Formats: - HTML - YAML - JSON - 2025-12-18T07:00:26.556396
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '2872152979032705728553454588851,3124727895450341011173125916445,3638200324178670245426229526606,3804740087235767779286606133260', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 2, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.10925426854464874, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -2, 0, 4]], [3, [1, -2, 1, -6, 9]]], 'bad_primes': [2, 3], 'central_character': '72.1', 'coefficient_field': '1.1.1.1', 'conductor': 26873856, 'conductor_radical': 6, 'degree': 8, 'euler_factors': [[1, 0, -2, 0, 4], [1, -2, 1, -6, 9], [1, 0, -10, 0, 75, 0, -250, 0, 625], [1, 0, 14, 0, 147, 0, 686, 0, 2401], [1, 18, 155, 846, 3276, 9306, 18755, 23958, 14641], [1, 0, 26, 0, 507, 0, 4394, 0, 28561], [1, 0, 2, 0, -285, 0, 578, 0, 83521], [1, 4, -26, 16, 1099, 304, -9386, 27436, 130321], [1, 0, -46, 0, 1587, 0, -24334, 0, 279841], [1, 0, -58, 0, 2523, 0, -48778, 0, 707281], [1, 0, 62, 0, 2883, 0, 59582, 0, 923521], [1, 0, -148, 0, 8214, 0, -202612, 0, 1874161], [1, -18, 185, -1386, 8676, -56826, 310985, -1240578, 2825761], [1, 10, 43, -290, -2900, -12470, 79507, 795070, 3418801], [1, 0, -94, 0, 6627, 0, -207646, 0, 4879681], [1, 0, 212, 0, 16854, 0, 595508, 0, 7890481], [1, -18, 203, -1710, 11916, -100890, 706643, -3696822, 12117361], [1, 0, 122, 0, 11163, 0, 453962, 0, 13845841], [1, -14, 67, 70, -980, 4690, 300763, -4210682, 20151121], [1, 0, 284, 0, 30246, 0, 1431644, 0, 25411681], [1, 4, -134, 16, 16003, 1168, -714086, 1556068, 28398241], [1, 0, 158, 0, 18723, 0, 986078, 0, 38950081], [1, 0, 158, 0, 18075, 0, 1088462, 0, 47458321], [1, 0, -292, 0, 37158, 0, -2312932, 0, 62742241], [1, 10, 97, -1910, -19100, -185270, 912673, 9126730, 88529281], [1, 0, -202, 0, 30603, 0, -2060602, 0, 104060401], [1, 0, 206, 0, 31827, 0, 2185454, 0, 112550881], [1, 0, -178, 0, 20235, 0, -2037922, 0, 131079601], [1, 0, -436, 0, 71286, 0, -5180116, 0, 141158161], [1, 0, 98, 0, -3165, 0, 1251362, 0, 163047361]], 'euler_factors_factorization': [[[[1, 0, -2, 0, 4], 1]], [[[1, -2, 1, -6, 9], 1]], [[[1, 0, -5, 0, 25], 2]], [[[1, 0, 7, 0, 49], 2]], [[[1, 6, 11], 2], [[1, 6, 25, 66, 121], 1]], [[[1, 0, 13, 0, 169], 2]], [[[1, -6, 19, -102, 289], 1], [[1, 6, 19, 102, 289], 1]], [[[1, 2, -15, 38, 361], 2]], [[[1, 0, -23, 0, 529], 2]], [[[1, 0, -29, 0, 841], 2]], [[[1, 0, 31, 0, 961], 2]], [[[1, 0, -37], 4]], [[[1, -6, 41], 2], [[1, -6, -5, -246, 1681], 1]], [[[1, 10, 43], 2], [[1, -10, 57, -430, 1849], 1]], [[[1, 0, -47, 0, 2209], 2]], [[[1, 0, 53], 4]], [[[1, -6, 59], 2], [[1, -6, -23, -354, 3481], 1]], [[[1, 0, 61, 0, 3721], 2]], [[[1, -14, 67], 2], [[1, 14, 129, 938, 4489], 1]], [[[1, 0, 71], 4]], [[[1, 2, -69, 146, 5329], 2]], [[[1, 0, 79, 0, 6241], 2]], [[[1, -18, 241, -1494, 6889], 1], [[1, 18, 241, 1494, 6889], 1]], [[[1, -18, 89], 2], [[1, 18, 89], 2]], [[[1, 10, 97], 2], [[1, -10, 3, -970, 9409], 1]], [[[1, 0, -101, 0, 10201], 2]], [[[1, 0, 103, 0, 10609], 2]], [[[1, -6, -71, -642, 11449], 1], [[1, 6, -71, 642, 11449], 1]], [[[1, 0, -109], 4]], [[[1, -18, 211, -2034, 12769], 1], [[1, 18, 211, 2034, 12769], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'id': 9592799, 'index': 3, 