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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.401', 'a10': [0.6691306063588582, -0.7431448254773942], 'a2': [0.374606593415912, -0.9271838545667874], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.7193398003386512, -0.6946583704589973], 'a5': [0.9396926207859084, 0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.4383711467890774, 0.898794046299167], 'a8': [-0.9135454576426009, 0.4067366430758002], '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': '837.401', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.263', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^73', 0, 'a^56', 'a^5', 0, 'a^16', 'a^39', 0, 'a^78', 'a^76', 0, 'a^17', 'a^89', 0, 'a^22', 'a^24', 0, 'a^48', 'a^61', 0, 'a^59', 'a^74', 0, 'a^10', 'a^0', 0, 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'194.54894350758032085147333412323', '194.87200651291344139701534541532', '195.48625972963773199742727072377', '196.43782956901623303505418754449', '196.65704845046377871876667178063', '197.51710000994616716049774480889', '198.17542994746276986014535212416', '198.94772104124167192044952013837', '199.65872133207316815408271329437', '199.99391999187664623960423737518'], 'prelabel': '1-837-837.401-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.12210935566153214, 'root_number': '0.927316624567551908114970137601-0.374277808319758633431686957273*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0610546778308', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.40040905687150462868682740034-0.404586773267184707821356958586*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.37330002637', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.09004475214', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.00551013935', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.401', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/401'], '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': '1-837-837.401-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-837-837.401-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.06105467783076607, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37330002637', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.401', 'Lhash_array': ['dirichlet_L_837.401'], 'label': '1-837-837.401-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/401'}
Lfunction data - 1-837-837.401-r0-0-0