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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_847.177', 'a10': [0.5800569095711982, 0.8145759520503357], 'a2': [0.0475819158237423, -0.998867339183008], 'a3': [-0.5, 0.8660254037844386], 'a4': [-0.9954719225730846, -0.09505604330418266], 'a5': [-0.7860530947427875, 0.6181589862206052], 'a6': [0.8412535328311812, 0.5406408174555976], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.14231483827328514, 0.9898214418809327], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.177', 'coeff_info': ['x^33 - 1', '0.981928697262707 + 0.189251244360410*I', '\\\\zeta_{33}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.67', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^25', 'a^11', 'a^17', 'a^13', 'a^3', 0, 'a^9', 'a^22', 'a^5', 0, 'a^28', 'a^6', 0, 'a^24', 'a^1', 'a^26', 'a^14', 'a^7', 'a^30', 0, 0, 'a^1', 'a^20', 'a^26', 'a^31', 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'1.26833861536', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.84034590561', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.53746097786', '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': '847.177', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/177'], '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': '1-847-847.177-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': '1-847-847.177-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.304163611513199, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26833861536', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_847.177', 'Lhash_array': ['dirichlet_L_847.177'], 'label': '1-847-847.177-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/177'}