'label': '8-72e4-1.1-c1e4-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/72/2/l/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [0.9940479530411371, 0.9983426860850201, 1.003731306514431, 1.0113381517427713, 1.0223206627817212, 1.0376355920453917, 1.0572706434351808, 1.0809794671829804, 1.1085232585884335, 1.1397227531308958, 1.1746458141697453, 1.2134368630582635, 1.2562572046506142, 1.3032563108596928, 1.3544795226275226, 1.4099397710390011, 1.4696404864898396, 1.5335719039758082, 1.6017082854386584, 1.674002788372599, 1.7503829730901799, 1.8307397991938266, 1.914900993238706, 2.002644404330785, 2.093700320699944, 2.187743808569948, 2.284378840068522, 2.3831451632198903, 2.4835195500880065, 2.584910059715119, 2.686641961718647, 2.7879690308639318, 2.888079084049142, 2.9860938538883173, 3.081063751329826, 3.1719821363540346, 3.257795933675653, 3.3374138081826303, 3.409713670500763, 3.4735593841823746, 3.5278167700841756, 3.5713720431583607, 3.6031562585472225, 3.6221592253619677, 3.6274478171154083, 3.6181935368000118, 3.593713925596365, 3.5534746608252243, 3.497103428163949, 3.4244211029074445, 3.3354940869088265, 3.23061264737588, 3.1102906154178367, 2.9752904674797946, 2.8266742062177963, 2.6657470868877526, 2.4940337516713984, 2.3132863417156244, 2.1255188151633146, 1.9329126394166771, 1.7377659891797912, 1.5424787770722843, 1.349560001123786, 1.1615062601508062, 0.9807328013455014, 0.8095408720155426, 0.6501010366623929, 0.5043328352082699, 0.3738412693356711, 0.2598866926547377, 0.1633648121366715, 0.08472793878261263, 0.023959921132572285, -0.019421522710481677, -0.046355524880017804, -0.05823895942186524, -0.05688604494835526, -0.044469671675728, -0.023456897520694464, 0.0034766259641436873, 0.03355232809607606, 0.06400009120501353, 0.09217237514278119, 0.11567851134411011, 0.13251310396867902, 0.14117443174249367, 0.14077571953477677, 0.13114661674448183, 0.11290574657164439, 0.08750732725527795, 0.057263604176977116, 0.025322861023985895, -0.004391875585297577, -0.02727932502057042, -0.038195749148335595, -0.03164107953627035, -0.0019745422627312137, 0.056341855741416993, 0.14846570649160337, 0.27888450120346125, 0.45112691766171287, 0.6674785331394903, 0.9287073697195832, 1.2338304084500082, 1.5799233878357986, 1.9619921555861108, 2.3729395164071008, 2.8035639208865817, 3.242640908630639, 3.6771347595309214, 4.092607558899432, 4.473503241983366, 4.803540289714315, 5.066290994428089, 5.24602559203323, 5.328104825487439, 5.2994969868951705, 5.149502865970365, 4.870727446498346, 4.4592071123689925, 3.9146862760635286, 3.241081176000867, 2.4470716645358572, 1.545609016108417, 0.5536276264907857, -0.50810423541128, -1.6151818259897495, -2.740704943271619, -3.8561351371812522, -4.932064008892804, -5.939178209339756, -6.849583019919406, -7.637782973131014, -8.281613322664464, -8.763417894790399, -9.070763580254862, -9.196847771898089, -9.140902960799842, -8.908799058453747, -8.512539481484318, -7.969631693515969, -7.302541833853641, -6.538280506570214, -5.706790141606962, -4.839499593544055, -3.968100383081749, -3.123464168411231, -2.333857974491327, -1.6235952929905264, -1.0120447316761, -0.5128767147541545, -0.13331093489346973, 0.12612501127252157, 0.27144935784335233, 0.31477373581706053, 0.27348481588761975, 0.16910974223794284, 