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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1082', 'a10': [0.5586051717862636, -0.8294336996129582], 'a2': [-0.9495672539760007, -0.3135634388389013], 'a3': [-0.9276477791027373, 0.373456286499182], 'a4': [0.8033559396470452, 0.5954991471310542], 'a5': [-0.270353095890363, 0.9627612391151278], 'a6': [0.9979661917102114, -0.06374543280437904], 'a7': [0.3261544719433878, 0.9453164869139488], 'a8': [-0.5761137331759083, -0.81736954093367], 'a9': [0.7210608041484818, -0.6928717895258435], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1082', 'coeff_info': ['x^2364 - 1', '0.999996467887392 + 0.00265785867577771*I', '\\\\zeta_{2364}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.3361', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1302', 'a^1038', 'a^240', 'a^694', 'a^2340', 'a^466', 'a^1542', 'a^2076', 'a^1996', 'a^2169', 'a^1278', 'a^1348', 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-0.3400812980801754, 'root_number': '-0.536258016964130205176189028499-0.844054109190695570707289826754*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, '0.409304583838182999617207003877+0.202405727830083647450004372373*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.32236855567', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.00750897692', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.06042261321', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1082', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1082'], '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': '1-4729-4729.1082-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': '1-4729-4729.1082-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.3400812980801754, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32236855567', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1082', 'Lhash_array': ['dirichlet_L_4729.1082'], 'factors': ['1-4729-4729.1082-r0-0-0'], 'label': '1-4729-4729.1082-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1082'}
Lfunction data - 1-4729-4729.1082-r0-0-0