Formats: - HTML - YAML - JSON - 2026-09-15T02:37:30.762414
  • lfunc_lfunctions • Show schema
    {'Lhash': '1149505731775197420528102805767', 'a10': [0.0, 0.0], 'a2': [1.8370813160308892, 0.0], 'a3': [0.0, 0.0], 'a4': [1.3748677617097835, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [3.5481367222500597, 0.0], 'a8': [-1.1484187550115261, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.47545968271595, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 37], 'central_character': '8325.1', 'coefficient_field': 'CDF', 'conductor': 8325, 'conductor_radical': 555, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8370813160308892, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.5481367222500597, 0], [7.0, 0]], [[1.0, 0], [-1.741842607177344, 0], [11.0, 0]], [[1.0, 0], [1.9924718021184133, 0], [13.0, 0]], [[1.0, 0], [-6.520673039497608, 0], [17.0, 0]], [[1.0, 0], [4.616737882531851, 0], 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[[1.0, 0], [-10.270295012436826, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 122, 'label': '2-8325-1.1-c1-0-122', 'leading_term': '4.80290216544018879424095374318', '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/8325/2/a/cb/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 17}, 'plot_values': [4.802902165440189, 4.789741493301957, 4.7501843900199505, 4.684015596475367, 4.590909044590915, 4.470474721385027, 4.322320129038202, 4.1461226522855235, 3.9417086624439404, 3.709135006899932, 3.448768618672475, 3.161360275788166, 2.8481089803418156, 2.5107139525071793, 2.1514117978210634, 1.7729969743644156, 1.3788242419951047, 0.9727923118777496, 0.5593084318648736, 0.14323414590121994, -0.27018704209840605, -0.6754188850986717, -1.0667368000951858, -1.4383453127023058, -1.7845059450732832, -2.099672544061949, 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'5.72428849522135175290106485071335', '6.05659200553274862061392653174537', '6.97936487917321086352029542771175', '7.77027432964681639890922088121802'], 'prelabel': '2-8325-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.15324841291592, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.906800132124923830822231339161', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.06712875927414212374639836244', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.73558937701165853347356407623', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 66.47545968271595, 'bad_primes': [3, 5, 37], 'central_character': '1.1', 'conductor': 8325, 'conductor_radical': 555, 'degree': 2, 'index': 122, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8325/2/a/cb/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': '2-8325-1.1-c1-0-122', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-8325-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.15324841291592, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.906800132124923830822231339161', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1149505731775197420528102805767', 'Lhash_array': ['1149505731775197420528102805767'], 'factors': ['2-8325-1.1-c1-0-122'], 'label': '2-8325-1.1-c1-0-122', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8325/2/a/cb/1/5'}