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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_92.83', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.14231483827328514, -0.9898214418809327], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9594929736144974, -0.28173255684142967], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6548607339452851, -0.7557495743542583], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9594929736144974, -0.28173255684142967], 'algebraic': True, 'analytic_conductor': 0.42724620381935696, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [23, [1]]], 'bad_primes': [2, 23], 'central_character': '92.83', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 92, 'conductor_radical': 46, 'conjugate': 'dirichlet_L_92.51', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^17', 0, 'a^21', 0, 'a^14', 0, 'a^12', 0, 'a^24', 0, 'a^8', 0, 'a^16', 0, 'a^15', 0, 'a^18', 0, 'a^9', 0, 0, 0, 'a^20', 0, 'a^29', 0, 'a^4', 0, 'a^27', 0, 'a^19', 0, 'a^13', 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'unitary', 'types': ['DIR'], 'values': [[1, '1.03305494599513838736164304502-0.451332556659350328526241256116*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.33413034198', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.80587334312', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.80988775975', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.42724620381935696, 'bad_primes': [2, 23], 'central_character': '92.83', 'conductor': 92, 'conductor_radical': 46, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/92/83'], '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': '1-92-92.83-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-92-92.83-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.42724620381935696, 'root_angle': -0.20731689312196697, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33413034198', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_92.83', 'Lhash_array': ['dirichlet_L_92.83'], 'factors': ['1-92-92.83-r0-0-0'], 'label': '1-92-92.83-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/92/83'}