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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_161.136', 'a10': [0.9283679330160726, -0.3716624556603275], 'a2': [-0.9954719225730846, -0.09505604330418266], 'a3': [-0.7237340381050702, -0.690079011482112], 'a4': [0.9819286972627067, 0.18925124436041021], 'a5': [-0.8888354486549235, 0.4582265217274104], 'a6': [0.6548607339452851, 0.7557495743542583], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9594929736144974, -0.28173255684142967], 'a9': [0.0475819158237423, 0.998867339183008], 'algebraic': True, 'analytic_conductor': 0.7476808566838746, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [23, [1]]], 'bad_primes': [7, 23], 'central_character': '161.136', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 161, 'conductor_radical': 161, 'conjugate': 'dirichlet_L_161.103', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^34', 'a^41', 'a^2', 'a^28', 'a^9', 0, 'a^36', 'a^16', 'a^62', 'a^65', 'a^43', 'a^51', 0, 'a^3', 'a^4', 'a^20', 'a^50', 'a^46', 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'values': [[1, '0.457673247363853215262761549884-0.153811332521059557556647175642*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.574130428886', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.22421344364', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.84916409392', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7476808566838746, 'bad_primes': [7, 23], 'central_character': '161.136', 'conductor': 161, 'conductor_radical': 161, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/161/136'], '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': '1-161-161.136-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': '1-161-161.136-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7476808566838746, 'root_angle': -0.2629859074412635, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.574130428886', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_161.136', 'Lhash_array': ['dirichlet_L_161.136'], 'label': '1-161-161.136-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/161/136'}