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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_92.19', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.8412535328311812, 0.5406408174555976], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.41541501300188644, -0.9096319953545183], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9594929736144974, 0.28173255684142967], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.41541501300188644, -0.9096319953545183], 'algebraic': True, 'analytic_conductor': 0.42724620381935696, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [23, [1]]], 'bad_primes': [2, 23], 'central_character': '92.19', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 92, 'conductor_radical': 46, 'conjugate': 'dirichlet_L_92.63', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^31', 0, 'a^15', 0, 'a^32', 0, 'a^18', 0, 'a^14', 0, 'a^12', 0, 'a^24', 0, 'a^17', 0, 'a^16', 0, 'a^19', 0, 0, 0, 'a^8', 0, 'a^27', 0, 'a^6', 0, 'a^13', 0, 'a^1', 0, 'a^25', 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40}, 'spectral_label': 'r0-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.522938268693645610601056010993-0.111768273254935668451458119654*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.352483842505', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.14018341188', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.74827270959', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.42724620381935696, 'bad_primes': [2, 23], 'central_character': '92.19', 'conductor': 92, 'conductor_radical': 46, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/92/19'], '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': '1-92-92.19-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-92-92.19-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.42724620381935696, 'root_angle': -0.3387950450382671, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.352483842505', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_92.19', 'Lhash_array': ['dirichlet_L_92.19'], 'factors': ['1-92-92.19-r0-0-0'], 'label': '1-92-92.19-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/92/19'}