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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4000.723', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.8270805742745618, 0.5620833778521306], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8090169943749475, -0.5877852522924731], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.368124552684678, 0.9297764858882515], 'algebraic': True, 'analytic_conductor': 18.575921905189432, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '4000.723', 'coeff_info': ['x^200 - 1', '0.999506560365732 + 0.0314107590781283*I', '\\\\zeta_{200}'], 'conductor': 4000, 'conductor_radical': 10, 'conjugate': 'dirichlet_L_4000.1787', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^219', 0, 0, 0, 'a^120', 0, 'a^238', 0, 'a^367', 0, 'a^163', 0, 0, 0, 'a^266', 0, 'a^281', 0, 'a^139', 0, 'a^152', 0, 0, 0, 'a^257', 0, 'a^129', 0, 'a^116', 0, 'a^186', 0, 0, 0, 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'199.43169297002558133038351424232', '199.8767400431642725027827001435'], 'prelabel': '1-4000-4000.723-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.575921905189432, 'root_angle': -0.9745, 'root_number': '-0.996792860627226601567726735271-0.0800249523748087182642457736196*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(200)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.02448684188105999653558300352+0.0764969341783940351742338703866*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.30418235662', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.30588301658', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.1821623153', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.575921905189432, 'bad_primes': [2, 5], 'central_character': '4000.723', 'conductor': 4000, 'conductor_radical': 10, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4000/723'], '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': '1-4000-4000.723-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': '1-4000-4000.723-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.575921905189432, 'root_angle': -0.48725, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30418235662', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4000.723', 'Lhash_array': ['dirichlet_L_4000.723'], 'label': '1-4000-4000.723-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4000/723'}