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lfunc_lfunctions • Show schema
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{'Lhash': '885443579092630477880849042988', 'a10': [0, 0], 'a2': [0.8065036531013159, -1.1617021380432389], 'a3': [0, 0], 'a4': [-0.6991037150684646, -1.8738340362949626], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-0.7461746360961262, 0], 'a8': [-2.740666706401468, -0.6991037150684646], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.373072363830476, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8065036531013159, 1.1617021380432389]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.901', 'coefficient_field': 'CDF', 'conductor': 1800, 'conductor_radical': 30, 'conjugate': '1553786140090393723017282686598', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8065036531013159, 1.1617021380432389]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7461746360961262, 0], [7.0, 0]], [[1.0, 0], [0, -5.360675378792557], [-11.0, 0]], [[1.0, 0], [0, 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'positive_zeros': ['0.69849182332514504161715399679302', '2.86014267371486368250676389943015', '3.36272665139321949433189804205969', '4.45533169120703348974449859218610', '5.49384048734057389665599177302204', '5.98493182464189907680103581856766', '6.76866788729576619167533833110913', '7.85189956077013771129012703076290', '8.221202035198546409861692705750112', '9.115726452449161618122028401331192'], 'prelabel': '2-1800-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7911835043730706, 'root_angle': 0.07950077353443546, 'root_number': '0.9689720065343394054507707048742497710453628561812045866 + 0.2471704888388096232627872778407634845963651224255649625*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.03975038676721773', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69849182332514504161715399679', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86014267371486368250676389943', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36272665139321949433189804206', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.373072363830476, 'bad_primes': [2, 3, 5], 'central_character': '8.5', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/2/k/u/901/9'], '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': '2-1800-8.5-c1-0-30', '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': '2-1800-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7911835043730706, 'root_angle': 0.03975038676721773, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.69849182332514504161715399679', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '885443579092630477880849042988', 'Lhash_array': ['885443579092630477880849042988'], 'label': '2-1800-8.5-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/2/k/u/901/9'}