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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1157.564', 'a10': [-0.9898214418809327, -0.14231483827328514], 'a2': [-0.9096319953545183, -0.41541501300188644], 'a3': [0.9974521146102535, -0.07133918319923234], 'a4': [0.6548607339452851, 0.7557495743542583], 'a5': [0.9594929736144974, -0.28173255684142967], 'a6': [-0.9369497249997617, -0.3494641795990983], 'a7': [-0.47924898672005684, 0.8776789895672557], 'a8': [-0.28173255684142967, -0.9594929736144974], 'a9': [0.9898214418809327, -0.14231483827328514], 'algebraic': True, 'analytic_conductor': 5.373085411076043, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]], [89, [1]]], 'bad_primes': [13, 89], 'central_character': '1157.564', 'coeff_info': ['x^88 - 1', '0.997452114610254 + 0.0713391831992323*I', '\\\\zeta_{88}'], 'conductor': 1157, 'conductor_radical': 1157, 'conjugate': 'dirichlet_L_1157.359', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^50', 'a^87', 'a^12', 'a^84', 'a^49', 'a^29', 'a^62', 'a^86', 'a^46', 'a^26', 'a^11', 0, 'a^79', 'a^83', 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'root_analytic_conductor': 5.373085411076043, 'root_angle': 0.2841338294177831, 'root_number': '0.627364011066393906156552360186+0.778726137752345888503870101923*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.142066914709', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(88)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.07270045684570356255413054417+0.0712308440807464878445758764082*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.46725156047', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.1616209753', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.74128576978', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.373085411076043, 'bad_primes': [13, 89], 'central_character': '1157.564', 'conductor': 1157, 'conductor_radical': 1157, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1157/564'], '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': '1-1157-1157.564-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': '1-1157-1157.564-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.373085411076043, 'root_angle': 0.14206691470889155, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46725156047', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1157.564', 'Lhash_array': ['dirichlet_L_1157.564'], 'label': '1-1157-1157.564-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1157/564'}