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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.100', 'a10': [0.9064949082647783, -0.4222167468138033], 'a2': [0.19802208623090942, 0.9801975583344198], 'a3': [-0.9715260343384347, -0.2369328271950402], 'a4': [-0.9215745067295166, 0.38820153083965064], 'a5': [-0.23434981142250366, -0.9721523367694165], 'a6': [0.039857366558510465, -0.9992053794546046], 'a7': [-0.800179095524197, 0.5997611316900071], 'a8': [-0.5630062991105097, -0.8264526043046191], 'a9': [0.8877256707947304, 0.46037282001878205], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.100', 'coeff_info': ['x^591 - 1', '0.999943486697302 + 0.0106312469467839*I', '\\\\zeta_{591}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.1466', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^129', 'a^318', 'a^258', 'a^421', 'a^447', 'a^235', 'a^387', 'a^45', 'a^550', 'a^12', 'a^576', 'a^208', 'a^364', 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0.009767995548908576, 'root_number': '0.998117199441712742608347311461+0.0613356028635264004542489341441*I', '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, '0.530838056842360968811249146631+0.219513747773794494845435535410*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.246081382123', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.41544188039', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.41435017349', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.100', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/100'], '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': '1-4729-4729.100-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': '1-4729-4729.100-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.009767995548908576, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.246081382123', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.100', 'Lhash_array': ['dirichlet_L_4729.100'], 'factors': ['1-4729-4729.100-r0-0-0'], 'label': '1-4729-4729.100-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/100'}
Lfunction data - 1-4729-4729.100-r0-0-0