Starting with polynomial:
P : 676039/1024*t^12 - 969969/512*t^10 + 2078505/1024*t^8 - 255255/256*t^6 + 225225/1024*t^4 - 9009/512*t^2 + 231/1024
Extension levels are: 12 50
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P1 : 676039/1024*t^12 - 969969/512*t^10 + 2078505/1024*t^8 - 255255/256*t^6 + 225225/1024*t^4 - 9009/512*t^2 + 231/1024
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 676039/1024*t^62 - 1054250888442885184822316295461370426122466037580211540666882655911739439493609967649561977795639667/104012050961945999299387385257511527617173493890563996370828253311851839652350107698683154277376*t^60 + 18744843200174420553262471383988644524861169551125259804748638778879246454780275882357301211687550762695/253200002725030544294475358178535562062739341960929621832052911312151328327037612174494358562558976*t^58 - 380234717414331598336453805399448311543032332688480361021780787970088777907384369598620193171606330553462985/1110788411954708997819863396329235510769237493182598250977216121926407877370714004609506751013946227712*t^56 + 203400354189043679480195403609084682961591865114656060083275993369472070474598589431254652670008508065479725/180826020550766581040442878472201129660108429122748552484663089615926863758023210052710401327851711488*t^54 - 2238836951736962950829275008222194193702929960323888236757725420324282101966551481587802034846353478854499528741/800878445019345187428121508753378803264620232584653338954572823908940079584284797323454367481055230180352*t^52 + 310458889448039111980038018202698211487883247625603682182338593851724760068884698822353470623252142628296447553275431/56864772231708566342958911486016155168197830374208141025791534216006472470722973464357230454257364508495533056*t^50 - 628423706153041800858318843787493981507795609254421542320323217462765446833142512496809734251314088444821783603929725/73111850012196728155232886196306485216254353338267609890303401134865464605215251597030724869759468653779971072*t^48 + 26247164528293209249628474356934771716431664834566505687525384343180330542473050910825452554617429940411618154835184475/2363949817061027543685863320347243021992224091270652719786476636693983355568626468303993437455556153138885731328*t^46 - 178407604304891372098210872742345927473533355290890489442537863796730073949073366172661411903470926339616556195005343375/14971682174719841110010467695532539139284085911380800558647685365728561251934634299258625103885188969879609631744*t^44 + 11198255511676884298903070607760419940546583453786091128848682383432109424113644538155005093513230547255970674495488375/1044535965678128449535614025269712032973308319398660504091698979004318226879160532506415704922222486270670439424*t^42 - 898135857332424416815622220194230933161485002277040672738152360346462921959412478403114176522829479019117178437759125/110398110193623332064739693727693141696365919936443793115382818919155584954708023760840684260072295296900127744*t^40 + 3951469545299855059678482163873494651283678741290226530229884351476266648684332240017992355674460928655726089179394625/755802446710190504135525595520360739305889759564884429789928529523449773920693393439601607626648790878777797632*t^38 - 9197653896756530586469276189313670379321310655466976898371832524748623801630622718171423966549616392349933167987625/3225330498052022066012200265378495331319586456180161151308372103229515393687169531036706718179155579852536832*t^36 + 1420266995495880152209975579031301120639036847462499842556816622739060827822540171651742976541710394728169382471875/1075110166017340688670733421792831777106528818726720383769457367743171797895723177012235572726385193284178944*t^34 - 