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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_5600.5059', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.6293203910498375, 0.7771459614569709], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.20791169081775934, -0.9781476007338057], 'algebraic': True, 'analytic_conductor': 26.006290667265205, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '5600.5059', 'coeff_info': ['x^120 - 1', '0.998629534754574 + 0.0523359562429438*I', '\\\\zeta_{120}'], 'conductor': 5600, 'conductor_radical': 70, 'conjugate': 'dirichlet_L_5600.1739', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^163', 0, 0, 0, 0, 0, 'a^86', 0, 'a^109', 0, 'a^171', 0, 0, 0, 'a^172', 0, 'a^107', 0, 0, 0, 'a^134', 0, 0, 0, 'a^129', 0, 'a^63', 0, 'a^112', 0, 'a^32', 0, 0, 0, 'a^161', 0, 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{'__RealLiteral__': 0, 'data': '0.602428604853', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.5908578911', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.68140626452', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.006290667265205, 'bad_primes': [2, 5, 7], 'central_character': '5600.5059', 'conductor': 5600, 'conductor_radical': 70, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5600/5059'], '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': '1-5600-5600.5059-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': '1-5600-5600.5059-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 26.006290667265205, 'root_angle': 0.10357704694605388, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.602428604853', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_5600.5059', 'Lhash_array': ['dirichlet_L_5600.5059'], 'label': '1-5600-5600.5059-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5600/5059'}