Formats: - HTML - YAML - JSON - 2026-10-14T01:10:01.413979
  • lfunc_lfunctions • Show schema
    {'Lhash': '2857964733771270349792191386041', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [189.26489334679482, 0.0], 'a4': [0.0, 0.0], 'a5': [-729.9436112430899, 0.0], 'a6': [0.0, 0.0], 'a7': [-2401.0, 0.0], 'a8': [0.0, 0.0], 'a9': [16138.199853573615, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.842006825176902, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2401.0, 0]]]], 'bad_primes': [2, 7], 'central_character': '56.1', 'coefficient_field': 'CDF', 'conductor': 56, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-189.26489334679482, 0], [19683.0, 0]], [[1.0, 0], [729.9436112430899, 0], [1953125.0, 0]], [[1.0, 0], [2401.0, 0]], [[1.0, 0], [33434.102109928055, 0], [2357947691.0, 0]], [[1.0, 0], [131906.7963791702, 0], [10604499373.0, 0]], [[1.0, 0], [504407.5192585279, 0], [118587876497.0, 0]], [[1.0, 0], [-280046.8437980553, 0], 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-0.8475825986722852], 'positive_zeros': ['2.25453664697253233675057329534051', '3.29536195782328239556843341375582', '4.81319446127923288418302911127640', '6.95597219647352061561149595433640', '8.014783233017976394429587599809716', '9.053544037250333776475004945492890', '10.15659174999226919968439429931930', '11.71128867607423890126690001970593', '13.03837742796310815364330427980345'], 'prelabel': '2-56-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.370475474776596, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25453664697253233675057329534', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.29536195782328239556843341376', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.81319446127923288418302911128', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 28.842006825176902, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 56, 'conductor_radical': 14, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/56/10/a/a/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': '2-56-1.1-c9-0-13', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [9], 'order_of_vanishing': 1, 'prelabel': '2-56-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.370475474776596, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25453664697253233675057329534', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2857964733771270349792191386041', 'Lhash_array': ['2857964733771270349792191386041'], 'factors': ['2-56-1.1-c9-0-13'], 'label': '2-56-1.1-c9-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/56/10/a/a/1/3'}