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lfunc_lfunctions • Show schema
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{'Lhash': '1060520254537042432703263916000', 'a10': [10.0, 0.0], 'a2': [-2.0, 0.0], 'a3': [0.0, 0.0], 'a4': [4.0, 0.0], 'a5': [-5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [18.983664486982395, 0.0], 'a8': [-8.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 69.03223470671655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [5.0, 0]]], [13, [[1.0, 0], [13.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1170.1', 'coefficient_field': 'CDF', 'conductor': 1170, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [-18.983664486982395, 0], [343.0, 0]], [[1.0, 0], [-59.933558997749685, 0], [1331.0, 0]], [[1.0, 0], [13.0, 0]], [[1.0, 0], [46.55376581849014, 0], [4913.0, 0]], [[1.0, 0], [-102.91722348473208, 0], [6859.0, 0]], [[1.0, 0], [-4.521094792454926, 0], 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'4.22197455610273789586061479535417', '5.02934524250855976907649869468088', '6.36509336738283436197874156342513', '6.96962981609360572871928893670101', '8.006755913535589187572828777932820', '8.447441915292712639213330486719089', '9.431928803115621062834732986528384'], 'prelabel': '2-1170-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.308563937692034, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.836602967999309145616636039497', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.69715154244688280427516241313', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.05130688182241339941656957202', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 69.03223470671655, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 1170, 'conductor_radical': 390, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1170/4/a/bg/1/3'], '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': '2-1170-1.1-c3-0-16', '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': '2-1170-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.308563937692034, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.836602967999309145616636039497', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1060520254537042432703263916000', 'Lhash_array': ['1060520254537042432703263916000'], 'label': '2-1170-1.1-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1170/4/a/bg/1/3'}