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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_177.143', 'a10': [-0.9476531711828025, 0.31930153013597995], 'a2': [-0.2675283385292208, -0.9635499925192229], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8568571761675893, 0.5155538571770217], 'a5': [-0.054138908585417526, -0.9985334138511238], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.16178199655276473, -0.9868265225415261], 'a8': [0.7259954919231308, 0.6876994588534233], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 19.021291688648628, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [59, [1]]], 'bad_primes': [3, 59], 'central_character': '177.143', 'coeff_info': ['x^58 - 1', '0.994137957154360 + 0.108119018423942*I', '\\\\zeta_{58}'], 'conductor': 177, 'conductor_radical': 177, 'conjugate': 'dirichlet_L_177.26', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^41', 0, 'a^24', 'a^43', 0, 'a^42', 'a^7', 0, 'a^26', 'a^39', 0, 'a^18', 'a^25', 0, 'a^48', 'a^45', 0, 'a^50', 'a^9', 0, 'a^22', 'a^35', 0, 'a^28', 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'190.52855759679445393693421280977', '191.18471343993226223726549250875', '191.55840207733649803902255953712', '192.438294775576422795136153199960', '192.958517853756223741437922398088', '193.78527551697034469271097480344', '194.51163401235451187371142756698', '195.200587454357336265378918298187', '195.80072876936972474625919331077', '196.90310421509825698671777216283', '197.53371898724468747168577837751', '198.407102061378495635685552991347', '199.17454298803845574649258635061', '199.97983862539361147514713975043'], 'prelabel': '1-177-177.143-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.021291688648628, 'root_angle': 0.5803167092253317, 'root_number': '-0.249653476428574038881447757813+0.968335242417174149787922751574*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.290158354613', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(58)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.467731119679272412310167485523-0.510215144580096812958424033600*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.214004552641', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.30211077338', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.97188034289', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 19.021291688648628, 'bad_primes': [3, 59], 'central_character': '177.143', 'conductor': 177, 'conductor_radical': 177, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/177/143'], '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': '1-177-177.143-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': '1-177-177.143-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.021291688648628, 'root_angle': 0.29015835461266587, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.214004552641', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_177.143', 'Lhash_array': ['dirichlet_L_177.143'], 'label': '1-177-177.143-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/177/143'}
Lfunction data - 1-177-177.143-r1-0-0