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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1083.905', 'a10': [-0.7167825131684512, 0.6972968010939954], 'a2': [0.45153335831088937, 0.892254238618394], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.59223525266498, 0.8057651056609781], 'a5': [0.2985148110016945, 0.9544050018795074], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.4016954246529695, 0.9157733266550574], 'a8': [-0.9863613034027223, -0.1645945902807339], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 5.0294308558300385, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [19, [1]]], 'bad_primes': [3, 19], 'central_character': '1083.905', 'coeff_info': ['x^114 - 1', '0.998481516433316 + 0.0550877603558654*I', '\\\\zeta_{114}'], 'conductor': 1083, 'conductor_radical': 57, 'conjugate': 'dirichlet_L_1083.578', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^20', 0, 'a^40', 'a^23', 0, 'a^36', 'a^60', 0, 'a^43', 'a^45', 0, 'a^25', 'a^56', 0, 'a^80', 'a^17', 0, 0, 'a^63', 0, 'a^65', 'a^13', 0, 'a^46', 'a^45', 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'189.54676404448527622775533051226', '190.02041990765653880351997079119', '190.344489896349281442510470903771', '191.01451730530497351369060933660', '191.77571442400502609471434254065', '192.99229225120305171019217587886', '193.162334627841565234197819943822', '193.67989465627197939698705014380', '194.446504048992734250136849691302', '194.83566845155730125035660589132', '195.579926268290316484295910775052', '196.23867357234822887701573963616', '196.66475993928823976466243947179', '197.19147978773621259240009531480', '197.97310343810951096305278983791', '198.34127024764190482253567515585', '198.92711042115023910593866564404', '199.595202889031073239348527397622'], 'prelabel': '1-1083-1083.905-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.0294308558300385, 'root_angle': -0.3668051708217913, 'root_number': '-0.669777072658213964246746256636-0.742562235062754569734764019244*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.366805170822', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(114)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.600116639394625532894934306685+0.976085641650575971036741678255*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.99213765319', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.90899832835', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.75196777222', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.0294308558300385, 'bad_primes': [3, 19], 'central_character': '1083.905', 'conductor': 1083, 'conductor_radical': 57, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1083/905'], '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': '1-1083-1083.905-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': '1-1083-1083.905-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.0294308558300385, 'root_angle': -0.3668051708217913, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.99213765319', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1083.905', 'Lhash_array': ['dirichlet_L_1083.905'], 'factors': ['1-1083-1083.905-r0-0-0'], 'label': '1-1083-1083.905-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1083/905'}
Lfunction data - 1-1083-1083.905-r0-0-0