Formats: - HTML - YAML - JSON - 2026-08-11T23:31:22.477977
  • lfunc_lfunctions • Show schema
    {'Lhash': '1729119693155283463580779612174', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.526157602264757, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.32915702695051224, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.6708429730494877, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.274522214469247, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '3040.1', 'coefficient_field': 'CDF', 'conductor': 3040, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.526157602264757, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.32915702695051224, 0], [7.0, 0]], [[1.0, 0], [-0.8791267324606364, 0], [11.0, 0]], [[1.0, 0], [1.3529691301958795, 0], [13.0, 0]], [[1.0, 0], [-5.602284910039638, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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[[1.0, 0], [-8.608877096097762, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 48, 'label': '2-3040-1.1-c1-0-48', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/3040/2/a/r/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [-8.483720046771635e-61, 0.13836584733492258, 0.2760660033804181, 0.41239305767380224, 0.5465589841677728, 0.6776616688275646, 0.8046590538798667, 0.9263525555253482, 1.0413808194476726, 1.1482242951985273, 1.2452205860765775, 1.3305900933734987, 1.402471129961998, 1.4589634195982035, 1.4981787076155009, 1.5182970660867021, 1.517627364512766, 1.494670283111067, 1.4481821631105696, 1.3772379158457249, 1.2812911529616928, 1.1602296597967998, 1.0144243207805048, 0.844769627804925, 0.652713967935577, 0.4402780023571806, 0.21005961929557074, -0.03477582702374868, 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'8.250631447385302360866630123641496'], 'prelabel': '2-3040-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.926918125407529, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36403492637795508376909165950', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.54109357820725989505537620387', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.58693969579463836490442370877', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 24.274522214469247, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 3040, 'conductor_radical': 190, 'degree': 2, 'index': 48, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3040/2/a/r/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': '2-3040-1.1-c1-0-48', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-3040-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.926918125407529, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36403492637795508376909165950', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1729119693155283463580779612174', 'Lhash_array': ['1729119693155283463580779612174'], 'factors': ['2-3040-1.1-c1-0-48'], 'label': '2-3040-1.1-c1-0-48', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3040/2/a/r/1/2'}