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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4024.1189', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9475152734259388, 0.3197105044013543], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.8649804947905056, 0.5018054838600033], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.3374422009907982, -0.94134624925714], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.7955703867508632, -0.6058611719899881], 'algebraic': True, 'analytic_conductor': 18.68737743662057, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [503, [1]]], 'bad_primes': [2, 503], 'central_character': '4024.1189', 'coeff_info': ['x^502 - 1', '0.999921672072223 + 0.0125159785989932*I', '\\\\zeta_{502}'], 'conductor': 4024, 'conductor_radical': 1006, 'conjugate': 'dirichlet_L_4024.3029', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^727', 0, 'a^711', 0, 'a^404', 0, 'a^450', 0, 'a^495', 0, 'a^565', 0, 'a^434', 0, 'a^422', 0, 'a^337', 0, 'a^629', 0, 'a^182', 0, 'a^418', 0, 'a^675', 0, 'a^339', 0, 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'198.455673587953657175407760449057', '199.22271628960820009769305430502', '199.700268232524582587870876789613'], 'prelabel': '1-4024-4024.1189-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.68737743662057, 'root_angle': 0.6425583470058259, 'root_number': '-0.433037813246285319435046397429+0.901375755331191121079875399886*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(502)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.680241712591914833947759996181+0.0767492697207261088067836861016*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.91517596164', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.66997031256', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.16574108643', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.68737743662057, 'bad_primes': [2, 503], 'central_character': '4024.1189', 'conductor': 4024, 'conductor_radical': 1006, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4024/1189'], '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': '1-4024-4024.1189-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': '1-4024-4024.1189-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.68737743662057, 'root_angle': 0.32127917350291296, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.91517596164', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4024.1189', 'Lhash_array': ['dirichlet_L_4024.1189'], 'label': '1-4024-4024.1189-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4024/1189'}
Lfunction data - 1-4024-4024.1189-r0-0-0