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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_967.24', 'a10': [-0.9248101959793065, -0.38042883882891515], 'a2': [0.5606300178972284, 0.8280664122113355], 'a3': [-0.8740409688832762, 0.48585222518126203], 'a4': [-0.3713879660651067, 0.9284777749962695], 'a5': [-0.8334967003942021, 0.5525244342397698], 'a6': [-0.8923315129986835, -0.4513806275301149], 'a7': [-0.04876314871420185, 0.9988103700540342], 'a8': [-0.9770525020210205, 0.21299861101533926], 'a9': [0.5278952305728325, -0.8493094992630519], 'algebraic': True, 'analytic_conductor': 103.91858227640239, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.24', 'coeff_info': ['x^322 - 1', '0.999809627498073 + 0.0195117595865944*I', '\\\\zeta_{322}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.685', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^50', 'a^135', 'a^100', 'a^131', 'a^185', 'a^83', 'a^150', 'a^270', 'a^181', 'a^86', 'a^235', 'a^75', 'a^133', 'a^266', 'a^200', 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'primitive': True, 'rational': False, 'root_analytic_conductor': 103.91858227640239, 'root_angle': 0.1814645386637471, 'root_number': '0.841853666944026604043339427171+0.539705849007490309112738767849*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0907322693319', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(322)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.393792436092129111351625456222+0.600891124251562377234637459373*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0368187602903', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '2.17550682547', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.41184149973', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 103.91858227640239, 'bad_primes': [967], 'central_character': '967.24', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/24'], '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': '1-967-967.24-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-967-967.24-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 103.91858227640239, 'root_angle': 0.09073226933187355, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0368187602903', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_967.24', 'Lhash_array': ['dirichlet_L_967.24'], 'label': '1-967-967.24-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/24'}
Lfunction data - 1-967-967.24-r1-0-0