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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.3838', 'a10': [-0.8565735423029402, -0.5160249670574023], 'a2': [0.8686710174969784, -0.4953894057817187], 'a3': [-0.5826127159653203, 0.8127499143005265], 'a4': [0.5091786732784713, -0.8606608383552581], 'a5': [-0.4884473087541886, -0.8725933913173938], 'a6': [-0.10347108368979219, 0.9946324621889535], 'a7': [0.9520372666814378, -0.30598209563589956], 'a8': [0.015946494912164058, -0.9998728465660103], 'a9': [-0.3211248463910262, -0.947036869942422], 'algebraic': True, 'analytic_conductor': 508.20162935378175, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.3838', 'coeff_info': ['x^1576 - 1', '0.999992052752480 + 0.00398678214625284*I', '\\\\zeta_{1576}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.2330', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1446', 'a^550', 'a^1316', 'a^1054', 'a^420', 'a^1498', 'a^1186', 'a^1100', 'a^924', 'a^359', 'a^290', 'a^444', 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False, 'root_analytic_conductor': 508.20162935378175, 'root_angle': -0.3991175995752642, 'root_number': '0.311652268007091344600531069862-0.950196223864332197517601288820*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(1576)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.39571194724190385052502592405-0.382877028309396971859103503592*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.458065920898', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.40410434873', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.98773609859', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 508.20162935378175, 'bad_primes': [4729], 'central_character': '4729.3838', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/3838'], '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': '1-4729-4729.3838-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4729-4729.3838-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 508.20162935378175, 'root_angle': -0.1995587997876321, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.458065920898', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.3838', 'Lhash_array': ['dirichlet_L_4729.3838'], 'label': '1-4729-4729.3838-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/3838'}
Lfunction data - 1-4729-4729.3838-r1-0-0