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lfunc_lfunctions • Show schema
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{'Lhash': '559174976433651270733613672762', 'a10': [166.99556269252182, 289.24479922200146], 'a2': [2.0, -3.4641016151377544], 'a3': [-2.725650298306614, 4.720964800332322], 'a4': [-8.0, -13.856406460551018], 'a5': [-41.748890673130454, 72.31119980550037], 'a6': [10.902601193226456, 18.883859201329287], 'a7': [-105.8052023864529, 0.0], 'a8': [-64.0, 0.0], 'a9': [106.64166090268213, 184.70877488697695], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.0945851528932655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 3.4641016151377544]]], [19, [[1.0, 0], [-109.27107721052137, -1569.7639413890397]]]], 'bad_primes': [2, 19], 'central_character': '38.11', 'coefficient_field': 'CDF', 'conductor': 38, 'conductor_radical': 38, 'conjugate': '3493225334949225239440390681832', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 3.4641016151377544]], [[1.0, 0], [2.725650298306614, -4.720964800332322], [-121.5, 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'3.81236536584864477489035446404674', '5.39321988448181505915729968697451', '6.99341878588908051240404940588393', '8.340200419048235469688924656322039', '9.615236703134677380097957738323981', '11.78275971777423213504606478997747', '12.72384648293756968365428463521304', '13.43243030392477721651837419371742', '15.43814787620242112029514372498294'], 'prelabel': '2-38-19.11-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.468721359913521, 'root_angle': -0.5898751159141221, 'root_number': '-0.27861432782398243 - 0.9604030697218696*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.294937557957', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44111127808638808496798053669', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.81236536584864477489035446405', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.39321988448181505915729968697', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.0945851528932655, 'bad_primes': [2, 19], 'central_character': '19.11', 'conductor': 38, 'conductor_radical': 38, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/38/6/c/a/11/2'], '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': '2-38-19.11-c5-0-2', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-38-19.11-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.468721359913521, 'root_angle': -0.29493755795706106, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44111127808638808496798053669', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '559174976433651270733613672762', 'Lhash_array': ['559174976433651270733613672762'], 'label': '2-38-19.11-c5-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/38/6/c/a/11/2'}