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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_81.16', 'a10': [0.17364817766693036, -0.984807753012208], 'a2': [0.8936326403234123, 0.44879918020046217], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.5971585917027862, 0.8021231927550437], 'a5': [-0.28680323271109026, -0.9579895123154889], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.39607976603915684, 0.918216106880274], 'a8': [0.17364817766693036, 0.984807753012208], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.37616241858008603, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '81.16', 'coeff_info': ['x^27 - 1', '0.973044870579824 + 0.230615870742440*I', '\\\\zeta_{27}'], 'conductor': 81, 'conductor_radical': 3, 'conjugate': 'dirichlet_L_81.76', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 0, 'a^4', 'a^19', 0, 'a^5', 'a^6', 0, 'a^21', 'a^26', 0, 'a^16', 'a^7', 0, 'a^8', 'a^12', 0, 'a^15', 'a^23', 0, 'a^1', 'a^22', 0, 'a^11', 'a^18', 0, 'a^9', 'a^20', 0, 'a^13', 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'187.38268170297092827368531509983', '188.46313353034039647667926261902', '188.86462501801673970699443803304', '189.7067248348727972358816100973', '190.706514194084954871909416266899', '192.02415432713900161156706153344', '192.54511121855015430763112695548', '193.08980188848026232801401144172', '194.14821491967312758904070815801', '195.05611416321571672477523220376', '195.665986153590997984048591199405', '196.2670258809108850399642577743', '196.946806223992370452797065988277', '197.868649994673938207495032489682', '198.892192118505812568876383219232', '199.327899869227068572974109018678'], 'prelabel': '1-3e4-81.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.37616241858008603, 'root_angle': 0.19753086419753088, 'root_number': '0.813552070262967563714650849683+0.581492071288026667901088648583*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0987654320988', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(27)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.50835169064405134242268231975+0.356820217589290060437910647428*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.26893366163', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.14795056298', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.17359367324', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.37616241858008603, 'bad_primes': [3], 'central_character': '81.16', 'conductor': 81, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/81/16'], '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': '1-3e4-81.16-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': '1-3e4-81.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.37616241858008603, 'root_angle': 0.09876543209876544, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.26893366163', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_81.16', 'Lhash_array': ['dirichlet_L_81.16'], 'label': '1-3e4-81.16-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/81/16'}
Lfunction data - 1-3e4-81.16-r0-0-0