Formats: - HTML - YAML - JSON - 2026-07-18T21:27:34.163897
  • lfunc_lfunctions • Show schema
    {'Lhash': '867011754031786215401187149821', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.2798548279546993, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.6226177578077419, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.6993329290630097, 0.0], 'a8': [0.0, 0.0], 'a9': [2.1977380365483525, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.79269013540588, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 23], 'central_character': '4232.1', 'coefficient_field': 'CDF', 'conductor': 4232, 'conductor_radical': 46, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.2798548279546993, 0], [3.0, 0]], [[1.0, 0], [1.6226177578077419, 0], [5.0, 0]], [[1.0, 0], [3.6993329290630097, 0], [7.0, 0]], [[1.0, 0], [5.393190304519811, 0], [11.0, 0]], [[1.0, 0], [0.8696751806532482, 0], [13.0, 0]], [[1.0, 0], [-3.44422516809696, 0], [17.0, 0]], [[1.0, 0], [-5.992151236644468, 0], [19.0, 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'4.44516236038477792468198330051825', '5.43632939043528215005054862058836', '6.24902249438072554209683883234797', '7.33641579981887971317453325285055', '7.75359540655766198232098679992467', '8.196866873035724874478512532005092'], 'prelabel': '2-4232-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.813148040038708, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68395167712277210571966003749', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.43451376683400043615265172356', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01727334083145676058062497666', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 33.79269013540588, 'bad_primes': [2, 23], 'central_character': '1.1', 'conductor': 4232, 'conductor_radical': 46, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4232/2/a/x/1/9'], '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': '2-4232-1.1-c1-0-29', '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': '2-4232-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.813148040038708, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68395167712277210571966003749', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '867011754031786215401187149821', 'Lhash_array': ['867011754031786215401187149821'], 'factors': ['2-4232-1.1-c1-0-29'], 'label': '2-4232-1.1-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4232/2/a/x/1/9'}