0.025951494805067626, -0.1304610349105522, -0.27506729801399354, -0.3849256585914768, -0.4407801045169459, -0.42845979855229827, -0.3399436186784836, -0.17409870487478896, 0.06297151580116639, 0.35815356243576196, 0.6919341722337368, 1.039345991872158, 1.3714091131748787, 1.65730191706136, 1.8661296809718175, 1.9688046087484525, 1.940264798134073, 1.7621424772334622, 1.4238168629058783, 0.9233982476838001, 0.2687815880545077, -0.5214200475663155, -1.4191395805143832, -2.3880506347204298, -3.384829458712645, -4.360991616404778, -5.266059449848056, -6.050234674296584, -6.667039794914412, -7.076554771299213, -7.2479816152556475, -7.161395630571395, -6.809307261906824, -6.198488690970308, -5.3494001678212095, -4.295024275942924, -3.0795982165496065, -1.7573622673951206, -0.38881764871213076, 0.9628391763237614, 2.2349533684120613, 3.368454895163377, 4.311838382267981, 5.024199798506046, 5.47746841785792, 5.6579938143561606, 5.567362617323946, 5.2221755070311255, 4.652969540969668, 3.902324327500114, 3.0219553852318644, 2.0694633238967306, 1.1047628291865739, 0.18617569643545737, -0.6331725298896996, -1.3084473009796571, -1.805801571235395, -2.1045673561031846, -2.1978778867407316, -2.092590635937159, -1.8085327061163505, -1.3767779099304853, -0.836793311561342, -0.23350343001653334, 0.38596693802797616, 0.9761929313883294, 1.4964864592916298, 1.913339001809652, 2.2026796374124387, 2.352072878015783, 2.360414938217484, 2.2371669788873465, 2.0014056773936684, 1.6805385463284255, 1.306852744500498, 0.91452222759445, 0.5369930890965325, 0.20444495592993295, -0.05910692702442994, -0.23751150918727162, -0.32336772949272463, -0.3183645174783926, -0.232738038852084, -0.08383156135347218, 0.10583849992901027, 0.31085406585721953, 0.5055666541106788, 0.6666182749415226, 0.7751338704099217, 0.8185287791602427, 0.7915645570282003, 0.6966249029814519, 0.5432766354401924, 0.3471721234982003, 0.12817116870331008, -0.09187478023352531, -0.29151449505746574, -0.4520638819341281, -0.559605769774581, -0.6064933948773931, -0.5922227750067159, -0.5234289067132551, -0.4129954397483854, -0.27859410822555997, -0.1405778589193233, -0.01920529092023012, 0.0678742112120257, 0.107938828193689, 0.0953056030115478, 0.03286067047571172, -0.06791528232658399, -0.18756644453343535, -0.3000930509209945, -0.37574944027242624, -0.3844088359062854, -0.29890403225988305, -0.09866264376459369, 0.22611782735656308, 0.6723249165327924, 1.2227496710773929, 1.845582108589797, 2.494891406010789, 3.1140177632711628, 3.639625019728809, 4.006380949862669, 4.152792391037793, 4.027295906135208, 3.593462490097087, 2.8345130967527123, 1.7573551632899616, 0.3936726607375474, -1.2008329882551776, -2.9489043436620244, -4.756011090812346, -6.5166696580851395, -8.121712960013644, -9.466536463429918, -10.460099493503714, -11.031099458088327, -11.133594533462913, -10.751873101687258, -9.90339634449084, -8.636110995125971, -7.025401485083393, -5.169615240556348, -3.1823077056078053, -1.1828771276700698, 0.7113281677290093, 2.3934169142234327, 3.777366060419695, 4.802377501924208, 5.435127523687513, 5.671884900920357, 5.540784677345737, 5.094704874252745, 4.404458389075679, 3.5530230241774614, 2.6299761233280856, 1.7204856605552135, 0.8979004255339533, 