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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_431.109', 'a10': [0.8648051652647988, -0.5021075842200793], 'a2': [0.6396730215588913, -0.768647139778532], 'a3': [0.391104720490156, 0.9203461835691594], 'a4': [-0.18163685097943644, -0.9833656768294661], 'a5': [0.9391360915965425, 0.3435453412007947], 'a6': [0.957600599908406, 0.2880990993652376], 'a7': [0.1383691743415363, -0.9903807205272331], 'a8': [-0.8720494081438076, -0.4894178478110855], 'a9': [-0.6940741952206338, 0.7199034737579958], 'algebraic': True, 'analytic_conductor': 2.0015555852841613, 'analytic_normalization': 0, 'bad_lfactors': [[431, [1]]], 'bad_primes': [431], 'central_character': '431.109', 'coeff_info': ['x^215 - 1', '0.999573005862893 + 0.0292199580804198*I', '\\\\zeta_{215}'], 'conductor': 431, 'conductor_radical': 431, 'conjugate': 'dirichlet_L_431.87', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^185', 'a^40', 'a^155', 'a^12', 'a^10', 'a^166', 'a^125', 'a^80', 'a^197', 'a^158', 'a^195', 'a^202', 'a^136', 'a^52', 'a^95', 'a^201', 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-0.3141714251376624, 'root_number': '0.551196599418980167751904431702-0.834375400397777973583371409145*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.157085712569', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(215)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.71989818848575693575775075055-0.562954470865737036339945555020*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.18924534614', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.59016257847', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.49472179282', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.0015555852841613, 'bad_primes': [431], 'central_character': '431.109', 'conductor': 431, 'conductor_radical': 431, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/431/109'], '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': '1-431-431.109-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': '1-431-431.109-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0015555852841613, 'root_angle': -0.1570857125688312, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18924534614', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_431.109', 'Lhash_array': ['dirichlet_L_431.109'], 'label': '1-431-431.109-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/431/109'}
Lfunction data - 1-431-431.109-r0-0-0