-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '707653811672112251642037541244', 'a10': [-0.5969088731774137, 0.0], 'a2': [-2.265731890127938, 0.0], 'a3': [0.0, 0.0], 'a4': [3.1335409979427205, 0.0], 'a5': [0.2634507974126225, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-2.568299987806269, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.888306657226465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [127, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 127], 'central_character': '8001.1', 'coefficient_field': 'CDF', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.265731890127938, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.2634507974126225, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.114622510781337, 0], [11.0, 0]], [[1.0, 0], [-5.029350493007077, 0], [13.0, 0]], [[1.0, 0], [0.60073987153524, 0], [17.0, 0]], [[1.0, 0], [0.6623624556163187, 0], [19.0, 0]], [[1.0, 0], [-0.8625308692654173, 0], [23.0, 0]], [[1.0, 0], [7.497177883974277, 0], [29.0, 0]], [[1.0, 0], [6.272581559755069, 0], [31.0, 0]], [[1.0, 0], [-1.8879409167219643, 0], [37.0, 0]], [[1.0, 0], [9.921481784916262, 0], [41.0, 0]], [[1.0, 0], [0.8374353057305132, 0], [43.0, 0]], [[1.0, 0], [-6.328799348207993, 0], [47.0, 0]], [[1.0, 0], [2.2297892571517233, 0], [53.0, 0]], [[1.0, 0], [-8.92253257955641, 0], [59.0, 0]], [[1.0, 0], [-12.671586981439512, 0], [61.0, 0]], [[1.0, 0], [6.636586412859896, 0], [67.0, 0]], [[1.0, 0], [3.0415963156667742, 0], [71.0, 0]], [[1.0, 0], [-3.584226146308688, 0], [73.0, 0]], [[1.0, 0], [6.240816796644575, 0], [79.0, 0]], [[1.0, 0], [-15.59399553072311, 0], [83.0, 0]], [[1.0, 0], [10.298841273301038, 0], [89.0, 0]], [[1.0, 0], [-10.805774970016719, 0], [97.0, 0]], [[1.0, 0], [-11.17834026268995, 0], [101.0, 0]], [[1.0, 0], [-8.913002503354797, 0], [103.0, 0]], [[1.0, 0], [1.4023258462007182, 0], [107.0, 0]], [[1.0, 0], [7.845061279867901, 0], [109.0, 0]], [[1.0, 0], [-5.514086850349521, 0], [113.0, 0]], [[1.0, 0], [-1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 54, 'label': '2-8001-1.1-c1-0-54', 'leading_term': '0.76360094574183654387821059134091', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/8001/2/a/v/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.7636009457418366, 0.7578044932053438, 0.7404359201787033, 0.7115613470292643, 0.6713032254245576, 0.6198576775505591, 0.5575167919328805, 0.4846941045089379, 0.4019512485678916, 0.31002365508541596, 0.20984321459131902, 0.10255595194066468, -0.010467009025224247, -0.12762662752187154, -0.24710238470543677, -0.3668687386587944, -0.4847219900911249, -0.5983175817246973, -0.7052174801817903, -0.8029469161476699, -0.8890593907246354, -0.9612084984902545, -1.0172247777627654, -1.055195484606627, -1.0735449093329428, -1.0711126239038886, -1.0472268775191542, -1.0017702574396383, -0.9352347137283398, -0.8487631195736955, -0.7441747106459047, -0.6239720222875854, -0.4913273238185962, -0.35004703276176213, -0.20451317232534677, -0.05960160280129718, 0.0794225027612842, 0.20703067468193975, 0.3175765655383882, 0.40545785180252586, 0.46529088974269217, 0.49209364147916207, 0.48147171556258517, 0.42980181022946834, 0.33440643649055735, 0.19371355984094432, 0.007394757306377323, -0.22352434055457363, -0.4965871526197849, -0.8078679916346452, -1.1519769827031723, -1.5221113051856308, -1.910154724727562, -2.306825929054524, -2.701874595095193, -3.084322441338732, -3.4427448103541476, -3.7655866398409503, -4.04150507794474, -4.259729543121981, -4.410428783368586, -4.485073514067585, -4.476782562657687, -4.380640168575836, -4.193972215133403, -3.916569730507012, -3.550848998100977, -3.101939056867021, -2.577689227979505, -1.9885915369704608, -1.3476154548880128, -0.6699551874997335, 0.02730728674095674, 0.7256171878089939, 1.4054306663163902, 2.0467551893832847, 2.6297318720037057, 3.1352428133985795, 3.545524736578618, 3.8447690304244273, 4.019687732711003, 4.060025125866251, 3.958995478248455, 3.713629060277531, 3.3250108775075673, 2.7983995442242335, 2.1432172960568856, 1.372906206560138, 0.5046501048668617, -0.4410336569625578, -1.4408237294899906, -2.4692321333282243, -3.499331715473088, -4.50355210510707, -5.454519372679998, -6.32591216658965, -7.093305573900331, -7.734973420245091, -8.23262024985692, -8.572015831547088, -8.74350770120884, -8.742390914626315, -8.56911874289724, -8.229343354180523, -7.73378141202546, -7.097905774923804, -6.341470874256159, -5.487885634830639, -4.563453735508676, -3.5965063441509435, -2.616456974028987, -1.6528115961669707, -0.7341694367989602, 