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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1055', 'a10': [0.7969796408599039, -0.6040061688880491], 'a2': [-0.9444462754567683, 0.3286658375551652], 'a3': [-0.08759702548841304, 0.9961559923654439], 'a4': [0.7839575344483235, -0.6208144522977099], 'a5': [-0.9512206468110863, 0.30851139538159467], 'a6': [-0.24467175910276207, -0.9696059665129748], 'a7': [0.3009170294480148, 0.9536503244838659], 'a8': [-0.5363652715952123, 0.8439859568894462], 'a9': [-0.9846535222511646, -0.17452060370734235], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1055', 'coeff_info': ['x^1182 - 1', '0.999985871574519 + 0.00531569857584313*I', '\\\\zeta_{1182}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.4218', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^528', 'a^312', 'a^1056', 'a^532', 'a^840', 'a^238', 'a^402', 'a^624', 'a^1060', 'a^915', 'a^186', 'a^100', 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'0.517580080753960126654712884120-0.855634770218417499584738164281*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(1182)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.428209912060999652639509036007+0.272558219658342847438972950685*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0284639844226', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.25991425305', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.54973844895', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1055', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1055'], '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': '1-4729-4729.1055-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': '1-4729-4729.1055-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.16341647878937332, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0284639844226', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1055', 'Lhash_array': ['dirichlet_L_4729.1055'], 'factors': ['1-4729-4729.1055-r0-0-0'], 'label': '1-4729-4729.1055-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1055'}
Lfunction data - 1-4729-4729.1055-r0-0-0