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{'Lhash': 'dirichlet_L_847.369', 'a10': [-0.9954719225730846, -0.09505604330418266], 'a2': [-0.9884217748453624, 0.15173132508333165], 'a3': [0.9781476007338057, 0.20791169081775934], 'a4': [0.9539552099769126, -0.29994909127701064], 'a5': [0.9695231451106913, 0.2449997369277637], 'a6': [-0.9983691039261356, -0.057088810862767986], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8973984286913584, 0.4412211012432213], 'a9': [0.9135454576426009, 0.4067366430758002], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.369', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.101', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^157', 'a^11', 'a^314', 'a^13', 'a^168', 0, 'a^141', 'a^22', 'a^170', 0, 'a^325', 'a^72', 0, 'a^24', 'a^298', 'a^158', 'a^179', 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'types': ['DIR'], 'values': [[1, '1.06740733582362313321926041332+0.364765049599071901096575687586*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.6439485476', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.03651298648', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.14749480758', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.369', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/369'], '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': '1-847-847.369-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': '1-847-847.369-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.21908324529316134, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.6439485476', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_847.369', 'Lhash_array': ['dirichlet_L_847.369'], 'label': '1-847-847.369-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/369'}