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lfunc_lfunctions • Show schema
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{'Lhash': '2605039357992325058764600090073', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [5.196152422706632, 0.0], 'a4': [0.0, 8.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [5.588457268119896, -5.588457268119896], 'a8': [0.0, 0.0], 'a9': [27.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.301074490223885, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-5.196152422706632, 0]]], [13, [[1.0, 0], [31.176914536239792, 35.0]]]], 'bad_primes': [3, 13], 'central_character': '39.8', 'coefficient_field': 'CDF', 'conductor': 39, 'conductor_radical': 39, 'conjugate': '3477053642938866095620168991683', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0, -8.0]], [[1.0, 0], [-5.196152422706632, 0]], [[1.0, 0], [0, 0], [0, -125.0]], [[1.0, 0], [-5.588457268119896, 5.588457268119896], [0, -343.0]], [[1.0, 0], [0, 0], [0, 1331.0]], [[1.0, 0], [31.176914536239792, 35.0]], [[1.0, 0], [0, 0], [4913.0, 0]], [[1.0, 0], 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'9.444776700306060226029440777901099', '10.46745627477810550433774939699376', '12.14147354196192610328973512447005', '13.65549281705725832436917740110617', '14.60319707010382095749599833101760', '15.22573075528765689074228374078239'], 'prelabel': '2-39-39.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5169292963826246, 'root_angle': -0.13804791656140034, 'root_number': '0.907421176940968 - 0.4202223311998881*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0690239582807', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.05501370608218898058971466377', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.49618854745559273726366511349', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.42228761989683509583741006475', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.301074490223885, 'bad_primes': [3, 13], 'central_character': '39.8', 'conductor': 39, 'conductor_radical': 39, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/39/4/f/a/8/2'], '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': '2-39-39.8-c3-0-4', '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': '2-39-39.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5169292963826246, 'root_angle': -0.06902395828070017, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.05501370608218898058971466377', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2605039357992325058764600090073', 'Lhash_array': ['2605039357992325058764600090073'], 'label': '2-39-39.8-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/39/4/f/a/8/2'}