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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_185.92', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.17364817766693036, -0.984807753012208], 'a3': [0.984807753012208, 0.17364817766693036], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [2.9010907910729803e-30, -1.0], 'a7': [-0.6427876096865394, 0.766044443118978], 'a8': [0.5, 0.8660254037844386], 'a9': [0.9396926207859084, 0.3420201433256687], 'algebraic': True, 'analytic_conductor': 0.8591363881150113, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [37, [1]]], 'bad_primes': [5, 37], 'central_character': '185.92', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 185, 'conductor_radical': 185, 'conjugate': 'dirichlet_L_185.183', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 'a^1', 'a^16', 0, 'a^27', 'a^13', 'a^6', 'a^2', 0, 'a^6', 'a^17', 'a^34', 'a^3', 0, 'a^32', 'a^20', 'a^28', 'a^1', 0, 'a^14', 'a^32', 'a^30', 'a^7', 0, 'a^24', 'a^3', 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'189.54078120741078845691580147064', '190.262550102587034813457487950647', '190.61582856463684943142699952675', '191.39403325986316251393445371687', '192.133679685759445162715797432018', '192.86943719573125725527820260206', '193.24271438852769187430771469845', '193.848383369121257985636988668521', '195.12004508879314032263754594368', '195.518572018345161755033665322746', '196.449404004798611142698661595326', '197.34175117534875583294808432177', '197.77175549653064861920392643973', '198.99465627888481094111829061015', '199.19444965390086003614243737769'], 'prelabel': '1-185-185.92-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8591363881150113, 'root_angle': -0.06336815928548702, 'root_number': '0.921778334168123250048199823642-0.387717297342070753916521895380*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0633681592855', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.16976774065093423896593451463-0.279780904192119677984540585020*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.65998142107', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.82980485842', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.75723602864', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.8591363881150113, 'bad_primes': [5, 37], 'central_character': '185.92', 'conductor': 185, 'conductor_radical': 185, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/185/92'], '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': '1-185-185.92-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': '1-185-185.92-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8591363881150113, 'root_angle': -0.06336815928548702, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65998142107', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_185.92', 'Lhash_array': ['dirichlet_L_185.92'], 'factors': ['1-185-185.92-r0-0-0'], 'label': '1-185-185.92-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/185/92'}
Lfunction data - 1-185-185.92-r0-0-0