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lfunc_lfunctions • Show schema
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{'Lhash': '3858894094713112745128115795485', 'a10': [0.0, 0.0], 'a2': [0.17364817766693036, -0.984807753012208], 'a3': [0.266044443118978, 0.22323779409789932], 'a4': [-0.9396926207859084, -0.3420201433256687], 'a5': [0.0, 0.0], 'a6': [0.266044443118978, -0.22323779409789932], 'a7': [0.0, 0.0], 'a8': [-0.5, 0.8660254037844386], 'a9': [-0.1527036446661393, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.07585788192021636, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.17364817766693036, 0.984807753012208]]], [19, [[1.0, 0], [0.9396926207859084, 0.3420201433256687]]]], 'bad_primes': [2, 19], 'central_character': '152.131', 'coefficient_field': 'CDF', 'conductor': 152, 'conductor_radical': 38, 'conjugate': '2901353475390529802402351381485', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.17364817766693036, 0.984807753012208]], [[1.0, 0], [-0.266044443118978, -0.22323779409789932], 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'10.29414127559180691733208346013705', '11.42047336298945611090097665128403', '12.93554009645926971070636102264532', '13.48963246185039348730714480292547'], 'prelabel': '2-152-152.131-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2754230961996767, 'root_angle': 0.3383644197524766, 'root_number': '0.48625004475238473623229553529926 + 0.87381971480294711947493835982028*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.16918220987623828', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.04413068870740298625400270153', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.80112177596242387302279731740', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.83413913608135674393486940162', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.07585788192021636, 'bad_primes': [2, 19], 'central_character': '152.131', 'conductor': 152, 'conductor_radical': 38, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/152/1/u/a/131/1'], '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': '2-152-152.131-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-152-152.131-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2754230961996767, 'root_angle': 0.1691822098762383, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.04413068870740298625400270153', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3858894094713112745128115795485', 'Lhash_array': ['3858894094713112745128115795485'], 'label': '2-152-152.131-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/152/1/u/a/131/1'}