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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_456.269', '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': [-0.9396926207859084, -0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.1176550971915953, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1]]], 'bad_primes': [2, 3, 19], 'central_character': '456.269', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 456, 'conductor_radical': 114, 'conjugate': 'dirichlet_L_456.317', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^10', 0, 'a^6', 0, 0, 0, 'a^12', 0, 'a^20', 0, 0, 0, 'a^13', 0, 0, 0, 0, 0, 'a^17', 0, 'a^2', 0, 0, 0, 'a^23', 0, 'a^15', 0, 0, 0, 'a^16', 0, 'a^0', 0, 0, 0, 'a^16', 0, 'a^19', 0, 0, 0, 'a^5', 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'191.67532957630095497622680708897', '192.309431761356308123729490170068', '192.99466898132612795962430896192', '193.6388639294219766343760049900', '194.37834707657981252916088986117', '195.11066263678862226369364977603', '195.5913071472409724219060920462', '196.2372176704677449289534982632', '196.98858412076417487836343142962', '197.47136576978418206486105912899', '198.34619220121424240516638462026', '199.18781988526769337078485618153', '199.5906497441087000520890186533', '199.99632848938032300563575481194'], 'prelabel': '1-456-456.269-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1176550971915953, 'root_angle': -0.1109033491931041, 'root_number': '0.939915658286829819470128346483-0.341406730026277248422232872533*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0554516745966', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.889453227664864121398452514110-0.0449096425654832863961024887727*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.776216345384', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.56456850664', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.47597854414', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1176550971915953, 'bad_primes': [2, 3, 19], 'central_character': '456.269', 'conductor': 456, 'conductor_radical': 114, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/456/269'], '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': '1-456-456.269-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': '1-456-456.269-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1176550971915953, 'root_angle': -0.05545167459655205, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.776216345384', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_456.269', 'Lhash_array': ['dirichlet_L_456.269'], 'label': '1-456-456.269-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/456/269'}