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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_231.230', 'a10': [1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [1.0, 0.0], 'a7': [1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 24.82439762755838, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '231.230', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 231, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_231.230', 'degree': 1, 'dirichlet_coefficients': [1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, -1, 0, 1, 1, 0, 0, -1, 0, 1, 1, 0, 0, 1, 0, -1, 1, 0, -1, 0, 0, 1, 1, 0, 1, -1, 0, -1, 0, 0, -1, 1, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 1, 1, 0, 1, -1, 0, 1, 1, 0, 1, -1, 0, 0, -1, 0, 1, 1, 0, 1, 0, 0, -1, 1, 0, -1, -1, 0, -1, -1, 0, 0, 1, 0, 0, -1, 0, 1, 1, 0, -1, 0, 0, 1], 'euler_factors': [[1, 1], [0], [1, 1], [0], [0], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], 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'196.91154031848920333704984068256', '197.61342700641563454379565691879', '198.0163242310759826236528803970', '199.25171908228733412722395299381', '199.97162955888852377547394436206'], 'prelabel': '1-231-231.230-r1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.82439762755838, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'r1-0', 'st_group': 'mu(2)', 'symmetry_type': 'orthogonal', 'types': ['DIR'], 'values': [[1, '2.48041945356307541448779878186']], 'z1': {'__RealLiteral__': 0, 'data': '1.41283231189', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.56455585443', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.84135256058', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 24.82439762755838, 'bad_primes': [3, 7, 11], 'central_character': '231.230', 'conductor': 231, 'conductor_radical': 231, 'degree': 1, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 1, 1, 0, -1, -1, 0, 0, 1, 0, 1, 1, 0, 0, -1, 0, 1, -1, 0, -1, 0, 0, -1, 1, 0, 1, 1, 0, 1, 0, 0, -1, -1, 0, 0, -1, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, -1, -1, 0, 1, 1, 0, -1, 1, 0, 0, 1, 0, -1, 1, 0, -1, 0, 0, 1, -1, 0, -1, 1, 0, -1, -1, 0, 0, -1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1], 'euler11': [1, 0], 'euler13': [1, 1], 'euler17': [1, -1], 'euler19': [1, 1], 'euler2': [1, 1], 'euler23': [1, -1], 'euler29': [1, 1], 'euler3': [1, 0], 'euler31': [1, -1], 'euler37': [1, 1], 'euler41': [1, -1], 'euler43': [1, -1], 'euler47': [1, 1], 'euler5': [1, 1], 'euler53': [1, -1], 'euler59': [1, 1], 'euler61': [1, 1], 'euler67': [1, 1], 'euler7': [1, 0], 'euler71': [1, -1], 'euler73': [1, 1], 'euler79': [1, -1], 'euler83': [1, -1], 'euler89': [1, 1], 'euler97': [1, -1], 'euler_factors': [[1, 1], [1, 0], [1, 1], [1, 0], [1, 0], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/231/230'], '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': '1-231-231.230-r1-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-231-231.230-r1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.82439762755838, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41283231189', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_231.230', 'Lhash_array': ['dirichlet_L_231.230'], 'factors': ['1-231-231.230-r1-0-0'], 'label': '1-231-231.230-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/231/230'}