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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4235.4163', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9621315416867272, -0.2725855764553978], 'a3': [-0.20791169081775934, 0.9781476007338057], 'a4': [0.8513942070169569, 0.5245263618331943], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.4666673232256737, -0.8844329309978143], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6761749002740194, -0.7367411378764049], 'a9': [-0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 19.66725731711931, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.4163', 'coeff_info': ['x^660 - 1', '0.999954685354173 + 0.00951983393957664*I', '\\\\zeta_{660}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.647', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^359', 'a^187', 'a^58', 0, 'a^546', 0, 'a^417', 'a^374', 0, 0, 'a^245', 'a^399', 0, 0, 'a^116', 'a^541', 'a^73', 'a^152', 0, 0, 0, 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{'__RealLiteral__': 0, 'data': '2.20866522857', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.89210423686', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 19.66725731711931, 'bad_primes': [5, 7, 11], 'central_character': '4235.4163', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/4163'], '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': '1-4235-4235.4163-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': '1-4235-4235.4163-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': 0.4943400312484694, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.91310316322', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4235.4163', 'Lhash_array': ['dirichlet_L_4235.4163'], 'label': '1-4235-4235.4163-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/4163'}
Lfunction data - 1-4235-4235.4163-r0-0-0