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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2020.979', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9685831611286311, 0.2486898871648548], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9297764858882515, 0.368124552684678], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.8763066800438636, -0.48175367410171527], 'algebraic': True, 'analytic_conductor': 217.07914808514255, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [101, [1]]], 'bad_primes': [2, 5, 101], 'central_character': '2020.979', 'coeff_info': ['x^50 - 1', '0.992114701314478 + 0.125333233564304*I', '\\\\zeta_{50}'], 'conductor': 2020, 'conductor_radical': 1010, 'conjugate': 'dirichlet_L_2020.619', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^73', 0, 0, 0, 'a^53', 0, 'a^46', 0, 'a^46', 0, 'a^47', 0, 0, 0, 'a^35', 0, 'a^57', 0, 'a^26', 0, 'a^62', 0, 0, 0, 'a^69', 0, 'a^47', 0, 'a^53', 0, 'a^19', 0, 0, 0, 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'196.44253595316279892205201764913', '197.37514484930436672040381908433', '197.75854356363178909480085646470', '198.466097202042929649709020145192', '198.85153644734471440881813436113', '199.61148769956349242458811466807'], 'prelabel': '1-2020-2020.979-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 217.07914808514255, 'root_angle': 0.45955281370150985, 'root_number': '0.126726908735858023146647111710+0.991937644513128411524665438037*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.229776406851', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(50)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.00871343822755042801516722160+0.184285152885770269769375851126*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.05263921578', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.39426909312', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.92673242483', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 217.07914808514255, 'bad_primes': [2, 5, 101], 'central_character': '2020.979', 'conductor': 2020, 'conductor_radical': 1010, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2020/979'], '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': '1-2020-2020.979-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': '1-2020-2020.979-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 217.07914808514255, 'root_angle': 0.22977640685075493, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05263921578', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2020.979', 'Lhash_array': ['dirichlet_L_2020.979'], 'label': '1-2020-2020.979-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2020/979'}
Lfunction data - 1-2020-2020.979-r1-0-0