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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_161.5', 'a10': [0.9819286972627067, -0.18925124436041021], 'a2': [0.0475819158237423, -0.998867339183008], 'a3': [-0.9283679330160726, -0.3716624556603275], 'a4': [-0.9954719225730846, -0.09505604330418266], 'a5': [0.23575893550942723, 0.9718115683235417], 'a6': [-0.41541501300188644, 0.9096319953545183], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.14231483827328514, 0.9898214418809327], 'a9': [0.7237340381050702, 0.690079011482112], 'algebraic': True, 'analytic_conductor': 0.7476808566838746, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [23, [1]]], 'bad_primes': [7, 23], 'central_character': '161.5', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 161, 'conductor_radical': 161, 'conjugate': 'dirichlet_L_161.129', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^50', 'a^37', 'a^34', 'a^14', 'a^21', 0, 'a^18', 'a^8', 'a^64', 'a^49', 'a^5', 'a^9', 0, 'a^51', 'a^2', 'a^10', 'a^58', 'a^56', 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'unitary', 'types': ['DIR'], 'values': [[1, '0.759383279168434487333233692954-0.310529371566671436257551776494*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.2247698481', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.71403069595', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.05727780119', 'prec': 44}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.7476808566838746, 'bad_primes': [7, 23], 'central_character': '161.5', 'conductor': 161, 'conductor_radical': 161, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/161/5'], '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': '1-161-161.5-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': '1-161-161.5-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7476808566838746, 'root_angle': -0.13103787811379736, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.2247698481', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_161.5', 'Lhash_array': ['dirichlet_L_161.5'], 'factors': ['1-161-161.5-r0-0-0'], 'label': '1-161-161.5-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/161/5'}