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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2028.1055', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.8229838658936564, 0.5680647467311558], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.3166679938014725, -0.9485364419471455], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 217.93886748349954, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '2028.1055', 'coeff_info': ['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}'], 'conductor': 2028, 'conductor_radical': 78, 'conjugate': 'dirichlet_L_2028.371', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^63', 0, 'a^125', 0, 0, 0, 'a^175', 0, 0, 0, 0, 0, 'a^8', 0, 'a^143', 0, 0, 0, 'a^130', 0, 'a^126', 0, 0, 0, 'a^46', 0, 'a^147', 0, 0, 0, 'a^188', 0, 'a^43', 0, 0, 0, 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'196.35863717565950355680848302989', '197.02562939058550500808120558606', '197.68614830150944054389167945072', '198.10699857989020312474406171284', '198.67495084677242536800985882025', '198.99882108021280165143036096227', '199.77828143215122471195210152705'], 'prelabel': '1-2028-2028.1055-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 217.93886748349954, 'root_angle': -0.03944773175542406, 'root_number': '0.969440282917266275665439223864-0.245327409510822335382217409569*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0394477317554', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(156)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.13770241493453700796603151176+0.0111397300273948997211137949799*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.625881025111', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.39597618622', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.7319931564', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 217.93886748349954, 'bad_primes': [2, 3, 13], 'central_character': '2028.1055', 'conductor': 2028, 'conductor_radical': 78, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2028/1055'], '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': '1-2028-2028.1055-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': '1-2028-2028.1055-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 217.93886748349954, 'root_angle': -0.03944773175542406, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.625881025111', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2028.1055', 'Lhash_array': ['dirichlet_L_2028.1055'], 'factors': ['1-2028-2028.1055-r1-0-0'], 'label': '1-2028-2028.1055-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2028/1055'}
Lfunction data - 1-2028-2028.1055-r1-0-0