Formats: - HTML - YAML - JSON - 2026-09-07T09:04:39.594247
  • lfunc_lfunctions • Show schema
    {'Lhash': '1036740112430401042346895252851', 'a10': [0.0, 0.0], 'a2': [-1.1319409479332767, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.7187096903919147, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.110092071022816, 0.0], 'a8': [3.0774188240976095, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.13604686409738, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 19], 'central_character': '4275.1', 'coefficient_field': 'CDF', 'conductor': 4275, 'conductor_radical': 285, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1319409479332767, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.110092071022816, 0], [7.0, 0]], [[1.0, 0], [-5.784322462899888, 0], [11.0, 0]], [[1.0, 0], [-6.782764761261801, 0], [13.0, 0]], [[1.0, 0], [-5.4138072776045565, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'4.42371175340781856095559766199320', '5.72587740312920340713143082154101', '6.28981967398762436247361419850151', '6.92840296431310345324356536107370', '7.77319371030302314620335320313957', '8.645559630602223469002747658667057'], 'prelabel': '2-4275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.842606170545588, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.817843743570779719769716503409', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.42653737968929985886927062712', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.18827542961897747808853792720', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 34.13604686409738, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 4275, 'conductor_radical': 285, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4275/2/a/bt/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': '2-4275-1.1-c1-0-43', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.842606170545588, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.817843743570779719769716503409', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1036740112430401042346895252851', 'Lhash_array': ['1036740112430401042346895252851'], 'factors': ['2-4275-1.1-c1-0-43'], 'label': '2-4275-1.1-c1-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4275/2/a/bt/1/3'}