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lfunc_lfunctions • Show schema
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{'Lhash': '3028484637352396251766961367764', 'a10': [48581.840368746576, 0.0], 'a2': [40.0876693168952, 0.0], 'a3': [243.31632240401842, 0.0], 'a4': [1095.0212312607412, 0.0], 'a5': [1211.8898702916472, 0.0], 'a6': [9753.984271935351, 0.0], 'a7': [-12007.950970839853, 0.0], 'a8': [23371.962323509677, 0.0], 'a9': [39519.83274821624, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.14654095504655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-3418801.0, 0]]]], 'bad_primes': [43], 'central_character': '43.1', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'euler_factors': [[[1.0, 0], [-40.0876693168952, 0], [512.0, 0]], [[1.0, 0], [-243.31632240401842, 0], [19683.0, 0]], [[1.0, 0], [-1211.8898702916472, 0], [1953125.0, 0]], [[1.0, 0], [12007.950970839853, 0], [40353607.0, 0]], [[1.0, 0], [5734.293524448915, 0], [2357947691.0, 0]], [[1.0, 0], [119754.23736004154, 0], 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'data': '2.93505626480794264876763720517', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24750549642198569585161166911', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.14654095504655, 'bad_primes': [43], 'central_character': '1.1', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/10/a/b/1/16'], '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': '2-43-1.1-c9-0-27', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-43-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.706011151181705, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '2.38905313246973896845043014507', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3028484637352396251766961367764', 'Lhash_array': ['3028484637352396251766961367764'], 'label': '2-43-1.1-c9-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/10/a/b/1/16'}