Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 51
-------------------------------------------------
Trying to find an order 51 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^55 - 18382225325370997463750235915086428596837378/1638769036930719812305100920195870680311*t^53 + 280546374192707494320492583177371059543531973054/77022144735743831178339743249205921974617*t^51 - 112181796988658283776776485689443088587415752906425/154044289471487662356679486498411843949234*t^49 + 7742782489315119499774373269800136236747000019938900/77022144735743831178339743249205921974617*t^47 - 66753623081276346979498684393308292572703540280463675/6555076147722879249220403680783482721244*t^45 + 5149435802153154124352817870923009062153076073528162525/6555076147722879249220403680783482721244*t^43 - 1239317861634305486558009862598510270028767354206265103025/26220304590891516996881614723133930884976*t^41 + 59098483492718788410283375216900301173728071874605425401375/26220304590891516996881614723133930884976*t^39 - 1389248185028250086072551503886305732990700510186338355221375/16135572055933241228850224445005495929216*t^37 + 42800739749777854448495006643825952784858718842794559677549875/16135572055933241228850224445005495929216*t^35 - 4270131765906186371200463111926680140160453693007352810492246625/64542288223732964915400897780021983716864*t^33 + 168622832798092484489394950857907931502233729365703494920892625/126059156686978447100392378476605436947*t^31 - 1413631033966456457988948486478635747755163044887890217439836393125/64542288223732964915400897780021983716864*t^29 + 18687988442114136753568938971310569032982181877658791691942165799375/64542288223732964915400897780021983716864*t^27 - 793726915573986055286015115195341037617289552941320007531656780884375/258169152894931859661603591120087934867456*t^25 + 13437697295601950963405001692595401982146699352404774448768060764915625/516338305789863719323207182240175869734912*t^23 - 718202276273469634647823504759869204105431670913740622583274807368221875/4130706446318909754585657457921406957879296*t^21 + 3737600356108367425899747691375342954047741997467155180264832881148796875/4130706446318909754585657457921406957879296*t^19 - 59590214829042041929899352502861921085538166418723456145633772253982453125/16522825785275639018342629831685627831517184*t^17 + 22249372313045153482381588823993991821870371656526870481383783280269640625/2065353223159454877292828728960703478939648*t^15 - 774529430253434711786246474794175987200607162653277679499770470310783609375/33045651570551278036685259663371255663034368*t^13 + 1181872424829791671862194207455643747992250136977335730597828649049551390625/33045651570551278036685259663371255663034368*t^11 - 4802751632057571412267230153605331327638097998750562536726575593071597578125/132182606282205112146741038653485022652137472*t^9 + 3013213086442204712942375697497926378490367829195342546933875112375796015625/132182606282205112146741038653485022652137472*t^7 - 8308517580061238040162375517640377707954179802957298552906554062889165515625/1057460850257640897173928309227880181217099776*t^5 + 1279865181082955879411807597928359648909161278352742380418686836626903578125/1057460850257640897173928309227880181217099776*t^3 - 220715386972487411701857022151893591061880873484069933055968924798926234375/4229843401030563588695713236911520724868399104*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 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:
| (7.8411058049485859777 - 1.0745597021686831938e-561j)  +/-  (3.26e-243, 3.26e-243j)
| (-7.8411058049485859777 + 5.0950371655562866533e-570j)  +/-  (3.1e-243, 3.1e-243j)
| (-8.3227820549388846134 + 6.9676570965640921411e-573j)  +/-  (7.48e-244, 7.48e-244j)
| (-7.3964109583449798818 - 1.3162608648959428446e-573j)  +/-  (9.08e-243, 9.08e-243j)
| (5.8281256586015434508 + 7.5730098561518449647e-587j)  +/-  (3.84e-242, 3.84e-242j)
| (2.5448433749455704512 - 3.3993701135429282346e-606j)  +/-  (4.16e-246, 4.16e-246j)
| (8.8620076658364700778 - 1.1820544012229060366e-613j)  +/-  (1.02e-244, 1.02e-244j)
| (-8.8620076658364700778 + 9.9807828033925134557e-631j)  +/-  (1.04e-244, 1.04e-244j)
| (6.978113903801950225 + 1.2442003484403979013e-648j)  +/-  (1.89e-242, 1.89e-242j)
| (4.4439979332110594479 + 3.1744017642294106173e-664j)  +/-  (7.04e-243, 7.04e-243j)
