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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_384.221', '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': [0.5555702330196022, -0.8314696123025452], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9238795325112867, 0.3826834323650898], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 41.26653112113601, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '384.221', 'coeff_info': ['x^32 - 1', '0.980785280403230 + 0.195090322016128*I', '\\\\zeta_{32}'], 'conductor': 384, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_384.245', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^27', 0, 'a^14', 0, 0, 0, 'a^23', 0, 'a^5', 0, 0, 0, 'a^36', 0, 'a^29', 0, 0, 0, 'a^42', 0, 'a^22', 0, 0, 0, 'a^25', 0, 'a^24', 0, 0, 0, 'a^41', 0, 'a^19', 0, 0, 0, 'a^26', 0, 'a^31', 0, 0, 0, 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'193.43613335673981572852345526089', '194.314799445216525450656119187735', '194.699860813142735797917384364376', '195.73943314396473802895331073276', '196.32326234947367437373702043740', '196.940507630770171735318613280196', '197.31839182381083289939767027356', '198.09658314887485100260909331543', '199.11833295603306093426394474403', '199.74391144387923585692362933073'], 'prelabel': '1-384-384.221-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 41.26653112113601, 'root_angle': -0.2890625, 'root_number': '-0.242980179903263889948274162077-0.970031253194543992603984207286*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2890625', 'prec': 34}, 'spectral_label': 'r1-0', 'st_group': 'mu(32)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.02414280945475689319102454388-0.267189326892435447870150057884*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.44847713838', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.74533413146', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.1096830247', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 41.26653112113601, 'bad_primes': [2, 3], 'central_character': '384.221', 'conductor': 384, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/384/221'], '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': '1-384-384.221-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': '1-384-384.221-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 41.26653112113601, 'root_angle': -0.2890625, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44847713838', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_384.221', 'Lhash_array': ['dirichlet_L_384.221'], 'factors': ['1-384-384.221-r1-0-0'], 'label': '1-384-384.221-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/384/221'}
Lfunction data - 1-384-384.221-r1-0-0