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lfunc_lfunctions • Show schema
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{'Lhash': '1695975616458973635218579170963', 'a10': [-102.5466074463031, 0.0], 'a2': [-4.837500676934202, 0.0], 'a3': [3.0, 0.0], 'a4': [15.40141279933887, 0.0], 'a5': [21.198262138806083, 0.0], 'a6': [-14.512502030802608, 0.0], 'a7': [16.280608771553837, 0.0], 'a8': [-35.80433942707125, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.913968372910507, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.1', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.837500676934202, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [-21.198262138806083, 0], [125.0, 0]], [[1.0, 0], [-16.280608771553837, 0], [343.0, 0]], [[1.0, 0], [-30.753237296192424, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-46.237126934217606, 0], [4913.0, 0]], [[1.0, 0], 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'1.70185259895792534204976877913313', '3.01785232433449180035147183957710', '5.09703954685105148207997446783252', '6.16297599270322822999854703428935', '7.17429139590880076852285152235587', '8.020662569089521234884803754439427', '9.015272700522131117629562163207949', '9.533991889329287485883968564777441', '10.01302722680998578743603635965563'], 'prelabel': '2-507-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33788886003258947017753531651', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.70185259895792534204976877913', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01785232433449180035147183958', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.913968372910507, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/4/a/p/1/1'], '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': '2-507-1.1-c3-0-44', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-507-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33788886003258947017753531651', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1695975616458973635218579170963', 'Lhash_array': ['1695975616458973635218579170963'], 'label': '2-507-1.1-c3-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/4/a/p/1/1'}