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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_88.83', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.8090169943749475, 0.5877852522924731], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.30901699437494745, -0.9510565162951535], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 0.40867028191416754, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [11, [1]]], 'bad_primes': [2, 11], 'central_character': '88.83', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 88, 'conductor_radical': 22, 'conjugate': 'dirichlet_L_88.35', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^2', 0, 'a^11', 0, 'a^8', 0, 'a^4', 0, 0, 0, 'a^14', 0, 'a^13', 0, 'a^1', 0, 'a^7', 0, 'a^0', 0, 'a^5', 0, 'a^2', 0, 'a^6', 0, 'a^8', 0, 'a^9', 0, 0, 0, 'a^9', 0, 'a^13', 0, 'a^6', 0, 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'189.566744141258067670290152049858', '190.63714488630613750917681141983', '191.15666476814715936225233908320', '192.2416077709803955493956475323', '192.75043974603395628758723811962', '193.58861042857319506813589056603', '194.40812190317766437907635515126', '194.74765220471814598983771418037', '196.28980702619472052207046713680', '196.89507873052287640423368063583', '197.79577392915108868527299091512', '198.397005437957048628979601115101', '198.69068818905282031508602181077'], 'prelabel': '1-88-88.83-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.40867028191416754, 'root_angle': 0.1534991328282215, 'root_number': '0.569857826831750412204520679098+0.821743303713875577791979199193*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.153499132828', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.14238361747642109335755242974+0.379842151355383322748172082393*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.26154930418', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.80569895172', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.08878051463', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.40867028191416754, 'bad_primes': [2, 11], 'central_character': '88.83', 'conductor': 88, 'conductor_radical': 22, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/88/83'], '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': '1-88-88.83-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': '1-88-88.83-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.40867028191416754, 'root_angle': 0.1534991328282215, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.26154930418', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_88.83', 'Lhash_array': ['dirichlet_L_88.83'], 'factors': ['1-88-88.83-r0-0-0'], 'label': '1-88-88.83-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/88/83'}
Lfunction data - 1-88-88.83-r0-0-0