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lfunc_lfunctions • Show schema
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{'Lhash': '2226466011411602755379197492781', 'a10': [-70.70221575974207, 1.0939317450736394], 'a2': [2.0, 2.0], 'a3': [5.562220958213714, -5.562220958213714], 'a4': [0, 8.0], 'a5': [-17.402071003667107, 17.949036876203927], 'a6': [22.248883832854855, 0], 'a7': [-33.374427070103465, -33.374427070103465], 'a8': [-16.0, 16.0], 'a9': [0, 19.123396024016227], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.775091509284202, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, -2.0]]], [5, [[1.0, 0], [17.402071003667107, -17.949036876203927]]], [23, [[1.0, 0], [-77.99679480594058, 77.99679480594058]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.47', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': '395613361986243565805880314214', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, -2.0]], [[1.0, 0], [-5.562220958213714, 5.562220958213714], [0, -81.0]], [[1.0, 0], 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'rational': False, 'root_analytic_conductor': 4.875970827361891, 'root_angle': 0.5688671893767534, 'root_number': '-0.2146687459149995802215479815189039842874122667296222375 + 0.9766869147926992428256444440895561855773854314291618604*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2844335946883767', 'prec': 60}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75637199320597254997885593177', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.49420579338487593720879561117', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95886343983929548347485939853', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.775091509284202, 'bad_primes': [2, 5, 23], 'central_character': '5.2', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/5/f/b/47/16'], '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': '2-230-5.2-c4-0-38', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-230-5.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.875970827361891, 'root_angle': 0.2844335946883767, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75637199320597254997885593177', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2226466011411602755379197492781', 'Lhash_array': ['2226466011411602755379197492781'], 'label': '2-230-5.2-c4-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/5/f/b/47/16'}