46341179936631012135232447515126864942431276776463049763613294919898335379640654762104973413686932478951296575063405/89234143779439277159670874008805037499841891954317791852864961522683259225345023692015552536289971042586852352*t^32 + 1249393690836034287189660201439663433319209455002356968910317287146017150422202429973568268235734340674775479807071835/7227965646134581449933340794713208037487193248299741140082061883337343997252946919053259755439487654449535040512*t^30 - 9237826219827055585240656085114968299111474057351855230692982453476136756247723698729250928872052313247924447048565275/190336428681543978181577974260781144987162755538559850022160962927883391927660935535069173559906508233837756066816*t^28 + 2218670002332933159535035663757768559406978155772510574794838728753470799354779461356925272656701312297003760990975/194022863080065217310477037982447650343692921038287308891091705329136994829419913899153082120190120523789761536*t^26 - 142432842762221185887031632839132929338549410583671982595566818017960502792396879269761828601560899788182048543492125/63445476227181326060525991420260381662387585179519950007386987642627797309220311845023057853302169411279252022272*t^24 + 7696693505960315733766807635143924938117264054944553901504894333494131215948684416596657125449665507609113291555855/21148492075727108686841997140086793887462528393173316669128995880875932436406770615007685951100723137093084007424*t^22 - 1018519133840052953475161381591697055822995997143187763184018013346245911823446608564239176358177261899034005700435/21148492075727108686841997140086793887462528393173316669128995880875932436406770615007685951100723137093084007424*t^20 + 17120937868899530724515811275068412626657712308562941531215869339201725524686470754693888043770642093905633302275/3339235590904280318975052180013704298020399219974734210915104612769884068906332202369634623858008916383118527488*t^18 - 760839290274712387595162954779780847479093335054544479771574264184920414819598115918376642575881868122014386418675/1764971522881295719707147024480576816187004343268867849035905849216259835087491365185816878410283157248277203917824*t^16 + 140439871122533026323491417174598779032161060005180999580361426084037461122177620117297033462818040488247874568065625/5024873925643048914006247578696202195684401365286466766205223952718691750494087916684020652834076148685845199554044928*t^14 - 89517100197778694994951620163537589442164564246299029935746081021004212368110262211702712735027235955084163994355667/66096418560381643407312948919773121189387125651075832078545638147299714564191464134843656279586693955790733009518590976*t^12 + 9504321768324175944732507802377486300904906793887901478130897066423226419961587024503817900485887178934833299237/202129720368139582285360700060468260518003442358030067518488190052904325884377566161601395350418024329635269142258688*t^10 - 2697776055562137258506309806906467624257604962295480163859007386761607709285479507845886252721493551238842266045/2448015502236357163233812922954560044051375024113919706612801412862952391266350523512728010355062739103360481834021888*t^8 + 741691658912358955965706317027924388615313850381508861699563882122422727390454398338727304006878862109876608295/46512294542490786101442445536136640836976125458164474425643226844396095434060659946741832196746192042963849154846415872*t^6 - 5717071653660356375828205165923089491046152349822839321157467337116289426267140872518910853629182512334645675/46512294542490786101442445536136640836976125458164474425643226844396095434060659946741832196746192042963849154846415872*t^4 + 52698045979638038175011968574138691236910103716530006744476195638156678399487618261043090474687193770934241/139536883627472358304327336608409922510928376374493423276929680533188286302181979840225496590238576128891547464539247616*t^2 - 80855481908007529481592835637333792115006555410485239763941429431472523750811428759909886160796073598431/418610650882417074912982009825229767532785129123480269830789041599564858906545939520676489770715728386674642393617742848
