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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_245.219', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9888308262251285, 0.14904226617617444], 'a3': [-0.8262387743159949, 0.5633200580636221], 'a4': [0.9555728057861407, 0.2947551744109042], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.9009688679024191, 0.4338837391175581], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9009688679024191, 0.4338837391175581], 'a9': [0.36534102436639504, -0.9308737486442042], 'algebraic': True, 'analytic_conductor': 1.1377752166928528, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '245.219', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 245, 'conductor_radical': 35, 'conjugate': 'dirichlet_L_245.179', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^17', 'a^2', 0, 'a^18', 0, 'a^3', 'a^34', 0, 'a^8', 'a^19', 'a^15', 0, 0, 'a^4', 'a^5', 'a^35', 'a^28', 0, 0, 'a^9', 'a^37', 'a^20', 0, 'a^16', 'a^9', 0, 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False, 'root_analytic_conductor': 1.1377752166928528, 'root_angle': 0.40816326530612246, 'root_number': '0.284527586631032441870502993463+0.958667853036660622150983388310*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.204081632653', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.39656228463602357603298505433+0.556519530366765535288242437135*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.80735328269', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.44568274002', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.55285247668', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1377752166928528, 'bad_primes': [5, 7], 'central_character': '245.219', 'conductor': 245, 'conductor_radical': 35, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/245/219'], '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': '1-245-245.219-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': '1-245-245.219-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1377752166928528, 'root_angle': 0.20408163265306123, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.80735328269', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_245.219', 'Lhash_array': ['dirichlet_L_245.219'], 'label': '1-245-245.219-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/245/219'}