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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_179.161', 'a10': [0.9603921063437793, -0.2786521165764922], 'a2': [-0.19292606540949683, -0.9812132965291546], 'a3': [-0.5202394486108822, -0.8540204424421264], 'a4': [-0.9255590665712211, 0.37860324125370337], 'a5': [0.08813249156360176, 0.9961087610952891], 'a6': [-0.7376084637406223, 0.6752286680956305], 'a7': [0.9776556239997144, -0.2102129417084711], 'a8': [0.5500550034448413, 0.8351284291564356], 'a9': [-0.4587018322180905, 0.8885902481570269], 'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'analytic_normalization': 0, 'bad_lfactors': [[179, [1]]], 'bad_primes': [179], 'central_character': '179.161', 'coeff_info': ['x^89 - 1', '0.997509025150764 + 0.0705389590423110*I', '\\\\zeta_{89}'], 'conductor': 179, 'conductor_radical': 179, 'conjugate': 'dirichlet_L_179.169', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^64', 'a^59', 'a^39', 'a^21', 'a^34', 'a^86', 'a^14', 'a^29', 'a^85', 'a^70', 'a^9', 'a^87', 'a^61', 'a^80', 'a^78', 'a^33', 'a^4', 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-0.5137970215816964, 'root_number': '-0.0433310505877508690265129196630-0.999060768949998243833246831777*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.256898510791', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(89)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.729774956582178044806486126799-0.483456336338102883425674253322*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.10527688477', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.33822716103', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.65693858095', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'bad_primes': [179], 'central_character': '179.161', 'conductor': 179, 'conductor_radical': 179, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/179/161'], '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': '1-179-179.161-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': '1-179-179.161-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8312725052572271, 'root_angle': -0.2568985107908482, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10527688477', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_179.161', 'Lhash_array': ['dirichlet_L_179.161'], 'label': '1-179-179.161-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/179/161'}
Lfunction data - 1-179-179.161-r0-0-0