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lfunc_lfunctions • Show schema
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{'Lhash': '151310994303889774772016586304', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.25881904510252074, 0.9659258262890683], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [2.3657669960222503, -1.1845448579652258], 'a8': [0, 0], 'a9': [-0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.768584424468887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.3657669960222503, 1.1845448579652258]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '2100.493', 'coefficient_field': 'CDF', 'conductor': 2100, 'conductor_radical': 210, 'conjugate': '2475006796504354425313199380858', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.3657669960222503, 1.1845448579652258]], [[1.0, 0], 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'6.29616852211731106989665005103510', '7.30501802976155754507234917857182', '8.128455213480508456786109018836298', '8.315565496891621294388416648495057'], 'prelabel': '2-2100-35.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': 0.9368136662418783, 'root_number': '-0.98036235077369629320815451056099604832145907043934685252 + 0.1972046175561618714545796570846645279448904869255320207*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4684068331209392', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11936332793645784877664562919', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.66679498378904363258962505189', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.63669971002524555076434447405', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.768584424468887, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.3', 'conductor': 2100, 'conductor_radical': 210, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2100/2/ce/c/493/4'], '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': '2-2100-35.3-c1-0-1', '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': '2-2100-35.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': 0.46840683312093917, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.11936332793645784877664562919', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '151310994303889774772016586304', 'Lhash_array': ['151310994303889774772016586304'], 'label': '2-2100-35.3-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2100/2/ce/c/493/4'}