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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_712.389', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9771468659711595, 0.21256528955297668], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.7557495743542583, 0.6548607339452851], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.07133918319923234, 0.9974521146102535], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9096319953545183, -0.41541501300188644], 'algebraic': True, 'analytic_conductor': 76.51502645377302, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [89, [1]]], 'bad_primes': [2, 89], 'central_character': '712.389', 'coeff_info': ['x^88 - 1', '0.997452114610254 + 0.0713391831992323*I', '\\\\zeta_{88}'], 'conductor': 712, 'conductor_radical': 178, 'conjugate': 'dirichlet_L_712.205', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^129', 0, 'a^98', 0, 'a^21', 0, 'a^82', 0, 'a^56', 0, 'a^63', 0, 'a^51', 0, 'a^70', 0, 'a^115', 0, 'a^62', 0, 'a^5', 0, 'a^20', 0, 'a^123', 0, 'a^131', 0, 'a^83', 0, 'a^9', 0, 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'198.44383502366876208085710851542', '199.07659327158709765479364740229', '199.682709474498944071380511531056'], 'prelabel': '1-712-712.389-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 76.51502645377302, 'root_angle': 0.8164482042114474, 'root_number': '-0.838296573766401552435552410339+0.545214503119196271179541725675*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.408224102106', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(88)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.791072174955865297229645955605+0.251968921873267037170502337209*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.12274955281', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.51508972005', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.3149109362', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 76.51502645377302, 'bad_primes': [2, 89], 'central_character': '712.389', 'conductor': 712, 'conductor_radical': 178, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/712/389'], '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': '1-712-712.389-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-712-712.389-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 76.51502645377302, 'root_angle': 0.4082241021057237, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12274955281', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_712.389', 'Lhash_array': ['dirichlet_L_712.389'], 'label': '1-712-712.389-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/712/389'}