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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1008', 'a10': [-0.46273064330597236, -0.8864989293539169], 'a2': [-0.9590835257019713, 0.2831232783207275], 'a3': [0.5630062991105097, 0.8264526043046191], 'a4': [0.8396824185458478, -0.5430777439602876], 'a5': [0.19280885372573733, 0.9812363354080235], 'a6': [-0.773958037050753, -0.6332368884426628], 'a7': [0.999307785396187, 0.03720147909113634], 'a8': [-0.6515676231958488, 0.7585905564946828], 'a9': [-0.36604781432377465, 0.9305960442795721], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1008', 'coeff_info': ['x^2364 - 1', '0.999996467887392 + 0.00265785867577771*I', '\\\\zeta_{2364}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.2585', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1074', 'a^366', 'a^2148', 'a^518', 'a^1440', 'a^14', 'a^858', 'a^732', 'a^1592', 'a^1653', 'a^150', 'a^284', 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0.4045362730517092, 'root_number': '-0.825439333409330186697389823399+0.564490838597723070490878429391*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2364)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.825575149261111436109638740563+0.604470219647505959574539633793*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.15592681727', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.94630260648', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.96755572455', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1008', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1008'], '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': '1-4729-4729.1008-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': '1-4729-4729.1008-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.4045362730517092, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15592681727', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1008', 'Lhash_array': ['dirichlet_L_4729.1008'], 'factors': ['1-4729-4729.1008-r0-0-0'], 'label': '1-4729-4729.1008-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1008'}
Lfunction data - 1-4729-4729.1008-r0-0-0