0.2190472466340234, -0.2789933126274579, -0.5818892802107943, -0.697178891812569, -0.6511163004381318, -0.4842412008706858, -0.24577386558216113, 0.012794714577252349, 0.2438529649424985, 0.40901798720461185, 0.4830079436658947, 0.4557591850499868, 0.3326798711994278, 0.13299703943844446, -0.11374476252526415, -0.3721163091628332, -0.6058751686107136, -0.7833074880976569, -0.8813323984272367, -0.8883994067209429, -0.8061008997330158, -0.6490936926321487, -0.4423948092537363, -0.21774658798241428, -0.009158395592027717, 0.15237058483259697, 0.24376638366732617, 0.2534590947830153, 0.18371195031086346, 0.05136985423316311, -0.11428017514612325, -0.27527949255634204, -0.3900730804153962, -0.4198971395339968, -0.33544858961337337, -0.12249746910082053, 0.2137689074424456, 0.646247729729311, 1.1268708792663404, 1.5901331735896969, 1.959041751804864, 2.1538788700040987, 2.1022942470463537, 1.7492977592810777, 1.066750078723866, 0.06176419188070056, -1.2191301560374144, -2.6893778347141963, -4.22563841221287, -5.675625238231021, -6.869498051742223, -7.633861917627714, -7.807985205087661, -7.2610043339135135, -5.905229398480948, -3.7078955283246526, -0.6994157121885948, 3.0260268946558617, 7.314259836304251, 11.957892565791564, 16.710130000246803, 21.310702981185358, 25.50031410852365, 29.03590000382478, 31.71179886884167, 33.3893684977635, 33.99507691246839, 33.519964766421005, 32.02373960132279, 29.641895653253865, 26.5581709749525, 22.984857431029702, 19.149919728307648, 15.286557960285416, 11.604353360357587, 8.27376507918461, 5.419214788358494, 3.1162439334451166, 1.3867953146176857, 0.20435597373217543, -0.49606811762475256, -0.8061248454962632, -0.8316042540541984, -0.6792852231329354, -0.44542838138531193, -0.20698005433113667, -0.01639634354607213, 0.09977665756177873, 0.13893028776475633, 0.11748941907784749, 0.06371808708858948, 0.009986303416581813, -0.014633321642133611, 0.009568217863416663, 0.08922999373854175, 0.21671981557127032, 0.3715429907327011, 0.5247196691973652, 0.6440660286647442, 0.6998469829378609, 0.6706350181791114, 0.5487688890074386, 0.3416432609372351, 0.07112715662767496, -0.22874337089189836, -0.5164511872106985, -0.7504656973951903, -0.8960997250186896, -0.9317587988627094, -0.8545461013870137, -0.6824332146632219, -0.4532103552485357, -0.22088405248917628, -0.04943336201882016, -0.003336579172602559, -0.13777821544525054, -0.4894038339248303, -1.068277423888874, -1.8528845960256022, -2.7890145197868303, -3.7927991594981787, -4.758407687553186, -5.5682880313061, -6.105649603035528, -6.2686830966080445, -5.985125925534831, -5.220930796747876, -3.986698152809251, -2.3405667251459117, -0.38443275023096507, 1.745846079367863, 3.8916692817111103, 5.88671089758918, 7.57824073764435, 8.839934714851891, 9.58196575469406, 9.761279782718223, 9.392147921200529, 8.537039900971923, 7.29677632235311, 5.8013718100789875, 4.1997876233347915, 2.63740375286394, 1.2403314677772366, 0.10493358810494334, -0.7096839679117459, -1.1877150857938692, -1.3542794854013636, -1.2680581226705447, -1.0109933179275623, -0.6753907113454755, -0.35014086264151084, -0.10837689818382185, 0.0020137444069448906, -0.036162292366392186, -0.20846623828108338, -0.4724537650773168, -0.7657109193382987, -1.0161208026192112, -1.1531551868096717, -1.119235511873562, -0.8793098889159466, -0.42587032776302686, 