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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_475.136', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9902680687415704, -0.13917310096006544], 'a3': [0.9975640502598242, -0.0697564737441253], 'a4': [0.9612616959383189, 0.27563735581699916], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.9975640502598242, -0.0697564737441253], 'a7': [-0.5, 0.8660254037844386], 'a8': [-0.9135454576426009, -0.4067366430758002], 'a9': [0.9902680687415704, -0.13917310096006544], 'algebraic': True, 'analytic_conductor': 51.04583927744689, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '475.136', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 475, 'conductor_radical': 95, 'conjugate': 'dirichlet_L_475.241', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^47', 'a^89', 'a^4', 0, 'a^46', 'a^30', 'a^51', 'a^88', 0, 'a^42', 'a^3', 'a^73', 'a^77', 0, 'a^8', 'a^56', 'a^45', 0, 0, 'a^29', 'a^89', 'a^22', 'a^50', 0, 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'root_analytic_conductor': 51.04583927744689, 'root_angle': -0.7597922380819929, 'root_number': '-0.728521666009421729606177890893-0.685022760318849971933529219144*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.379896119041', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.771169319524231102502143259418-0.0816489611194008972480020910084*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.17835871608', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.76155175504', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.73292535433', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 51.04583927744689, 'bad_primes': [5, 19], 'central_character': '475.136', 'conductor': 475, 'conductor_radical': 95, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/475/136'], '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': '1-475-475.136-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': '1-475-475.136-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 51.04583927744689, 'root_angle': -0.37989611904099646, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.17835871608', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_475.136', 'Lhash_array': ['dirichlet_L_475.136'], 'label': '1-475-475.136-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/475/136'}