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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_837.110', 'a10': [-0.8090169943749475, -0.5877852522924731], 'a2': [-0.5591929034707468, -0.8290375725550417], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.374606593415912, 0.9271838545667874], 'a5': [0.9396926207859084, -0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.882947592858927, 0.46947156278589075], 'a8': [0.9781476007338057, -0.20791169081775934], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.110', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.662', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^59', 0, 'a^28', 'a^85', 0, 'a^38', 'a^87', 0, 'a^54', 'a^8', 0, 'a^1', 'a^7', 0, 'a^56', 'a^42', 0, 'a^54', 'a^23', 0, 'a^67', 'a^82', 0, 'a^80', 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  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.110', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/110'], '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': '1-837-837.110-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-837-837.110-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.0727458270871429, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02952794942', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_837.110', 'Lhash_array': ['dirichlet_L_837.110'], 'factors': ['1-837-837.110-r0-0-0'], 'label': '1-837-837.110-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/110'}