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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1323.1238', 'a10': [0.7330518718298263, -0.6801727377709194], 'a2': [0.969077286229078, 0.24675739769029365], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8782215733702285, 0.4782539786213182], 'a5': [0.5425462638657594, -0.8400259231507714], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.7330518718298263, 0.6801727377709194], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 6.143986170141405, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '1323.1238', 'coeff_info': ['x^126 - 1', '0.998756921218922 + 0.0498458856606972*I', '\\\\zeta_{126}'], 'conductor': 1323, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_1323.965', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 0, 'a^10', 'a^106', 0, 0, 'a^15', 0, 'a^111', 'a^47', 0, 'a^103', 0, 0, 'a^20', 'a^102', 0, 'a^105', 'a^116', 0, 'a^52', 'a^73', 0, 'a^86', 'a^108', 0, 0, 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'199.609534766373824019582901248129'], 'prelabel': '1-1323-1323.1238-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.143986170141405, 'root_angle': -0.0791761148904006, 'root_number': '0.878788784611987190925455031720-0.477210930344419484307425621024*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0791761148904', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(126)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.08155372717509598860632319826-0.119091212411895922808902582196*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.921400951613', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.26345010095', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.85996688171', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 6.143986170141405, 'bad_primes': [3, 7], 'central_character': '1323.1238', 'conductor': 1323, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1323/1238'], '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': '1-1323-1323.1238-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': '1-1323-1323.1238-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.143986170141405, 'root_angle': -0.0791761148904006, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.921400951613', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1323.1238', 'Lhash_array': ['dirichlet_L_1323.1238'], 'factors': ['1-1323-1323.1238-r0-0-0'], 'label': '1-1323-1323.1238-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1323/1238'}
Lfunction data - 1-1323-1323.1238-r0-0-0