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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_680.173', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.3826834323650898, -0.9238795325112867], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9238795325112867, 0.3826834323650898], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.7071067811865476, -0.7071067811865476], 'algebraic': True, 'analytic_conductor': 3.1579067238822036, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [17, [1]]], 'bad_primes': [2, 5, 17], 'central_character': '680.173', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 680, 'conductor_radical': 170, 'conjugate': 'dirichlet_L_680.397', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^13', 0, 0, 0, 'a^7', 0, 'a^10', 0, 'a^15', 0, 'a^0', 0, 0, 0, 0, 0, 'a^14', 0, 'a^20', 0, 'a^3', 0, 0, 0, 'a^23', 0, 'a^13', 0, 'a^9', 0, 'a^12', 0, 0, 0, 'a^21', 0, 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'prelabel': '1-680-680.173-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1579067238822036, 'root_angle': -0.4919270265379312, 'root_number': '0.0253592752727724550861207941509-0.999678401866140024652532466607*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.245963513269', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(16)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.07792033408655977605303330754-0.443014176918664672791955125879*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.76835104855', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.92472417346', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.14518874483', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.1579067238822036, 'bad_primes': [2, 5, 17], 'central_character': '680.173', 'conductor': 680, 'conductor_radical': 170, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/680/173'], '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': '1-680-680.173-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': '1-680-680.173-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1579067238822036, 'root_angle': -0.2459635132689656, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76835104855', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_680.173', 'Lhash_array': ['dirichlet_L_680.173'], 'label': '1-680-680.173-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/680/173'}
Lfunction data - 1-680-680.173-r0-0-0