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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3328.1109', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.986643332084879, -0.16289547339458874], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9569403357322088, -0.2902846772544624], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6593458151000688, 0.7518398074789774], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9469301294951057, 0.3214394653031616], 'algebraic': True, 'analytic_conductor': 15.455167025117607, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [13, [1]]], 'bad_primes': [2, 13], 'central_character': '3328.1109', 'coeff_info': ['x^192 - 1', '0.999464587476366 + 0.0327190828217761*I', '\\\\zeta_{192}'], 'conductor': 3328, 'conductor_radical': 26, 'conjugate': 'dirichlet_L_3328.3325', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^293', 0, 'a^183', 0, 'a^262', 0, 'a^202', 0, 'a^131', 0, 0, 0, 'a^92', 0, 'a^196', 0, 'a^241', 0, 'a^171', 0, 'a^194', 0, 'a^174', 0, 'a^111', 0, 'a^269', 0, 'a^216', 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15.455167025117607, 'root_angle': 0.18823886805923337, 'root_number': '0.378390264070813709078263272368+0.925646157047291947460039213303*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(192)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.866993046197768830296196911915+0.0705290739251513119121264186319*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.997070395919', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.68284486621', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.80893950778', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.455167025117607, 'bad_primes': [2, 13], 'central_character': '3328.1109', 'conductor': 3328, 'conductor_radical': 26, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3328/1109'], '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': '1-3328-3328.1109-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': '1-3328-3328.1109-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.455167025117607, 'root_angle': 0.18823886805923337, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.997070395919', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3328.1109', 'Lhash_array': ['dirichlet_L_3328.1109'], 'factors': ['1-3328-3328.1109-r0-0-0'], 'label': '1-3328-3328.1109-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3328/1109'}
Lfunction data - 1-3328-3328.1109-r0-0-0