0.2190145196882108, 1.0056190296008938, 1.8644436945380518, 2.714826131420891, 3.4739692389875776, 4.067773007306232, 4.444104745540427, 4.575594373669187, 4.4604938808881505, 4.123162618138306, 3.6135027143594054, 2.9949073924174106, 2.3345372499294483, 1.6959382704087445, 1.1327375178862362, 0.6802415345408467, 0.35299662325542197, 0.14620831832329387, 0.039445938164586636, 0.001992564580367313, 5.058899207547284e-05, 0.0037163965646136872, -0.007448676464190478, -0.041064639312640865, -0.0913964779418955, -0.14166520512274267, -0.1687375757266055, -0.14922220011331797, -0.065901263207935, 0.08671742388128863, 0.29936041160305155, 0.5476128477612654, 0.7942153750172728, 0.9945977547103254, 1.105999441126906, 1.0948359674916799, 0.9434760366859682, 0.6562624523659981, 0.26315773722111513, -0.18466698948632204, -0.6214332582886245, -0.9756070326251034, -1.182123578215623, -1.1954887097672007, -0.9990488363490584, -0.6109149237082808, -0.08603930104587112, 0.4909886903794554, 1.0189033743363445, 1.396727122279366, 1.5442800964364543, 1.424051778441024, 1.0587850696338554, 0.5430678301935906, 0.04698010222584945, -0.19195622478356045, 0.11257315502208809, 1.2676845256675064, 3.566388272964012, 7.248881062609145, 12.463863726784721, 19.23630437944197, 27.453453492766407, 36.85449496929919, 47.03200451026818, 57.45717840228833, 67.54457178979196, 76.68247014738971, 84.27172218048851, 89.78769598090273, 92.87302039992531, 93.33247189633998, 91.13455892214746, 86.42951460698573, 79.57776492976191, 71.06721115007447, 61.45594281549546, 51.33696038759775, 41.31055681171574, 31.899643202699593, 23.508088543706947, 16.406441467258745, 10.730549031521633, 6.475220888757985, 3.5164629296192214, 1.6462249583985191, 0.6101462315945926, 0.14377290963239583, 0.006506455058331702, 0.007223224360890552, 0.01896754958195409, -0.018055716889202735, -0.10409320689143824, -0.19575884379351824, -0.22719264007600143, -0.1318639924290691, 0.13804115266352313, 0.597415458411668, 1.22310322801512, 1.9559997178465636, 2.708855211262603, 3.3805723880307257, 3.8776878656614597, 4.127599567919292, 4.088831595398637, 3.759618947009944, 3.1832672636690336, 2.4357870616663178, 1.6124831085384215, 0.8146345439152033, 0.13502286689623014, -0.3597835266660304, -0.6384838471365257, -0.7074516901937751, -0.6080081622311364, -0.4072932018845646, -0.18405096827351175, -0.013062604243670508, 0.04948892708034285, -0.022348045924909837, -0.21856203914622058, -0.49424427103020363, -0.7771374082455562, -0.9804776750181834, -1.019471036455278, -0.8286113035870629, -0.3748537235317861, 0.3332375036491345, 1.2412075549324613, 2.253129317839507, 3.249941790234178, 4.103117535441096, 4.690166344034501, 4.9154096543836845, 4.736251198375602, 4.162648081713372, 3.254163441052145, 2.116699191550683, 0.8953166580844585, -0.2557682374225211, -1.1963397594638856, -1.8180502810474173, -2.0603788536172245, -1.9233801634514927, -1.467093453803352, -0.8025571615500432, -0.07691398342584115, 0.549364819359827, 0.9267889108505736, 0.9390357882360637, 0.5208199596448846, -0.3317789789448059, -1.5599276737033525, -3.049577993559991, -4.648382456392593, -6.186247619988343, -7.497155310396751, -8.441762571480876, -8.928962177715668, -8.922435464201913, -8.441780509991125, -7.558973221520826, -6.388220419282021, -5.0641831927408125, -3.7234093601364533, -2.4878993811225985, -1.4497771361476355, -0.6623894751711714, -0.13955188278370523, 