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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_967.36', 'a10': [-0.7241419573240463, 0.6896509447850405], 'a2': [0.7547806962237219, 0.655977210433437], 'a3': [0.3532010288815979, -0.9355474510664762], 'a4': [0.13938779878393262, 0.990237871195689], 'a5': [-0.09417306778097717, 0.9955558413794374], 'a6': [0.8802871256648868, -0.47444133081831286], 'a7': [0.035766199516670615, -0.9993601848043245], 'a8': [-0.5443662566012645, 0.8388476492629197], 'a9': [-0.7504980663939613, -0.6608726445684715], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.36', 'coeff_info': ['x^483 - 1', '0.999915388507649 + 0.0130082983359933*I', '\\\\zeta_{483}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.779', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^55', 'a^390', 'a^110', 'a^128', 'a^445', 'a^365', 'a^165', 'a^297', 'a^183', 'a^159', 'a^17', 'a^2', 'a^420', 'a^35', 'a^220', 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'185.55603353054968188148727434098', '186.33077416444994629956739667181', '186.967699693032854406159210726750', '187.74239445955281260803707366648', '187.9635524578137609554527206468', '188.931814441714959112460104690879', '189.56457199155081616091382313004', '189.98816094924074636451699816435', '190.477394334880947956150085241828', '191.341227389509547090023236748171', '191.668856819111870016042717537727', '192.51037289250845564593363305139', '193.634631206184708468810752688841', '193.822092652681447800476680362829', '194.61260412782684732690831926932', '194.90784322868780218035389892028', '195.55131217834325701734436607699', '196.276315619048009080180582418370', '196.62074702434666282450951247753', '197.48039177895651793630693071390', '197.87316439023638861920201948905', '198.27003463284610582256619928115', '198.87576926041057754984539564836', '199.863926922054087778192597098397'], 'prelabel': '1-967-967.36-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': 0.47280294503271764, 'root_number': '0.0853381465673540780188338851557+0.996352046588176981093299182820*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.236401472516', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(483)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.54558773218743618879590239313+0.606762237912768068558019770553*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.43102026297', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.62434183962', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.48272326476', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.490729120579545, 'bad_primes': [967], 'central_character': '967.36', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/36'], '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': '1-967-967.36-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': '1-967-967.36-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': 0.23640147251635882, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43102026297', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_967.36', 'Lhash_array': ['dirichlet_L_967.36'], 'label': '1-967-967.36-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/36'}
Lfunction data - 1-967-967.36-r0-0-0