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lfunc_lfunctions • Show schema
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{'Lhash': '2282717675532103726010163338475', 'a10': [9.668214662967566, 0.0], 'a2': [2.706070390195561, 0.0], 'a3': [0.9602178300929612, 0.0], 'a4': [5.322816956693155, 0.0], 'a5': [3.572787573448475, 0.0], 'a6': [2.5984170381523946, 0.0], 'a7': [-3.956013249431573, 0.0], 'a8': [8.991776578547073, 0.0], 'a9': [-2.0779817187715652, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.84418973575603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 13], 'central_character': '1859.1', 'coefficient_field': 'CDF', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.706070390195561, 0], [2.0, 0]], [[1.0, 0], [-0.9602178300929612, 0], [3.0, 0]], [[1.0, 0], [-3.572787573448475, 0], [5.0, 0]], [[1.0, 0], [3.956013249431573, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.7987649192783293, 0], [17.0, 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'3.01447808882951793963357447225469', '4.23915681023374013231739105146556', '5.41790398359387073740817473749188', '5.89195947133953518748741094394031', '6.39436902546612798338535316257065', '7.21042946660462663807473688075995', '8.379284513059002854531864481895106', '9.518973301619075393634408851053452'], 'prelabel': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80074673188425925656886414381', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89543048127897555257192748223', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01447808882951793963357447225', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.84418973575603, 'bad_primes': [11, 13], 'central_character': '1.1', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'index': 104, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1859/2/a/s/1/20'], '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': '2-1859-1.1-c1-0-104', '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': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.80074673188425925656886414381', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2282717675532103726010163338475', 'Lhash_array': ['2282717675532103726010163338475'], 'label': '2-1859-1.1-c1-0-104', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1859/2/a/s/1/20'}