Formats: - HTML - YAML - JSON - 2026-08-11T05:25:34.959890
  • lfunc_lfunctions • Show schema
    {'Lhash': '1284738446543743556998657646622', 'a10': [-0.2826301652303366, 0.0], 'a2': [0.23912327825655447, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.9428200577958383, 0.0], 'a5': [-1.181943336052393, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [-0.9428200577958384, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7], 'central_character': '567.1', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '1284738446543743556998657646622', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.23912327825655447, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.181943336052393, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.703696779539284, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0], [13.0, 0]], [[1.0, 0], [-6.9428200577958386, 0], [17.0, 0]], [[1.0, 0], 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[[1.0, 0], [-1.263199842926842, 0], [109.0, 0]], [[1.0, 0], [12.162513013748898, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-567-1.1-c1-0-3', '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/567/2/a/g/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.1957946065576455, 1.18490104630891, 1.150230793632931, 1.0862105207961243, 0.9847525195325915, 0.8367258718253487, 0.6335551217181005, 0.36876324326207616, 0.039361229680854766, -0.352979674316711, -0.8010455498891664, -1.2915816010053842, -1.805285075139911, -2.317387330119496, -2.7988891075378217, -3.2184554183435345, -3.544900040418391, -3.75010244697661, -3.812112705211776, -3.718125226901904, -3.4669537936800996, -3.070630748046495, -2.554792454306612, -1.9576058524587279, -1.3271349854919223, -0.7172314737500214, 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'8.145175021850109391241477118141231', '9.114854047520996330393765466280651', '9.667202982911172467936908893281524', '10.69008582043613053035910427525390'], 'prelabel': '2-567-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01347993391273402801437244725', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.30014270255967393831870514018', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.92990874286156576178906274739', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/a/g/1/2'], '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': '2-567-1.1-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-567-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01347993391273402801437244725', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1284738446543743556998657646622', 'Lhash_array': ['1284738446543743556998657646622'], 'factors': ['2-567-1.1-c1-0-3'], 'label': '2-567-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/a/g/1/2'}