angle': 0.5320471084244874, 'root_number': '-0.1005089620052081741751350490545468868646210230756781094 + 0.9949361530051240527388045165470573810408683669202883991*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2660235542122438', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.817105609953640065201371210041', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.48271524996292013803451496424', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99763760540529880106677376555', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.24460261872533, 'bad_primes': [2, 3, 5, 7], 'central_character': '5.4', 'conductor': 5040, 'conductor_radical': 210, 'degree': 2, 'index': 46, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5040/2/t/t/1009/1'], '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': '2-5040-5.4-c1-0-46', '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': '2-5040-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.343863382728645, 'root_angle': 0.2660235542122437, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.817105609953640065201371210041', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1035804416907585325155875220676', 'Lhash_array': ['1035804416907585325155875220676'], 'label': '2-5040-5.4-c1-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5040/2/t/t/1009/1'}