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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_837.193', 'a10': [-0.10452846326765347, -0.9945218953682733], 'a2': [-0.9975640502598242, -0.0697564737441253], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9902680687415704, 0.13917310096006544], 'a5': [0.17364817766693036, 0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.848048096156426, -0.5299192642332049], 'a8': [-0.9781476007338057, -0.20791169081775934], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.193', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.412', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 0, 'a^1', 'a^10', 0, 'a^41', 'a^24', 0, 'a^33', 'a^41', 0, 'a^7', 'a^19', 0, 'a^2', 'a^9', 0, 'a^3', 'a^11', 0, 'a^19', 'a^19', 0, 'a^20', 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'195.266265319092618448404562269232', '195.677567999869042792444817686131', '196.771768195280031823119885281114', '197.43539869814214561976252937430', '197.69063013450465731010320732730', '198.29151626778304415222753477369', '198.808499591990594696603848318908', '199.47844090062136173997249126241'], 'prelabel': '1-837-837.193-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.14294612683353847, 'root_number': '0.623052580250125351901734175722+0.782179955153327301300096138168*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.142946126834', 'prec': 40}, 'spectral_label': 'r0-0', 'st_group': 'mu(45)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.865891886452648012786987289146+0.167051569470461202822504464558*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.27928230912', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.94591061291', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.33639668795', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.193', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/193'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-837-837.193-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-837-837.193-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.14294612683353847, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27928230912', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_837.193', 'Lhash_array': ['dirichlet_L_837.193'], 'factors': ['1-837-837.193-r0-0-0'], 'label': '1-837-837.193-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/193'}