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lfunc_lfunctions • Show schema
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{'Lhash': '1001793575236410794073997233932', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.3311708822963197, 1.3459021364207977], 'a4': [0, 0], 'a5': [-2.1229051216441346, 0.7023345673517012], 'a6': [0, 0], 'a7': [2.904196564020108, 1.6767386680165957], 'a8': [0, 0], 'a9': [2.1229051216441346, -3.6769795303358292], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.304441810213165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.1229051216441346, -0.7023345673517012]]], [13, [[1.0, 0], [-1.2164791545650522, 3.3941388401932966]]]], 'bad_primes': [2, 5, 13], 'central_character': '1040.289', 'coefficient_field': 'CDF', 'conductor': 1040, 'conductor_radical': 130, 'conjugate': '1004229255873065077093505308933', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.3311708822963197, -1.3459021364207977], [1.5, -2.598076211353316]], [[1.0, 0], [2.1229051216441346, -0.7023345673517012]], 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'7.77727391363411594207273158841401', '8.832268339458207986855139533584241', '10.10392626298655817191125548388481'], 'prelabel': '2-1040-65.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.881742842484937, 'root_angle': -0.24419720877909265, 'root_number': '0.719879134009096337001634295361480493273371139128284280 - 0.694099439863131943727376502109165422651407766064372140*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.12209860438954633', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.790275786605588814677851577688', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.86579009227951594763340139866', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87533951912326488376339086050', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.304441810213165, 'bad_primes': [2, 5, 13], 'central_character': '65.29', 'conductor': 1040, 'conductor_radical': 130, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1040/2/dh/a/289/1'], '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': '2-1040-65.29-c1-0-13', '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': '2-1040-65.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.881742842484937, 'root_angle': -0.12209860438954633, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.790275786605588814677851577688', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1001793575236410794073997233932', 'Lhash_array': ['1001793575236410794073997233932'], 'label': '2-1040-65.29-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1040/2/dh/a/289/1'}