0.11274913281722229, 0.8640116200527789, 1.4992851780450562, 2.0025201445292957, 2.362478858130189, 2.573088864742591, 2.633606161874841, 2.5485813475389443, 2.327629162585618, 1.9850096373416406, 1.5390365592323951, 1.011335953354818, 0.4259834132296928, -0.19144583699212, -0.8148765551736511, -1.4187429727034526, -1.9789677942139783, -2.4738714375130373, -2.884975003873738, -3.1976647881732783, -3.401691854711548, -3.491487089390705, -3.466279908264516, -3.330017128178457, -3.0910870289591568, -2.7618619852852757, -2.358080848768182, -1.8980991644899219, -1.40204099418493, -0.890890323850752, -0.38556255407075224, 0.09400272164814252, 0.529687598328831, 0.9059433230806989, 1.2104069351520816, 1.4343608419517724, 1.5730164715462727, 1.6256114015255623, 1.5953181187958902, 1.4889714038434543, 1.316629836769179, 1.0909946828941477, 0.8267160564250347, 0.5396214552856416, 0.24590524950658058, -0.03868068899068403, -0.2995953935288512, -0.5241987540826019, -0.7023297060911249, -0.8267451925861387, -0.893399650646871, -0.9015530040862556, -0.8537039795534389, -0.7553545567124391, -0.6146200560772468, -0.44170731244235223, -0.248290163556676, -0.04681674444203865, 0.15021346558577264, 0.3309634357077753, 0.48492443425283405, 0.6034978478341912, 0.6804615109844144, 0.7122954260411073, 0.6983494711348266, 0.6408443889277347, 0.5447065592208176, 0.4172462900651024, 0.26769811239042596, 0.10664934961013367, -0.05461038077597118, -0.20478145846876333, -0.33324849386881183, -0.43073628692009314, -0.4898891851896439, -0.5057395862672741, -0.47603738250939553, -0.4014198686475453, -0.2854106142631652, -0.13424555553738626, 0.04346545586929076, 0.2372237570678464, 0.43524697552823327, 0.6251601066282203, 0.7947330258897677, 0.9326215695767628, 1.0290684183897076, 1.0765216438078098, 1.0701328806339754, 1.0081034849888622, 0.8918554012744869, 0.7260133510175039, 0.5181958296411816, 0.27862364346978624, 0.01956569207249994, -0.24534824582292566, -0.5019094398421693, -0.7361621045033382, -0.9352365509328266, -1.0881336968751196, -1.186412781224154, -1.22473877120575, -1.2012532935747773, -1.1177426049043044, -0.9795876323519472, -0.7954938356296961, -0.5770118451985727, -0.33787275364430897, -0.09317380353800302, 0.1415397083138496, 0.35124285448412096, 0.5223917048383279, 0.6438167042366998, 0.7074915353866054, 0.7091258953413075, 0.6485395861469666, 0.5297871463250544, 0.36101632367906555, 0.1540592525307992, -0.07622862164777319, -0.31285096714423005, -0.537728846817107, -0.7328769474584923, -0.8816304239598601, -0.9698492483652955, -0.9870252996501754, -0.92722014422132, -0.7897685389886693, -0.579693882209095, -0.3077966367676169, 0.009605577395890191, 0.35128790706830637, 0.6920593997015353, 1.0039963373140828, 1.2579100278537445, 1.4249751914845052, 1.4784326001878665, 1.3952716445491566, 1.1577956348882572, 0.7549752442432, 0.18350361418049557, -0.5515199987134317, -1.436333137650654, -2.4487129074654375], 'positive_zeros': ['0.55824042645876188061607035632439', '1.66037284783311726600813647603466', '2.15790301366867370295441003728591', '3.37317386894169226145739586445614', '4.15041958035353041420345833943293', '5.29034545127872856704031103248822', '5.89185567193853185365689128831386', '6.74051975729620273136208408587933', '7.39969620697137300394199693519369', '7.979686218406969879947428209586398'], 'prelabel': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55824042645876188061607035632', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.66037284783311726600813647603', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.15790301366867370295441003729', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 63.888306657226465, 'bad_primes': [3, 7, 127], 'central_character': '1.1', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'index': 54, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8001/2/a/v/1/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-8001-1.1-c1-0-54', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55824042645876188061607035632', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '707653811672112251642037541244', 'Lhash_array': ['707653811672112251642037541244'], 'label': '2-8001-1.1-c1-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8001/2/a/v/1/4'}