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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1441.1007', 'a10': [-0.943311813257743, -0.33190785312852844], 'a2': [-0.6810158587867972, 0.7322686665977736], 'a3': [0.9953316347176486, -0.09651392091451512], 'a4': [-0.07243480016176236, -0.9973731496914912], 'a5': [0.39936458356569554, 0.9167921953165824], 'a6': [-0.6071625078187112, 0.7945776797137543], 'a7': [-0.5680647467311558, 0.8229838658936564], 'a8': [0.7796743540632224, 0.6261851975383137], 'a9': [0.9813701261394134, -0.19212671735370837], 'algebraic': True, 'analytic_conductor': 6.691975866344493, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [131, [1]]], 'bad_primes': [11, 131], 'central_character': '1441.1007', 'coeff_info': ['x^130 - 1', '0.998832226832327 + 0.0483133795255071*I', '\\\\zeta_{130}'], 'conductor': 1441, 'conductor_radical': 1441, 'conjugate': 'dirichlet_L_1441.508', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^48', 'a^128', 'a^96', 'a^24', 'a^46', 'a^45', 'a^14', 'a^126', 'a^72', 0, 'a^94', 'a^45', 'a^93', 'a^22', 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'195.65454014243212469781553894687', '196.158597388058556975772815345622', '196.95767173164667467553866302051', '197.221062236549498907946557078833', '197.60441110603263394532448241685', '198.32724622236894671742745741596', '198.96987385020883081109524415353', '199.10872743950358908237448593963'], 'prelabel': '1-1441-1441.1007-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': 0.8289424401848938, 'root_number': '-0.859046029001271157272135845372+0.511898349340127481706906364448*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.414471220092', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(130)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.850443313450049464539105131782+0.654885978324654362163926542844*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.51984464035', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.30863956657', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.10760772777', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 6.691975866344493, 'bad_primes': [11, 131], 'central_character': '1441.1007', 'conductor': 1441, 'conductor_radical': 1441, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1441/1007'], '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': '1-1441-1441.1007-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': '1-1441-1441.1007-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': 0.4144712200924469, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51984464035', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1441.1007', 'Lhash_array': ['dirichlet_L_1441.1007'], 'label': '1-1441-1441.1007-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1441/1007'}
Lfunction data - 1-1441-1441.1007-r0-0-0