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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1792.1227', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9108638249211758, -0.4127070298043947], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.032719082821776144, -0.9994645874763657], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.6593458151000688, 0.7518398074789774], 'algebraic': True, 'analytic_conductor': 192.57714523196805, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '1792.1227', 'coeff_info': ['x^192 - 1', '0.999464587476366 + 0.0327190828217761*I', '\\\\zeta_{192}'], 'conductor': 1792, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_1792.739', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^109', 0, 'a^143', 0, 0, 0, 'a^218', 0, 'a^91', 0, 'a^129', 0, 'a^60', 0, 'a^100', 0, 'a^185', 0, 0, 0, 'a^242', 0, 'a^94', 0, 'a^135', 0, 'a^117', 0, 'a^88', 0, 'a^200', 0, 0, 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'196.28812770532838816626348036449', '196.66180172815701609267811995930', '197.31718653095004357471800884856', '198.14049031161068175483187424699', '198.93159930232439854801732295131', '199.34988671557880721509874414245', '199.7914871413352050098523598485'], 'prelabel': '1-1792-1792.1227-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 192.57714523196805, 'root_angle': 0.027985453053946122, 'root_number': '0.996137622953472651922890784965+0.0878056725764637306208143450662*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.013992726527', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(192)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.553529487859081529447454282429-0.210263789013239865185855622222*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.440823848388', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.53526310113', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.41651802603', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 192.57714523196805, 'bad_primes': [2, 7], 'central_character': '1792.1227', 'conductor': 1792, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1792/1227'], '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': '1-1792-1792.1227-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1792-1792.1227-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 192.57714523196805, 'root_angle': 0.013992726526973061, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.440823848388', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1792.1227', 'Lhash_array': ['dirichlet_L_1792.1227'], 'label': '1-1792-1792.1227-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1792/1227'}