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{'Lhash': 'dirichlet_L_664.107', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.6062254109666381, -0.7952928712734264], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.33801687840850275, 0.9411400479795615], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.4090686371713399, -0.91250361647655], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.26498150219666167, -0.964253495453141], 'algebraic': True, 'analytic_conductor': 3.083603036261446, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [83, [1]]], 'bad_primes': [2, 83], 'central_character': '664.107', 'coeff_info': ['x^82 - 1', '0.997065801183740 + 0.0765492528364956*I', '\\\\zeta_{82}'], 'conductor': 664, 'conductor_radical': 166, 'conjugate': 'dirichlet_L_664.211', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^70', 0, 'a^98', 0, 'a^67', 0, 'a^58', 0, 'a^78', 0, 'a^76', 0, 'a^86', 0, 'a^18', 0, 'a^81', 0, 'a^55', 0, 'a^113', 0, 'a^32', 0, 'a^46', 0, 'a^121', 0, 'a^103', 0, 'a^66', 0, 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False, 'root_analytic_conductor': 3.083603036261446, 'root_angle': -0.12397058794695826, 'root_number': '0.711665515742265852906728169459-0.702518465026574766612556785979*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.123970587947', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(82)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.47741862730759807832530122253-0.356483251573525921330829009775*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.17266630356', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.93672373198', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.51814704335', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.083603036261446, 'bad_primes': [2, 83], 'central_character': '664.107', 'conductor': 664, 'conductor_radical': 166, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/664/107'], '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': '1-664-664.107-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': '1-664-664.107-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.083603036261446, 'root_angle': -0.12397058794695826, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17266630356', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_664.107', 'Lhash_array': ['dirichlet_L_664.107'], 'factors': ['1-664-664.107-r0-0-0'], 'label': '1-664-664.107-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/664/107'}