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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1058', 'a10': [0.7427890291629893, 0.6695255470518686], 'a2': [-0.9715260343384347, 0.2369328271950402], 'a3': [0.9590835257019713, 0.2831232783207275], 'a4': [0.8877256707947304, -0.46037282001878205], 'a5': [-0.5630062991105097, -0.8264526043046191], 'a6': [-0.9988558131018185, -0.047823264555078175], 'a7': [-0.9897180218885506, 0.14303229407729687], 'a8': [-0.7533711667168278, 0.6575955331050582], 'a9': [0.8396824185458478, 0.5430777439602876], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1058', 'coeff_info': ['x^197 - 1', '0.999491418600033 + 0.0318889345211518*I', '\\\\zeta_{197}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.3473', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^91', 'a^9', 'a^182', 'a^129', 'a^100', 'a^94', 'a^76', 'a^18', 'a^23', 'a^123', 'a^191', 'a^162', 'a^185', 'a^138', 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(197)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.710327011254879414505435432195+0.0224425232010797516255289168810*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.712355846291', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.61077363388', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.88707177128', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1058', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1058'], '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': '1-4729-4729.1058-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': '1-4729-4729.1058-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.14385632483929459, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.712355846291', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1058', 'Lhash_array': ['dirichlet_L_4729.1058'], 'factors': ['1-4729-4729.1058-r0-0-0'], 'label': '1-4729-4729.1058-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1058'}
Lfunction data - 1-4729-4729.1058-r0-0-0