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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_475.261', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.374606593415912, 0.9271838545667874], 'a3': [-0.5591929034707468, -0.8290375725550417], 'a4': [-0.7193398003386512, 0.6946583704589973], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.5591929034707468, -0.8290375725550417], 'a7': [-0.5, 0.8660254037844386], 'a8': [-0.9135454576426009, -0.4067366430758002], 'a9': [-0.374606593415912, 0.9271838545667874], 'algebraic': True, 'analytic_conductor': 51.04583927744689, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '475.261', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 475, 'conductor_radical': 95, 'conjugate': 'dirichlet_L_475.91', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 'a^59', 'a^34', 0, 'a^76', 'a^30', 'a^51', 'a^28', 0, 'a^42', 'a^3', 'a^13', 'a^47', 0, 'a^68', 'a^26', 'a^45', 0, 0, 'a^89', 'a^59', 'a^52', 'a^20', 0, 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'185.51985539427328107574887880464', '186.05472006265085919449744496826', '186.56122684990883885571035784611', '187.55633187829463668933017261752', '188.117614140546725995865538846975', '188.49776841108297478893369018399', '189.38862842126683438625990603652', '189.895616325213955189317210979162', '190.34746921490491839073360758765', '190.875930849269374050839159877', '191.80448506304592739139438515299', '192.94526705136035228143963974145', '193.38773209951713479683981230890', '194.18082750905004876352632738112', '194.6289206520661753975483273155', '195.39564827904928213986101196066', '195.8324026483654567034140845200', '196.58959797821450300478824971452', '196.95373364747909949531308392593', '197.45200780080688765786280860096', '198.70010841935950591993162172832', '199.06057075540496807502615743174', '199.69661806947556741768065879858'], 'prelabel': '1-475-475.261-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 51.04583927744689, 'root_angle': -0.3883399300369756, 'root_number': '0.343640232576320381406991089033-0.939101373950061067911560265975*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.194169965018', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.620742398928303283763281827999+0.360241319292778082556981990180*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.00727526250909', 'prec': 54}, 'z2': {'__RealLiteral__': 0, 'data': '1.86668593425', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.12616341793', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 51.04583927744689, 'bad_primes': [5, 19], 'central_character': '475.261', 'conductor': 475, 'conductor_radical': 95, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/475/261'], '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': '1-475-475.261-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-475-475.261-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 51.04583927744689, 'root_angle': -0.1941699650184878, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.00727526250909', 'prec': 54}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_475.261', 'Lhash_array': ['dirichlet_L_475.261'], 'label': '1-475-475.261-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/475/261'}
Lfunction data - 1-475-475.261-r1-0-0