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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_368.283', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.9096319953545183, 0.41541501300188644], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.7557495743542583, 0.6548607339452851], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8412535328311812, 0.5406408174555976], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.6548607339452851, 0.7557495743542583], 'algebraic': True, 'analytic_conductor': 1.7089848152774278, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [23, [1]]], 'bad_primes': [2, 23], 'central_character': '368.283', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 368, 'conductor_radical': 46, 'conjugate': 'dirichlet_L_368.355', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^47', 0, 'a^49', 0, 'a^18', 0, 'a^50', 0, 'a^67', 0, 'a^37', 0, 'a^52', 0, 'a^2', 0, 'a^53', 0, 'a^21', 0, 0, 0, 'a^54', 0, 'a^53', 0, 'a^57', 0, 'a^30', 0, 'a^26', 0, 'a^23', 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'3.01320145047', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.47483985518', 'prec': 44}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1.7089848152774278, 'bad_primes': [2, 23], 'central_character': '368.283', 'conductor': 368, 'conductor_radical': 46, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/368/283'], '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': '1-368-368.283-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': '1-368-368.283-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7089848152774278, 'root_angle': 0.2062484098247742, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84356685032', 'prec': 44}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_368.283', 'Lhash_array': ['dirichlet_L_368.283'], 'factors': ['1-368-368.283-r0-0-0'], 'label': '1-368-368.283-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/368/283'}