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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6003.1184', 'a10': [0.30124618953723425, -0.9535463980789276], 'a2': [0.9232276375115515, -0.3842534701662944], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.7046985413303214, -0.7095068469344868], 'a5': [0.6445223203022166, -0.7645854946520022], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9764184991921175, -0.21588634610695698], 'a8': [0.37796670142890654, -0.9258191900208981], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 27.87781479921304, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1184', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.2459', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^433', 0, 'a^404', 'a^398', 0, 'a^247', 'a^375', 0, 'a^369', 'a^304', 0, 'a^248', 'a^218', 0, 'a^346', 'a^168', 0, 'a^327', 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'-0.334457679071939258779347846060+0.942410770794674058809130426135*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(462)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.12737874288019145426619922269-0.811320354557541044982675249480*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.148611285316', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.06560656806', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.12764110151', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.87781479921304, 'bad_primes': [3, 23, 29], 'central_character': '6003.1184', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/1184'], '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': '1-6003-6003.1184-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': '1-6003-6003.1184-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': 0.30427656408679177, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.148611285316', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6003.1184', 'Lhash_array': ['dirichlet_L_6003.1184'], 'label': '1-6003-6003.1184-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/1184'}