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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1053.734', 'a10': [-0.766044443118978, 0.6427876096865394], 'a2': [0.549508978070806, -0.8354878114129364], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.39607976603915684, -0.918216106880274], 'a5': [-0.9579895123154889, -0.28680323271109026], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8021231927550437, 0.5971585917027862], 'a8': [-0.984807753012208, -0.17364817766693036], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 4.890111441541118, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1053.734', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 1053, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_1053.713', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^91', 0, 'a^74', 'a^59', 0, 'a^43', 'a^57', 0, 'a^42', 'a^49', 0, 0, 'a^26', 0, 'a^40', 'a^96', 0, 'a^57', 'a^25', 0, 'a^32', 'a^92', 0, 'a^10', 0, 0, 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'187.524717664785744884691811228045', '188.16647478424469688870511622733', '188.85777642006444003892252948976', '189.91583071980611895780380779667', '190.26165280280680515693354451688', '191.031426327502386048002674544056', '191.412917012597038784820569944828', '192.04093111827859098804042052422', '192.50727842114124842992897218397', '193.425858633051301452240578995289', '193.83656999870749913248830363219', '194.12807244723960197253104884439', '195.121335116831926211123754277210', '195.53586680173720537835250549130', '196.06620778139179957230801537121', '196.71679335987445172588699541941', '197.02949761164870069890720542316', '198.26094210185892686339966260885', '198.97149943591357440062055211805', '199.232417953382068841768971452427', '199.97551340230974525778531517055'], 'prelabel': '1-1053-1053.734-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.890111441541118, 'root_angle': -0.061673855014115486, 'root_number': '0.981288316045495224058889942469-0.192544126871209136843113124935*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0308369275071', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(108)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.801328565417781513759493474690-0.356625251166830769981622561415*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.856075359917', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.39707842415', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.02944986088', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.890111441541118, 'bad_primes': [3, 13], 'central_character': '1053.734', 'conductor': 1053, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1053/734'], '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': '1-1053-1053.734-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': '1-1053-1053.734-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.890111441541118, 'root_angle': -0.030836927507057743, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.856075359917', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1053.734', 'Lhash_array': ['dirichlet_L_1053.734'], 'label': '1-1053-1053.734-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1053/734'}
Lfunction data - 1-1053-1053.734-r0-0-0