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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1047', 'a10': [0.9943539375176164, 0.10611431073711196], 'a2': [-0.7533711667168278, 0.6575955331050582], 'a3': [0.6515676231958488, 0.7585905564946828], 'a4': [0.1351362296805486, -0.9908270280062641], 'a5': [-0.6793372892978713, -0.7338261697223807], 'a6': [-0.9897180218885506, -0.14303229407729687], 'a7': [0.8158354250084526, 0.5782841510030146], 'a8': [0.5497556886765316, 0.8353254951022341], 'a9': [-0.1509192648058248, 0.9885460917481134], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1047', 'coeff_info': ['x^591 - 1', '0.999943486697302 + 0.0106312469467839*I', '\\\\zeta_{591}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.1486', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^228', 'a^81', 'a^456', 'a^373', 'a^309', 'a^58', 'a^93', 'a^162', 'a^10', 'a^516', 'a^537', 'a^79', 'a^286', 'a^454', 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(591)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.921206942558692803360302619847+0.376757935903622062983140204701*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.730518034876', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.63992416687', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.49251993838', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1047', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1047'], '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': '1-4729-4729.1047-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': '1-4729-4729.1047-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.15005068099299754, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.730518034876', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1047', 'Lhash_array': ['dirichlet_L_4729.1047'], 'factors': ['1-4729-4729.1047-r0-0-0'], 'label': '1-4729-4729.1047-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1047'}
Lfunction data - 1-4729-4729.1047-r0-0-0