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{'Lhash': 'dirichlet_L_4008.1157', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9545040627715552, -0.29819791104666543], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.3870502972022171, -0.9220586030376136], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 18.61307374899981, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [167, [1]]], 'bad_primes': [2, 3, 167], 'central_character': '4008.1157', 'coeff_info': ['x^166 - 1', '0.999283754816331 + 0.0378414767176703*I', '\\\\zeta_{166}'], 'conductor': 4008, 'conductor_radical': 1002, 'conjugate': 'dirichlet_L_4008.821', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^91', 0, 'a^114', 0, 0, 0, 'a^224', 0, 'a^160', 0, 0, 0, 'a^92', 0, 'a^215', 0, 0, 0, 'a^128', 0, 'a^16', 0, 0, 0, 'a^204', 0, 'a^56', 0, 0, 0, 'a^205', 0, 'a^156', 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.61307374899981, 'bad_primes': [2, 3, 167], 'central_character': '4008.1157', 'conductor': 4008, 'conductor_radical': 1002, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4008/1157'], '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': '1-4008-4008.1157-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': '1-4008-4008.1157-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.61307374899981, 'root_angle': -0.4264965268399188, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.166885679186', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4008.1157', 'Lhash_array': ['dirichlet_L_4008.1157'], 'label': '1-4008-4008.1157-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4008/1157'}