Formats: - HTML - YAML - JSON - 2026-09-22T05:27:54.339524
  • lfunc_lfunctions • Show schema
    {'Lhash': '537317616768156845153239888216', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.3789652764535001, 0.0], 'a4': [0.0, 0.0], 'a5': [-4.27752837599464, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.431003372474467, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.856385319242522, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.287106896341061, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 13], 'central_character': '1664.1', 'coefficient_field': 'CDF', 'conductor': 1664, 'conductor_radical': 26, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.3789652764535001, 0], [3.0, 0]], [[1.0, 0], [4.27752837599464, 0], [5.0, 0]], [[1.0, 0], [4.431003372474467, 0], [7.0, 0]], [[1.0, 0], [2.38882559217585, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.5195978230876395, 0], [17.0, 0]], [[1.0, 0], [-7.745088103061312, 0], [19.0, 0]], [[1.0, 0], 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[[1.0, 0], [-10.104076192041934, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-1664-1.1-c1-0-1', 'leading_term': '0.43808293140246162794814986190816', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1664/2/a/bb/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [0.43808293140246163, 0.43008455030681875, 0.4059877739719946, 0.3654971752171938, 0.3081512506428027, 0.23336639685128, 0.14049415619384062, 0.028888134498115836, -0.1020232151452092, -0.2526616285341231, -0.4232252396805774, -0.6136188899208959, -0.8233910363809139, -1.0516793870111518, -1.2971670897759018, -1.558051067118443, -1.8320238882562876, -2.1162703805773195, -2.4074799687652377, -2.7018754737579256, -2.9952587885770225, -3.2830734678738764, -3.560483823594623, -3.8224696178811355, -4.063934899117169, 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'7.24578993007610007048365975007034', '7.62979640908105475922766698344908', '8.643065681912566251684364337444393', '9.133482450373126231868926688774804'], 'prelabel': '2-1664-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.645148405256096, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42386886155492492061098730422', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.81919016637088894864324213115', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.31940245358544435839949988333', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 13.287106896341061, 'bad_primes': [2, 13], 'central_character': '1.1', 'conductor': 1664, 'conductor_radical': 26, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1664/2/a/bb/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': '2-1664-1.1-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1664-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.645148405256096, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.42386886155492492061098730422', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '537317616768156845153239888216', 'Lhash_array': ['537317616768156845153239888216'], 'factors': ['2-1664-1.1-c1-0-1'], 'label': '2-1664-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1664/2/a/bb/1/3'}