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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_837.268', 'a10': [0.9135454576426009, 0.4067366430758002], 'a2': [0.9612616959383189, -0.27563735581699916], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.848048096156426, -0.5299192642332049], 'a5': [0.766044443118978, 0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6156614753256583, 0.7880107536067219], 'a8': [0.6691306063588582, -0.7431448254773942], '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': '837.268', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.634', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^43', 0, 'a^41', 'a^5', 0, 'a^16', 'a^39', 0, 'a^3', 'a^16', 0, 'a^17', 'a^14', 0, 'a^37', 'a^9', 0, 'a^33', 'a^1', 0, 'a^14', 'a^14', 0, 'a^10', 'a^15', 0, 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'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.268', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/268'], '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': '1-837-837.268-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-837-837.268-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.14403447692315352, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.7392031056', 'prec': 37}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_837.268', 'Lhash_array': ['dirichlet_L_837.268'], 'factors': ['1-837-837.268-r0-0-0'], 'label': '1-837-837.268-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/268'}