0.1405558138513944, 0.2277511169435743, 0.18590019484670836, 0.08002825796290826, -0.03407864420578001, -0.11767916601346613, -0.15288881491709597, -0.1411008674363833, -0.09801051566843488, -0.04664127138200274, -0.009199293173549446, -0.00042990618591974593, -0.023685744387454476, -0.07025850183036529, -0.12201993952482712, -0.15661008179422128, -0.15396889122736457, -0.10262823773574326, -0.003678901889169545, 0.127891510426772, 0.265131401290555, 0.375022743441832, 0.4257281317958322, 0.39383390971291576, 0.2711194326089799, 0.06939318009198171, -0.18120298260567982, -0.43700662799965156, -0.6482662681265408, -0.7695990316781203, -0.7710973685703764, -0.6458180742794062, -0.41346936158120395, -0.11960133594587133, 0.17237929003737726, 0.39353945867793355, 0.4839224512146047, 0.4074465663055581, 0.1627266773397864, -0.21253582001362012, -0.6450458335839987, -1.038815869292449, -1.2958762731648603, -1.3408520360713658, -1.1471095694594804, -0.7603045928275943, -0.3088354967485369, -0.0030065645866350532, -0.12074973332646084, -0.976969380952791, -2.8798932552108925, -6.082569842231894, -10.733002769855611, -16.83385500675217, -24.21716039611227, -32.534415185264585, -41.27146039044115, -49.808045155193945, -57.469815923287136, -63.5874776607558, -67.57560429493023, -69.04131206535723, -67.80802118669394, -63.92692365340526, -57.686946501489345, -49.619056072408995, -40.40489877879785, -30.79254355416368, -21.521318097966223, -13.249238014358484, -6.470256466840196, -1.468192954801711, 1.7000975321331, 3.195534669945959, 3.351046877917394, 2.6106954434281255, 1.4595995563581943, 0.34953541883888223, -0.3670825368138111, -0.4794439905878625, 0.06087580284852761, 1.1468107024493464, 2.549464523377033, 3.9637999756653493, 5.064949919778829, 5.5770136642404555, 5.315392555763828, 4.211660418503485, 2.327218683796695, -0.14653168773480216, -2.9316247516529197, -5.70911718119445, -8.163370868575603, -10.028242039817297, -11.127357770505393, -11.391812571552249, -10.862438892863196, -9.680785127220524, -8.055326585521216, -6.223088504480359, -4.413435334741291, -2.816741189290776, -1.558084588020471, -0.6878634920869434, -0.1862572786648073, 0.021122864593608605, 0.039130227963486995, -0.023003339144256497, -0.07521212756658185, -0.06370287713741077, 0.0224938669552025, 0.15508762237008555, 0.2785636263876268, 0.3291520203566766, 0.25402301658492143, 0.026952448430580138, -0.34140919037303796, -0.8020725450080421, -1.277395992266842, -1.6759748923987576, -1.9113800868773747, -1.924211078357059, -1.6961741485810191, -1.2557990893727387, -0.6767526451182991, -0.06824829518682943, 0.446649342192142, 0.7545545724092363, 0.7738373650401776, 0.4723774782644945, -0.12388255638540818, -0.9328490283302779, -1.82874812006728, -2.665499903133478, -3.3024229459445498, -3.6288788992232774, -3.586427493631092, -3.1845840328095663, -2.496668090789503, -1.647377006066609, -0.7928337504312356, -0.0919795388904672, 0.325190572777475, 0.38133546970800264, 0.06798503234086252, -0.5480074760247158, -1.3361821249717685, -2.1238642871650066, -2.724169419963025, -2.9699657021044303, -2.744299689736418, -2.000980585267805, -0.775332169469614, 