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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1287.358', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.9945218953682733, 0.10452846326765347], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9781476007338057, -0.20791169081775934], 'a5': [0.4067366430758002, 0.9135454576426009], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9510565162951535, 0.30901699437494745], 'a8': [-0.9510565162951535, 0.30901699437494745], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 5.9768028729947, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [11, [1]], [13, [1]]], 'bad_primes': [3, 11, 13], 'central_character': '1287.358', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1287, 'conductor_radical': 429, 'conjugate': 'dirichlet_L_1287.1003', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 0, 'a^58', 'a^11', 0, 'a^3', 'a^27', 0, 'a^40', 0, 0, 0, 'a^32', 0, 'a^56', 'a^56', 0, 'a^17', 'a^9', 0, 0, 'a^30', 0, 'a^22', 0, 0, 'a^1', 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'0.126417979306390561565757820709+0.991977063498994924090040442256*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.22982597314', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.819130057229068698905923629000+0.271225765755870791444062207344*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.21246134073', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.12417812477', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.86448648016', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.9768028729947, 'bad_primes': [3, 11, 13], 'central_character': '1287.358', 'conductor': 1287, 'conductor_radical': 429, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1287/358'], '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': '1-1287-1287.358-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': '1-1287-1287.358-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.9768028729947, 'root_angle': 0.22982597314024342, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21246134073', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1287.358', 'Lhash_array': ['dirichlet_L_1287.358'], 'label': '1-1287-1287.358-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1287/358'}