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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1053.160', 'a10': [0.766044443118978, 0.6427876096865394], 'a2': [-0.39607976603915684, -0.918216106880274], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.6862416378687336, 0.7273736415730487], 'a5': [-0.8936326403234123, 0.44879918020046217], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.6862416378687336, 0.7273736415730487], 'a8': [0.9396926207859084, 0.3420201433256687], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 4.890111441541118, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1053.160', 'coeff_info': ['x^54 - 1', '0.993238357741943 + 0.116092914125230*I', '\\\\zeta_{54}'], 'conductor': 1053, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_1053.283', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^37', 0, 'a^20', 'a^23', 0, 'a^7', 'a^3', 0, 'a^6', 'a^49', 0, 0, 'a^44', 0, 'a^40', 'a^24', 0, 'a^39', 'a^43', 0, 'a^32', 'a^20', 0, 'a^46', 0, 0, 'a^27', 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'189.13085936250419573363796275269', '189.66124348864819184778604196395', '190.384565167963361929558489396', '190.60111201058378714892015472551', '191.393428058294777879798982853560', '192.08073738229580012612396149721', '192.49597716814574484741396444075', '192.87084954941827750678116707381', '193.72496012752358850427419651305', '194.52738967188519621474898203144', '194.78207929343429779503115004282', '195.35349911517089261462090180775', '195.93455194303867975542808273541', '196.81830608138801511846850266552', '197.61931435057347235363188389578', '198.33222187618502785811560364071', '198.61934083042198834248840340089', '199.28593648629995719264670705894', '199.846209331690423879315325134515'], 'prelabel': '1-1053-1053.160-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.890111441541118, 'root_angle': -0.2243131589432617, 'root_number': '0.761805556935460836909014573660-0.647805752847450666393084182773*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.112156579472', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(54)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.770980337720240023678720508021-0.217757789396969740609601267012*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.750322970294', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.08632073719', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.83155360809', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.890111441541118, 'bad_primes': [3, 13], 'central_character': '1053.160', 'conductor': 1053, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1053/160'], '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': '1-1053-1053.160-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': '1-1053-1053.160-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.890111441541118, 'root_angle': -0.11215657947163085, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.750322970294', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1053.160', 'Lhash_array': ['dirichlet_L_1053.160'], 'label': '1-1053-1053.160-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1053/160'}
Lfunction data - 1-1053-1053.160-r0-0-0