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (0.95742974176544047958 - 2.3548540097075186278e-860j)  +/-  (1.37e-233, 1.37e-233j)
| (-0.9992229685946246751 - 7.328024186929470965e-858j)  +/-  (3.31e-234, 3.31e-234j)
| (-0.90411725637047485668 + 1.6405335449461816565e-874j)  +/-  (2.26e-234, 2.26e-234j)
| (-0.99000623484745041642 - 1.7322985377762848947e-879j)  +/-  (1.56e-233, 1.56e-233j)
| (0.92415348393158124411 + 1.460924582942221763e-889j)  +/-  (4.77e-234, 4.77e-234j)
| (0.83017715024575492263 + 4.6701324765865965576e-892j)  +/-  (1e-235, 1e-235j)
| (0.99591578523499621313 + 3.0903406041325036834e-888j)  +/-  (1.02e-233, 1.02e-233j)
| (-0.94191613896694414839 - 1.7382542547380652228e-889j)  +/-  (8.67e-234, 8.67e-234j)
| (-0.075276995526422139819 - 3.3772016388727321825e-911j)  +/-  (1.01e-253, 1.01e-253j)
| (0.9992229685946246751 - 9.3476403775204739352e-890j)  +/-  (3.33e-234, 3.33e-234j)
| (0.85710843813524379791 + 2.7597092206302266913e-893j)  +/-  (3.12e-235, 3.12e-235j)
| (0.94191613896694414839 - 1.242519846846734596e-891j)  +/-  (8.59e-234, 8.59e-234j)
| (-0.85710843813524379791 - 1.3374016103766304326e-891j)  +/-  (3.07e-235, 3.07e-235j)
| (-0.83017715024575492263 - 1.8697470944631534865e-892j)  +/-  (9.5e-236, 9.5e-236j)
| (-0.97066946906233475059 + 2.7720205535003116279e-890j)  +/-  (1.7e-233, 1.7e-233j)
| (0.88177060063618075242 + 1.7453916958966618104e-897j)  +/-  (9.3e-235, 9.3e-235j)
| (0.70191246925677183574 + 3.6523093111538441848e-901j)  +/-  (2.41e-238, 2.41e-238j)
| (-0.95742974176544047958 + 1.0194879638594274911e-894j)  +/-  (1.29e-233, 1.29e-233j)
| (-0.80106853104629246937 - 1.0673751329602368722e-902j)  +/-  (2.78e-236, 2.78e-236j)
| (-0.88177060063618075242 - 9.6628545468598274027e-901j)  +/-  (9.39e-235, 9.39e-235j)
| (0.99000623484745041642 - 3.2401893610741516332e-901j)  +/-  (1.63e-233, 1.63e-233j)
| (0.76990267419430468704 - 3.5865394485271684455e-908j)  +/-  (6.45e-237, 6.45e-237j)
| (0.98156063424671925069 + 6.1598069625157518306e-903j)  +/-  (1.85e-233, 1.85e-233j)
| (-0.73680958027190251296 - 7.7819834456317536863e-909j)  +/-  (1.34e-237, 1.34e-237j)
| (-0.76990267419430468704 + 2.4191369864626343997e-907j)  +/-  (6.19e-237, 6.19e-237j)
| (0.80106853104629246937 + 1.6454811713091122895e-907j)  +/-  (2.73e-236, 2.73e-236j)
| (0.73680958027190251296 - 9.1537834926807518157e-909j)  +/-  (1.39e-237, 1.39e-237j)
| (0.90411725637047485668 - 2.48022338165015035e-906j)  +/-  (2.34e-234, 2.34e-234j)
| (-0.2726739322774404677 - 4.1086072458271905535e-920j)  +/-  (1.67e-248, 1.67e-248j)
| (-0.66531494353729954402 + 3.0976290130905762231e-909j)  +/-  (4.35e-239, 4.35e-239j)
| (0.97066946906233475059 + 1.2707789306736603523e-904j)  +/-  (1.77e-233, 1.77e-233j)
| (-0.12523340851146891547 + 5.9007356536000361104e-923j)  +/-  (2.48e-252, 2.48e-252j)
| (0.6270962110223330682 - 8.7304111566498568988e-912j)  +/-  (6.11e-240, 6.11e-240j)
| (-0.92415348393158124411 - 5.6453238593887177607e-903j)  +/-  (4.87e-234, 4.87e-234j)
| (-0.6270962110223330682 - 3.86059744005703647e-927j)  +/-  (5.92e-240, 5.92e-240j)
| (-0.70191246925677183574 + 3.6808492273990638623e-922j)  +/-  (2.63e-238, 2.63e-238j)
| (0.32064375870299714099 + 5.2203908438747804084e-936j)  +/-  (2.62e-247, 2.62e-247j)
| (0.54604066989677421514 + 3.016282114286684447e-930j)  +/-  (8.66e-242, 8.66e-242j)
| (0.45932024898159586096 - 1.8202711837035945271e-932j)  +/-  (7.52e-244, 7.52e-244j)
