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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_353.76', 'a10': [0.3826834323650898, -0.9238795325112867], 'a2': [-0.9096319953545183, 0.41541501300188644], 'a3': [0.6814179395938911, 0.7318945221817255], 'a4': [0.6548607339452851, -0.7557495743542583], 'a5': [-0.7318945221817255, 0.6814179395938911], 'a6': [-0.9238795325112867, -0.3826834323650898], 'a7': [0.9238795325112867, -0.3826834323650898], 'a8': [-0.28173255684142967, 0.9594929736144974], 'a9': [-0.07133918319923234, 0.9974521146102535], 'algebraic': True, 'analytic_conductor': 1.6393251081329674, 'analytic_normalization': 0, 'bad_lfactors': [[353, [1]]], 'bad_primes': [353], 'central_character': '353.76', 'coeff_info': ['x^176 - 1', '0.999362825656992 + 0.0356923338389805*I', '\\\\zeta_{176}'], 'conductor': 353, 'conductor_radical': 353, 'conjugate': 'dirichlet_L_353.144', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^76', 'a^23', 'a^152', 'a^67', 'a^99', 'a^165', 'a^52', 'a^46', 'a^143', 'a^148', 'a^175', 'a^7', 'a^65', 'a^90', 'a^128', 'a^140', 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'a^21'], [1, 'a^36'], [1, 'a^47'], [1, 'a^80'], [1, 'a^11']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-353-353.76-r0-0-0', 'leading_term': '0.901539977716950073433204834931+0.691446330050080002849292005951*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/353/76', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.1361656387875856, 1.3913416133684817, 1.5666732354272686, 1.213057838622466, 0.17780756173355564, -1.2578932199404111, -2.4672584515333673, -2.784901588398283, -1.9199089905357385, -0.23318619393049428, 1.3520146992062025, 1.8425347746865481, 0.8219023689333144, -1.1744918821410162, -2.8795023282099645, -3.0607152523590666, -1.3692720366105156, 1.3324761098041074, 3.4667950658270033, 3.7803489211582395, 2.205110799581474, -0.11057668340079514, 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47}, 'spectral_label': 'r0-0', 'st_group': 'mu(176)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.860158672282470941455957836020+0.407787481786131634593492773323*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.29131281516', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.85279908307', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.88733201644', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.6393251081329674, 'bad_primes': [353], 'central_character': '353.76', 'conductor': 353, 'conductor_radical': 353, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/353/76'], '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': '1-353-353.76-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': '1-353-353.76-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6393251081329674, 'root_angle': 0.20826006841656516, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29131281516', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_353.76', 'Lhash_array': ['dirichlet_L_353.76'], 'label': '1-353-353.76-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/353/76'}
Lfunction data - 1-353-353.76-r0-0-0