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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_712.115', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9369497249997617, 0.3494641795990983], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9898214418809327, -0.14231483827328514], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8005412409243604, 0.599277666511347], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.7557495743542583, -0.6548607339452851], 'algebraic': True, 'analytic_conductor': 3.306514099123719, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [89, [1]]], 'bad_primes': [2, 89], 'central_character': '712.115', 'coeff_info': ['x^88 - 1', '0.997452114610254 + 0.0713391831992323*I', '\\\\zeta_{88}'], 'conductor': 712, 'conductor_radical': 178, 'conjugate': 'dirichlet_L_712.291', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^39', 0, 'a^46', 0, 'a^123', 0, 'a^78', 0, 'a^20', 0, 'a^61', 0, 'a^85', 0, 'a^58', 0, 'a^45', 0, 'a^74', 0, 'a^67', 0, 'a^4', 0, 'a^29', 0, 'a^57', 0, 'a^109', 0, 'a^59', 0, 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'198.39709359207854606003703974324', '199.11795981373762110751094532296', '199.46247834120193062846263818696'], 'prelabel': '1-712-712.115-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.306514099123719, 'root_angle': 0.09770241469283202, 'root_number': '0.953262230206368835717194242534+0.302144204746640584777504576663*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0488512073464', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(88)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.554349286250590742079522256166+0.0614185955343484595368823753419*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.555342302984', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.38146790773', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.56876948071', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.306514099123719, 'bad_primes': [2, 89], 'central_character': '712.115', 'conductor': 712, 'conductor_radical': 178, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/712/115'], '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': '1-712-712.115-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': '1-712-712.115-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.306514099123719, 'root_angle': 0.04885120734641601, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.555342302984', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_712.115', 'Lhash_array': ['dirichlet_L_712.115'], 'label': '1-712-712.115-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/712/115'}