Formats: - HTML - YAML - JSON - 2026-10-17T04:05:50.572842
  • lfunc_lfunctions • Show schema
    {'Lhash': '903460698137431677524522227351', 'a10': [-2.6718146237444933, 0.0], 'a2': [0.7922869913932613, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.3722813232690143, 0.0], 'a5': [-3.3722813232690143, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.5243377989621387, 0.0], 'a8': [-2.6718146237444933, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.695708780117439, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '1089.1', 'coefficient_field': 'CDF', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7922869913932613, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.3722813232690143, 0], [5.0, 0]], [[1.0, 0], [2.5243377989621387, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.840962589317538, 0], [13.0, 0]], [[1.0, 0], [-2.6718146237444933, 0], [17.0, 0]], [[1.0, 0], [-0.939763816175616, 0], 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[1.3722813232690143, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-33e2-1.1-c1-0-4', 'leading_term': '1.0309611964950374767113832679749', '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/1089/2/a/u/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [1.0309611964950374, 1.0251422512698, 1.0075594692743588, 0.977842836068472, 0.935401176168021, 0.8794585377671734, 0.809101667487525, 0.723335749796679, 0.6211454946514949, 0.5015588416331371, 0.36371090015614344, 0.2069061524445628, 0.030677322852984548, -0.16516038621537943, -0.3804607906841575, -0.6147049375593334, -0.8669669651962125, -1.1358885218099228, -1.4196626371128067, -1.7160279074138394, -2.022273784071007, -2.3352576376882572, -2.6514341001280357, -2.9668969620657135, -3.277433628021723, -3.5785918092827886, 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'7.42767989539387870356800633747738', '8.305548445921314219213501365251078', '8.880851184601707278697834858679938', '9.831328178356190437070853201096959'], 'prelabel': '2-33e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.948848721131255, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71270482416430164752155725411', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '3.12387589977623021308529661498', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.72211247330740265275086492277', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 8.695708780117439, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/2/a/u/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': '2-33e2-1.1-c1-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-33e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.948848721131255, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71270482416430164752155725411', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '903460698137431677524522227351', 'Lhash_array': ['903460698137431677524522227351'], 'factors': ['2-33e2-1.1-c1-0-4'], 'label': '2-33e2-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/2/a/u/1/3'}