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lfunc_lfunctions • Show schema
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{'Lhash': '924751426590167589693439762089', 'a10': [-5.601945879737605, 0.0], 'a2': [-1.2570511543775675, 0.0], 'a3': [-2.1850119225171736, 0.0], 'a4': [-0.41982239527802484, 0.0], 'a5': [4.45641838856703, 0.0], 'a6': [2.7466717595289616, 0.0], 'a7': [-4.531354268970776, 0.0], 'a8': [3.041840535372932, 0.0], 'a9': [1.7742771015421959, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.008995322734426, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [1.0, 0]]], [59, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [17, 59], 'central_character': '1003.1', 'coefficient_field': 'CDF', 'conductor': 1003, 'conductor_radical': 1003, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2570511543775675, 0], [2.0, 0]], [[1.0, 0], [2.1850119225171736, 0], [3.0, 0]], [[1.0, 0], [-4.45641838856703, 0], [5.0, 0]], [[1.0, 0], [4.531354268970776, 0], [7.0, 0]], [[1.0, 0], [0.9156330822409096, 0], [11.0, 0]], [[1.0, 0], [-3.8250660728968797, 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'3.64094641572084543362986909079463', '5.28224623131527969756597005192871', '5.72463823865093981038831541056351', '6.46317496411785414008912838622712', '7.17363853146481787768687165640365', '8.880940969579053544300017897944057', '9.214769863436551967753815177837706', '9.998573986212528646112670703884423'], 'prelabel': '2-1003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8300168414224016, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72950024748434165125500007565', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08427766360933779650479689036', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64094641572084543362986909079', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.008995322734426, 'bad_primes': [17, 59], 'central_character': '1.1', 'conductor': 1003, 'conductor_radical': 1003, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1003/2/a/j/1/7'], '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': '2-1003-1.1-c1-0-11', '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': '2-1003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8300168414224016, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.72950024748434165125500007565', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '924751426590167589693439762089', 'Lhash_array': ['924751426590167589693439762089'], 'label': '2-1003-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1003/2/a/j/1/7'}