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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1081', 'a10': [-0.22400137597858477, -0.9745888279473045], 'a2': [0.4246245908531884, 0.9053695139791059], 'a3': [0.8646934155473022, 0.5023000070765883], 'a4': [-0.6393879136855247, 0.7688843188886557], 'a5': [-0.9774795061135753, -0.21103036541683032], 'a6': [-0.08759702548841304, 0.9961559923654439], 'a7': [0.9662689258749554, 0.2575351682556386], 'a8': [-0.9676242533435677, -0.25239513533605024], 'a9': [0.4953894057817187, 0.8686710174969784], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1081', 'coeff_info': ['x^2364 - 1', '0.999996467887392 + 0.00265785867577771*I', '\\\\zeta_{2364}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.1588', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^426', 'a^198', 'a^852', 'a^1262', 'a^624', 'a^98', 'a^1278', 'a^396', 'a^1688', 'a^933', 'a^1050', 'a^1988', 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21.961383672410207, 'root_angle': -0.43002047633063206, 'root_number': '-0.904881824284677024520221345362-0.425662876087679149066513997312*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, '0.914868690848235914568249366364+1.06156847381546681787763898643*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.25661881795', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.45087435636', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.24583215795', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1081', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1081'], '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': '1-4729-4729.1081-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': '1-4729-4729.1081-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.43002047633063206, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25661881795', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1081', 'Lhash_array': ['dirichlet_L_4729.1081'], 'factors': ['1-4729-4729.1081-r0-0-0'], 'label': '1-4729-4729.1081-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1081'}
Lfunction data - 1-4729-4729.1081-r0-0-0