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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1061', 'a10': [-0.5182997958199616, 0.8551989953531203], 'a2': [0.9897180218885506, -0.14303229407729687], 'a3': [-0.46743646674681383, 0.8840266678982341], 'a4': [0.9590835257019713, -0.2831232783207275], 'a5': [-0.6352917228621284, 0.7722722491860423], 'a6': [-0.33618593289223675, 0.9417956352231499], 'a7': [-0.018603959307268346, 0.9998269313726719], 'a8': [0.9087264778787534, -0.41739212786308705], 'a9': [-0.5630062991105097, -0.8264526043046191], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1061', 'coeff_info': ['x^2364 - 1', '0.999996467887392 + 0.00265785867577771*I', '\\\\zeta_{2364}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.156', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2310', 'a^774', 'a^2256', 'a^850', 'a^720', 'a^598', 'a^2202', 'a^1548', 'a^796', 'a^531', 'a^666', 'a^1324', 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21.961383672410207, 'root_angle': -0.34452447995858493, 'root_number': '-0.559609737475717300333059193031-0.828756261950616433544237750021*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2364)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.06422347824331939939099957707+0.589789735849885661873714191074*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.65364205189', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.5454454074', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.27132977994', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1061', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1061'], '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': '1-4729-4729.1061-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': '1-4729-4729.1061-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.34452447995858493, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65364205189', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1061', 'Lhash_array': ['dirichlet_L_4729.1061'], 'factors': ['1-4729-4729.1061-r0-0-0'], 'label': '1-4729-4729.1061-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1061'}
Lfunction data - 1-4729-4729.1061-r0-0-0