0.8173579513748184, 2.600902648662019, 4.364674339625176, 5.894864376150633, 7.0100643223703525, 7.587260639190377, 7.577069948856567, 7.009155936267697, 5.987465588889142, 4.667917135207923, 3.231764121985026, 1.8572974190257074, 0.6927956480867089, -0.16180962073339303, -0.6643551433090231, -0.8311079777740896, -0.7264279371587526, -0.4430971809712821, -0.08376331832992713, 0.2574395766499068, 0.5131691307387011, 0.6490224343801191, 0.6620641286102235, 0.5757978110228352, 0.43200697541340816, 0.27498408931008167, 0.14029232415612758, 0.04860021649325392, 0.0036761328829561313, -0.0056409256061440765, 0.0016376750934523983, 0.007215646178915692, 0.0009988259548643118, -0.014345687117465993, -0.023308520810508725, -0.002174555485777973, 0.07285174582024741, 0.21623543589355831, 0.42460235947586056, 0.6719467695426306, 0.9119963414538114, 1.0849263543597514, 1.128319408419159, 0.9924948643304581, 0.6581559936406326, 0.14320624383154662, -0.4953948292574738, -1.1655320625780519, -1.7536909195110424, -2.1489510545514237, -2.2648276265667406, -2.058987843744826, -1.5500958787997963, -0.8182339615574331, 0.007905131387740313, 0.7733355082547502, 1.327901209912923, 1.5642089631609901, 1.4488976738824106, 1.042713861101468, 0.5055446152561098, 0.08015721153350436, 0.057071492373849196, 0.7249472674594041, 2.3148382802989476, 4.947029331434991, 8.587209908544237, 13.025191747970672, 17.897755277914598, 22.7178836899784, 26.92200657509281, 29.950460899535102, 31.37136304154687, 30.91879504189543, 28.524634264450164, 24.356404132892862, 18.848820095696055, 12.602105845200695, 6.295601829960926, 0.6154814482862911, -3.8229343438156485, -6.590165207323166, -7.494728224692327, -6.594386856802442, -4.182631326849473, -0.7410924042192494, 3.14206751234599, 6.863975630136363, 9.896897088139763, 11.860240680742555, 12.565674067810946, 12.03191312335977, 10.467387365361226, 8.214228300899615, 5.681396865717154, 3.2732179995779123, 1.3212273348725372, 0.036033982211409195, -0.5141032437343762, -0.4004310097726973, 0.1967895912449358, 1.036780938422686, 1.8681655488430564, 2.478080548675541, 2.737222035348266, 2.611212352974979, 2.153453407772898, 1.4861260393071651, 0.769377378161728, 0.15457211588722614, -0.2505251417694168, -0.40338029070382975, -0.33517069447337045, -0.14117495861596033, 0.04465218057462987, 0.08254706678490714, -0.13865776341318517, -0.6731376337601493, -1.5026493066961801, -2.536965452579569, -3.6316961295663166, -4.615437015636144, -5.322432854003043, -5.62708105446987, -5.47357937262528, -4.881681615731589, -3.942239123220765, -2.80188343193668, -1.6337834831345386, -0.6012965275674278, 0.16955033445431797, 0.610886705335468, 0.7256360850192359, 0.5769477212343411, 0.2677845171465285, -0.08352224171227304, -0.3705767153402587, -0.5250312734076916, -0.528001129355367, -0.4087305492360489, -0.23228521791478834, -0.0752552164246125, 0.0020386134713865334, -0.020519330284616912, -0.10765676826618706, -0.1669685605158042, -0.06324544754902164, 0.3536437095185251, 1.2144887920179075, 2.5946996367746404, 4.4826540037191895, 6.76326362268099, 9.233125783731381, 11.618725106155981, 13.606867861215646, 14.89628143051898, 15.274670381366775, 14.638456536631475, 13.005563402030676, 10.527542198277937, 