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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_161.158', 'a10': [-0.5800569095711982, 0.8145759520503357], 'a2': [0.23575893550942723, -0.9718115683235417], 'a3': [-0.32706796331742166, 0.9450008187146685], 'a4': [-0.8888354486549235, -0.4582265217274104], 'a5': [-0.9283679330160726, -0.3716624556603275], 'a6': [0.8412535328311812, 0.5406408174555976], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6548607339452851, 0.7557495743542583], 'a9': [-0.7860530947427875, -0.6181589862206052], 'algebraic': True, 'analytic_conductor': 17.30185289193463, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [23, [1]]], 'bad_primes': [7, 23], 'central_character': '161.158', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 161, 'conductor_radical': 161, 'conjugate': 'dirichlet_L_161.107', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^52', 'a^20', 'a^38', 'a^37', 'a^6', 0, 'a^24', 'a^40', 'a^23', 'a^47', 'a^58', 'a^12', 0, 'a^57', 'a^10', 'a^17', 'a^26', 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'0.85178989235', 'prec': 37}, 'z2': {'__RealLiteral__': 0, 'data': '2.99620804246', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.04237421223', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 17.30185289193463, 'bad_primes': [7, 23], 'central_character': '161.158', 'conductor': 161, 'conductor_radical': 161, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/161/158'], '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': '1-161-161.158-r1-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-161-161.158-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.30185289193463, 'root_angle': -0.02305667581426909, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.85178989235', 'prec': 37}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_161.158', 'Lhash_array': ['dirichlet_L_161.158'], 'factors': ['1-161-161.158-r1-0-0'], 'label': '1-161-161.158-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/161/158'}