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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2912.1403', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.9659258262890683, 0.25881904510252074], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9659258262890683, 0.25881904510252074], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.8660254037844386, 0.5], 'algebraic': True, 'analytic_conductor': 13.523271146977907, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]], [13, [1]]], 'bad_primes': [2, 7, 13], 'central_character': '2912.1403', 'coeff_info': ['x^24 - 1', '0.965925826289068 + 0.258819045102521*I', '\\\\zeta_{24}'], 'conductor': 2912, 'conductor_radical': 182, 'conjugate': 'dirichlet_L_2912.467', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^25', 0, 'a^11', 0, 0, 0, 'a^26', 0, 'a^7', 0, 0, 0, 'a^12', 0, 'a^16', 0, 'a^17', 0, 0, 0, 'a^14', 0, 'a^22', 0, 'a^27', 0, 'a^9', 0, 'a^28', 0, 'a^8', 0, 0, 0, 'a^23', 0, 0, 0, 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{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(24)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.03632093887376607475645481685+0.301851157541729910788312438757*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.24686545258', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.57639951039', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.75352653219', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 13.523271146977907, 'bad_primes': [2, 7, 13], 'central_character': '2912.1403', 'conductor': 2912, 'conductor_radical': 182, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2912/1403'], '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': '1-2912-2912.1403-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': '1-2912-2912.1403-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.523271146977907, 'root_angle': 0.38475628638727943, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24686545258', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2912.1403', 'Lhash_array': ['dirichlet_L_2912.1403'], 'factors': ['1-2912-2912.1403-r0-0-0'], 'label': '1-2912-2912.1403-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2912/1403'}
Lfunction data - 1-2912-2912.1403-r0-0-0