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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1053', 'a10': [-0.013288917867428304, 0.9999116984323729], 'a2': [-0.9544467510209387, -0.2983812987865934], 'a3': [0.6270456034374474, 0.7789825487196536], 'a4': [0.8219372010688514, 0.5695781223845441], 'a5': [-0.28567138676700893, -0.9583276364493586], 'a6': [-0.36604781432377465, -0.9305960442795721], 'a7': [-0.07700169473884057, 0.9970309619100836], 'a8': [-0.6145438311858796, -0.7888826779384759], 'a9': [-0.21362762241953479, 0.976915164658312], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1053', 'coeff_info': ['x^1182 - 1', '0.999985871574519 + 0.00531569857584313*I', '\\\\zeta_{1182}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.3485', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^648', 'a^168', 'a^114', 'a^832', 'a^816', 'a^310', 'a^762', 'a^336', 'a^298', 'a^129', 'a^282', 'a^1054', 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0.9156781426698322, 'root_number': '-0.965117396881882621481155812570+0.261817513233814564812019029102*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(1182)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.716469779293128625449388168506+0.133769372762085595034010821240*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.21027557332', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.02279403731', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.78802279621', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1053', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1053'], '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': '1-4729-4729.1053-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': '1-4729-4729.1053-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.4578390713349161, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21027557332', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1053', 'Lhash_array': ['dirichlet_L_4729.1053'], 'label': '1-4729-4729.1053-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1053'}
Lfunction data - 1-4729-4729.1053-r0-0-0