| (-0.99591578523499621313 - 2.8827864920347317913e-925j)  +/-  (9.75e-234, 9.75e-234j)
| (-0.5873179542866174473 - 2.0700668886487431455e-960j)  +/-  (8.35e-241, 8.35e-241j)
| (-0.22404254032991898992 - 2.2022993413496547881e-963j)  +/-  (8.13e-250, 8.13e-250j)
| (0.66531494353729954402 + 7.5481555556756378616e-961j)  +/-  (3.95e-239, 3.95e-239j)
| (0.5873179542866174473 + 1.2639855853197449841e-964j)  +/-  (8.26e-241, 8.26e-241j)
| (-0.98156063424671925069 - 5.2906577433175906796e-971j)  +/-  (1.87e-233, 1.87e-233j)
| (-0.54604066989677421514 + 7.7756956223072741552e-997j)  +/-  (8.15e-242, 8.15e-242j)
| (-0.45932024898159586096 - 9.0079421792713502231e-1000j)  +/-  (8.13e-244, 8.13e-244j)
| (0.22404254032991898992 + 1.2392919188999260431e-1008j)  +/-  (8.19e-250, 8.19e-250j)
| (0.50334086420919863503 - 2.8313630250979425993e-1002j)  +/-  (8.85e-243, 8.85e-243j)
| (0.17485982960777582944 + 1.4667069375797292869e-1008j)  +/-  (4.26e-251, 4.26e-251j)
| (-0.4141040490347055521 - 6.6619679557666219929e-1001j)  +/-  (6.12e-245, 6.12e-245j)
| (-0.50334086420919863503 - 2.0968858726320043933e-1000j)  +/-  (8.66e-243, 8.66e-243j)
| (-0.025115568760553902467 + 3.1642438949105441998e-1013j)  +/-  (5.78e-255, 5.78e-255j)
| (0.4141040490347055521 + 3.3181246344037088222e-1004j)  +/-  (5.84e-245, 5.84e-245j)
| (0.2726739322774404677 + 2.8261962781777608922e-1007j)  +/-  (1.62e-248, 1.62e-248j)
| (0.025115568760553902467 - 2.8408666894203455902e-1013j)  +/-  (5.78e-255, 5.78e-255j)
| (-0.36783149899818019375 - 1.2494716047464099857e-1004j)  +/-  (4.3e-246, 4.3e-246j)
| (-0.32064375870299714099 - 4.6140305086947635889e-1005j)  +/-  (2.71e-247, 2.71e-247j)
| (0.075276995526422139819 + 4.9518107788988696465e-1012j)  +/-  (1.03e-253, 1.03e-253j)
| (0.36783149899818019375 - 1.6554489934823135853e-1005j)  +/-  (4.46e-246, 4.46e-246j)
| (0.12523340851146891547 - 1.9723802474539541152e-1011j)  +/-  (2.23e-252, 2.23e-252j)
| (-0.17485982960777582944 + 1.7043246638893161462e-1008j)  +/-  (4.86e-251, 4.86e-251j)
-------------------------------------------------
The weights are:
| (0.01438560440989446921 - 1.8712680427558240476e-859j)  +/-  (8.2e-46, 1.55e-156j)
| (0.0019929817046115911684 - 9.5169098322618748052e-858j)  +/-  (3.26e-46, 6.17e-157j)
| (0.021186758393382816074 - 7.7589198272071616139e-858j)  +/-  (1.09e-46, 2.07e-157j)
| (0.0071910556611521827694 - 1.1600337678753359189e-857j)  +/-  (2.16e-46, 4.09e-157j)
| (0.01889266696168861685 - 3.0507160959480784518e-859j)  +/-  (1.08e-46, 2.04e-157j)
| (0.0280382390804520951 - 5.7297200095502007557e-859j)  +/-  (4.4e-47, 8.34e-158j)
| (0.0046168016003319291784 - 2.7454959419763918353e-860j)  +/-  (3.36e-48, 6.36e-159j)
| (0.01663743843469873533 - 8.653091666914637481e-858j)  +/-  (1.67e-48, 3.15e-159j)
| (0.050080745907742261904 + 2.7877081885667144761e-858j)  +/-  (1.17e-49, 2.22e-160j)
| (0.0019929817046115911684 + 7.6223851829043553571e-861j)  +/-  (2.36e-48, 4.47e-159j)
| (0.025808729969854020831 + 5.0642449395860245245e-859j)  +/-  (2.01e-48, 3.8e-159j)
| (0.01663743843469873533 + 2.2670696671728673125e-859j)  +/-  (7.81e-48, 1.48e-158j)
| (0.025808729969854020831 - 6.7265448203578602112e-858j)  +/-  (2.94e-50, 5.57e-161j)
| (0.0280382390804520951 + 6.2813729599055050332e-858j)  +/-  (1.27e-50, 2.4e-161j)
| (0.012080862917818652144 - 9.42606978670098678e-858j)  +/-  (1.02e-50, 1.94e-161j)
| (0.023507719233785453826 - 4.4159157404487668414e-859j)  +/-  (1.49e-50, 2.83e-161j)
| (0.035762530001167668305 - 9.010305440630224573e-859j)  +/-  (2.25e-53, 4.25e-164j)
| (0.01438560440989446921 + 9.0091284244054057654e-858j)  +/-  (1.54e-50, 2.92e-161j)
| (0.030158673161763072366 - 5.9148943833247631642e-858j)  +/-  (2.3e-52, 4.36e-163j)