7.492253947142052, 4.255053788346417, 1.181347203496696, -1.4006036957484824, -3.2450899211087454, -4.233836519514149, -4.384560958534371, -3.8366408059959873, -2.8215710918251147, -1.612591724501164, -0.47120596442577645, 0.3987704065041125, 0.8841697367165501, 0.9771974807986251, 0.7669392383466961, 0.41205250463838733, 0.10037231845990285, 0.00503703840569743, 0.24526701327461634, 0.8586428327996585, 1.7947763379914652, 2.92638488975112, 4.072259086914749, 5.03359561118759, 5.644350934659081, 5.79697293324012, 5.457635823135327, 4.674910086081617, 3.57798660976154, 2.3386001673484045, 1.1362291593102016, 0.12852150919181468, -0.5753938791532055, -0.9350432709022606, -0.9782942187354484, -0.7881810625537392, -0.48159016681364036, -0.18013008298212257, 0.016612168313056796, 0.05014153595734815, -0.08838265069486584, -0.3613523760799037, -0.6978959314669583, -1.0138501695473259, -1.234768862791746, -1.3120780374251169, -1.2321466721846854, -1.0178488465851057, -0.7211422033807356, -0.4059263721727975, -0.13183252961090924, 0.05956154658639401, 0.15426423006418258, 0.1644762454595434, 0.12036697993788367, 0.05863412784456922, 0.010293994690515137, -0.009771888558855836, -0.006207082444836749, 0.002867238470806168, 0.0017170497717531488, -0.003595680528132721], 'positive_zeros': ['2.26572919897296598094005540026866', '2.46497567617430314622651811016352', '2.87003400110696441359977158822303', '3.00141070934747919454022704351449', '3.89150805359828389086771997983397', '4.73303866172930221653669861932095', '4.91148107712993364417179104960698', '5.14872745705443002593593979642487', '5.54245330779234409972191726848101', '6.10263812145192357411800228002206', '6.56921485253876360296646337170489', '6.88674705314451405041949624189037', '7.33584879936360968511900110449197', '7.51439919872580222149725574821190', '7.86177047040072258534126108663221', '8.193271439978103121820558346487514', '8.323805465493111519116727905456829', '8.542133080835188017557302649564727', '8.976847986167529653157356874981684', '9.487939876288600041548634650950714', '9.918566536362943500092950394429931', '10.12341874679207186463613675069773', '10.32980201828229267574607016979008', '10.65776290524712935405876278963696', '10.82257133950445822006569975190450', '11.01267020733973071648887699285909', '11.31416558398520816406580231265593', '11.66256123931092962844101076801299', '12.38232301493602413733278662323298', '12.59712718113872897415425981215383', '12.75793173445158789758196750730424', '12.80600452042692713469846878027157', '13.13253616871827371677520951234570', '13.46041437988458620714018389853376', '13.46430198330321125217758542966407', '13.94325831746413774485719409405142', '14.40965945685779600935486563877766', '14.68592575309039060882362215601067', '14.70411958085262587315876972993928', '14.99026046468207165228230224067485'], 'prelabel': '8-72e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7582367008746141, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 1535759756060347231, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.26572919897296598094005540027', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46497567617430314622651811016', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.87003400110696441359977158822', 'prec': 103}}