Formats: - HTML - YAML - JSON - 2026-10-11T08:49:45.139071
  • lfunc_lfunctions • Show schema
    {'Lhash': '648030843469044600375018386110', 'a10': [0.0, 0.0], 'a2': [1.1931295051621447, 0.0], 'a3': [-3.1623238488869077, 0.0], 'a4': [-0.5764419839115358, 0.0], 'a5': [0.0, 0.0], 'a6': [-3.7730618889848846, 0.0], 'a7': [1.3095756546449504, 0.0], 'a8': [-3.074028949343345, 0.0], 'a9': [7.0002921252389045, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.72183505611902, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 11, 19], 'central_character': '5225.1', 'coefficient_field': 'CDF', 'conductor': 5225, 'conductor_radical': 1045, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.1931295051621447, 0], [2.0, 0]], [[1.0, 0], [3.1623238488869077, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.3095756546449504, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.5399742649247066, 0], [13.0, 0]], [[1.0, 0], [-5.438922184456233, 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'4.78009566681599537957305680344477', '5.26359517317223457558953673446723', '5.80090171755709539531128738764806', '6.38777247523949585878708514680070', '7.35319509215355337987132999713462', '7.891108858679997076319501187587136'], 'prelabel': '2-5225-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.459244155171642, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51120619779012632961477916165', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.70246498799786798852036310025', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.12918528060248249361018131039', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 41.72183505611902, 'bad_primes': [5, 11, 19], 'central_character': '1.1', 'conductor': 5225, 'conductor_radical': 1045, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5225/2/a/n/1/5'], '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': '2-5225-1.1-c1-0-34', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-5225-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.459244155171642, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51120619779012632961477916165', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '648030843469044600375018386110', 'Lhash_array': ['648030843469044600375018386110'], 'factors': ['2-5225-1.1-c1-0-34'], 'label': '2-5225-1.1-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5225/2/a/n/1/5'}