| (0.023507719233785453826 + 7.2334553450717260116e-858j)  +/-  (4.95e-51, 9.37e-162j)
| (0.0071910556611521827694 + 5.6701136636177592246e-860j)  +/-  (7e-52, 1.32e-162j)
| (0.032151091826414731991 - 7.2271752596498598712e-859j)  +/-  (5.44e-54, 1.03e-164j)
| (0.0096847910055074310175 - 9.6973694818662636414e-860j)  +/-  (3.52e-52, 6.67e-163j)
| (0.034014334117712598191 - 5.3870408639327019304e-858j)  +/-  (2.23e-55, 4.22e-166j)
| (0.032151091826414731991 + 5.6225689128046492986e-858j)  +/-  (1.54e-54, 2.92e-165j)
| (0.030158673161763072366 + 6.4436177980597696815e-859j)  +/-  (9.85e-54, 1.87e-164j)
| (0.034014334117712598191 + 8.0863653686246361812e-859j)  +/-  (5.59e-55, 1.06e-165j)
| (0.021186758393382816074 + 3.7526036081540824455e-859j)  +/-  (5.93e-53, 1.12e-163j)
| (0.048319651608891292029 + 3.3527000201651169892e-858j)  +/-  (2.21e-60, 4.19e-171j)
| (0.037419439208695250635 - 4.9969462604428109575e-858j)  +/-  (2.41e-58, 4.57e-169j)
| (0.012080862917818652144 + 1.5492217756185274951e-859j)  +/-  (5.36e-53, 1.01e-163j)
| (0.04981123239138774302 - 2.9266845465483958434e-858j)  +/-  (1.35e-60, 2.56e-171j)
| (0.039008041397083340799 - 1.094917641105143272e-858j)  +/-  (1.97e-58, 3.73e-169j)
| (0.01889266696168861685 + 8.2447957039320858777e-858j)  +/-  (4.85e-56, 9.17e-167j)
| (0.039008041397083340799 + 4.8054328783389340338e-858j)  +/-  (2.24e-59, 4.25e-170j)
| (0.035762530001167668305 + 5.1856990689286987751e-858j)  +/-  (7.34e-58, 1.39e-168j)
| (0.047599956542519114145 + 1.7964060881219044799e-858j)  +/-  (1.75e-62, 3.32e-173j)
| (0.042003277440422807285 - 1.2860223155115002985e-858j)  +/-  (6.19e-61, 1.17e-171j)
| (0.044640843282769077966 - 1.4769178407469954946e-858j)  +/-  (5.15e-62, 9.74e-173j)
| (0.0046168016003319291784 + 1.5824768696172754379e-857j)  +/-  (3.12e-59, 5.9e-170j)
| (0.040538700078927386708 - 4.6051220551083309107e-858j)  +/-  (1.73e-61, 3.27e-172j)
| (0.048924896132825877097 - 3.2097830218573249796e-858j)  +/-  (1.47e-63, 2.78e-174j)
| (0.037419439208695250635 + 9.9743830448659408484e-859j)  +/-  (1.17e-59, 2.22e-170j)
| (0.040538700078927386708 + 1.1912775970285424231e-858j)  +/-  (9.37e-61, 1.77e-171j)
| (0.0096847910055074310175 + 1.0127334157595009579e-857j)  +/-  (1.9e-59, 3.6e-170j)
| (0.042003277440422807285 + 4.3987625368734663005e-858j)  +/-  (5.74e-63, 1.09e-173j)
| (0.044640843282769077966 + 3.9990499715413993777e-858j)  +/-  (1.97e-64, 3.72e-175j)
| (0.048924896132825877097 + 2.0321790355350533354e-858j)  +/-  (1.12e-66, 2.13e-177j)
| (0.043379344457527532793 + 1.3804515350498810177e-858j)  +/-  (4.26e-64, 8.07e-175j)
| (0.049422748895760871611 - 2.1525321416646301851e-858j)  +/-  (4.73e-67, 8.95e-178j)
| (0.045768138153613842062 - 3.8184046559555621765e-858j)  +/-  (3.85e-66, 7.28e-177j)
| (0.043379344457527532793 - 4.1940909701178936945e-858j)  +/-  (4.78e-65, 9.05e-176j)
| (0.050219445273133016945 - 2.6526003036163375186e-858j)  +/-  (4.07e-68, 7.71e-179j)
| (0.045768138153613842062 + 1.5777295928729442771e-858j)  +/-  (7.26e-67, 1.37e-177j)
| (0.048319651608891292029 - 1.912987761358618612e-858j)  +/-  (1.51e-67, 2.85e-178j)
| (0.050219445273133016945 + 2.5222793437133161403e-858j)  +/-  (1.2e-68, 2.27e-179j)
| (0.04675326074846452065 + 3.6526733201499789974e-858j)  +/-  (3.77e-68, 7.12e-179j)
| (0.047599956542519114145 - 3.4989454499879303547e-858j)  +/-  (2.11e-68, 3.99e-179j)
| (0.050080745907742261904 - 2.3964094050479283994e-858j)  +/-  (1.2e-69, 2.29e-180j)
| (0.04675326074846452065 - 1.6842362627664346671e-858j)  +/-  (1.73e-69, 3.26e-180j)
| (0.04981123239138774302 + 2.2736667418717329752e-858j)  +/-  (8.7e-70, 1.66e-180j)
| (0.049422748895760871611 + 3.0678339437538182082e-858j)  +/-  (7.12e-70, 1.27e-180j)
