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lfunc_lfunctions • Show schema
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{'Lhash': '1218279152697814806472704164169', 'a10': [7.192235935955849, 0.0], 'a2': [1.4384471871911697, 0.0], 'a3': [0.5615528128088303, 0.0], 'a4': [-5.930869689661812, 0.0], 'a5': [5.0, 0.0], 'a6': [0.8077640640441514, 0.0], 'a7': [31.053975315279473, 0.0], 'a8': [-20.038820320220758, 0.0], 'a9': [-26.684658438426492, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 35.69615555347309, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-5.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '605.1', 'coefficient_field': 'CDF', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4384471871911697, 0], [8.0, 0]], [[1.0, 0], [-0.5615528128088303, 0], [27.0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [-31.053975315279473, 0], [343.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-45.6155281280883, 0], [2197.0, 0]], [[1.0, 0], [-40.45360218224989, 0], [4913.0, 0]], 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['0.961052795209085454789672262332084', '2.38676096773606048045772383350470', '3.73946661765320663390552653761109', '4.74930780343235686892296600620579', '5.49588942808232872576462206605991', '6.30553913608353578590922633672904', '7.932210956650347655102640537734384', '8.502349391220599004124457374645289', '9.113300283836949239862552560289831', '10.40335165362817584604611235139983'], 'prelabel': '2-605-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.974625976031729, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.961052795209085454789672262332', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.38676096773606048045772383350', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73946661765320663390552653761', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 35.69615555347309, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/605/4/a/g/1/1'], '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': '2-605-1.1-c3-0-41', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-605-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.974625976031729, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.961052795209085454789672262332', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1218279152697814806472704164169', 'Lhash_array': ['1218279152697814806472704164169'], 'label': '2-605-1.1-c3-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/605/4/a/g/1/1'}