| (2.2429174439526855827 - 1.3712681758540818931e-677j)  +/-  (7.26e-247, 7.26e-247j)
| (-5.4695405268667318603 + 5.9527406641658685044e-672j)  +/-  (3.37e-242, 3.37e-242j)
| (9.5127201332951925762 - 1.6581360750437276125e-671j)  +/-  (5.96e-246, 5.96e-246j)
| (-1.6506801238857845559 + 2.4620988667452964981e-690j)  +/-  (1.56e-248, 1.56e-248j)
| (7.3964109583449798818 - 2.0149875862510629382e-689j)  +/-  (9.1e-243, 9.1e-243j)
| (3.1602414929523661266 - 9.4914847722194914467e-705j)  +/-  (8.76e-245, 8.76e-245j)
| (8.3227820549388846134 + 5.6868269789333023597e-708j)  +/-  (7.27e-244, 7.27e-244j)
| (-6.5798743494391913873 - 4.3080614106795751494e-712j)  +/-  (2.98e-242, 2.98e-242j)
| (-3.1602414929523661266 + 1.6900401344750293475e-717j)  +/-  (9.23e-245, 9.23e-245j)
| (6.5798743494391913873 - 1.0236390243860235715e-712j)  +/-  (3.17e-242, 3.17e-242j)
| (-4.7786209889860115121 - 7.8489487806792941486e-723j)  +/-  (1.43e-242, 1.43e-242j)
| (6.1975203860999324381 + 2.188352155518794889e-722j)  +/-  (4.49e-242, 4.49e-242j)
| (-9.5127201332951925762 - 6.3566188550709218807e-729j)  +/-  (5.97e-246, 5.97e-246j)
| (-6.978113903801950225 - 2.5153709933804065058e-724j)  +/-  (2.02e-242, 2.02e-242j)
| (-0.79687268562023448528 - 3.2771267057753851527e-734j)  +/-  (1.56e-251, 1.56e-251j)
| (-6.1975203860999324381 - 3.8498492198095164184e-724j)  +/-  (4.03e-242, 4.03e-242j)
| (1.3608673402817939877 + 7.2592282048648165488e-732j)  +/-  (1.76e-249, 1.76e-249j)
| (1.9448114122774450265 + 3.8165580862048489517e-730j)  +/-  (1.13e-247, 1.13e-247j)
| (1.6506801238857845559 + 8.8937760394404442431e-731j)  +/-  (1.58e-248, 1.58e-248j)
| (-1.0759668286888116161 - 7.658735991919806049e-733j)  +/-  (1.71e-250, 1.71e-250j)
| (-5.8281256586015434508 - 1.3962650822259295181e-724j)  +/-  (4.21e-242, 4.21e-242j)
| (-1.3608673402817939877 - 5.6115750136656900856e-732j)  +/-  (1.76e-249, 1.76e-249j)
| (4.7786209889860115121 + 2.2452874890551905388e-723j)  +/-  (1.42e-242, 1.42e-242j)
| (3.4740434280320073272 + 1.2753285149014338011e-731j)  +/-  (3.48e-244, 3.48e-244j)
| (-3.7923047588769127227 - 3.9712705746231473119e-731j)  +/-  (1.24e-243, 1.24e-243j)
| (-2.2429174439526855827 - 7.1911542535678216991e-735j)  +/-  (7.27e-247, 7.27e-247j)
| (5.1201306514911900994 - 5.1538398456257437722e-729j)  +/-  (2.36e-242, 2.36e-242j)
| (0.79687268562023448528 - 2.2825937918329182732e-747j)  +/-  (1.56e-251, 1.56e-251j)
| (4.1154457829447910372 - 1.1776463157528970055e-739j)  +/-  (3.26e-243, 3.26e-243j)
| (-2.5448433749455704512 + 5.0438549745758279615e-744j)  +/-  (4.36e-246, 4.36e-246j)
| (-0.52464762327529031788 - 1.3124770354123801762e-751j)  +/-  (1.09e-252, 1.09e-252j)
| (-2.8505807611530028098 + 3.1794470658830665413e-743j)  +/-  (2.32e-245, 2.32e-245j)
| (1.0759668286888116161 - 8.4373141062630582591e-749j)  +/-  (1.78e-250, 1.78e-250j)
| (-1.9448114122774450265 + 4.8407927289648958404e-746j)  +/-  (1.15e-247, 1.15e-247j)
| (5.4695405268667318603 + 4.680989493390386017e-740j)  +/-  (3.52e-242, 3.52e-242j)
| (-3.4740434280320073272 + 1.0378175723725243552e-750j)  +/-  (3.34e-244, 3.34e-244j)
| (-4.1154457829447910372 + 3.8319991254461910604e-749j)  +/-  (3.32e-243, 3.32e-243j)
| (3.7923047588769127227 + 1.7420850845683639539e-749j)  +/-  (1.15e-243, 1.15e-243j)
| (0.52464762327529031788 - 3.1878940713635069556e-759j)  +/-  (1.25e-252, 1.25e-252j)
| (-5.1201306514911900994 - 4.5495830869474959219e-748j)  +/-  (2.48e-242, 2.48e-242j)
| (-4.4439979332110594479 - 4.3612835268687415737e-757j)  +/-  (7.05e-243, 7.05e-243j)
| (1.3349765350104091206e-784 - 2.5748709072305366862e-784j)  +/-  (1.6e-782, 1.6e-782j)
| (-0.25970753112300069693 - 2.4290891835123746936e-767j)  +/-  (9.69e-254, 9.69e-254j)
| (0.25970753112300069693 + 3.9100107293460201299e-767j)  +/-  (9.69e-254, 9.69e-254j)
| (2.8505807611530028098 + 1.0465241773129592494e-761j)  +/-  (2.15e-245, 2.15e-245j)
-------------------------------------------------
The weights are:
| (5.1679791707848623859e-28 + 4.4908677670536568584e-588j)  +/-  (1.99e-70, 2.94e-191j)
| (5.1679791707848623859e-28 + 3.5411494436144709251e-590j)  +/-  (9.88e-71, 1.46e-191j)
| (2.3563702597871332709e-31 - 6.5384590043405373588e-592j)  +/-  (2.14e-72, 3.17e-193j)
| (4.2284251423534780272e-25 - 1.1663199362067945901e-588j)  +/-  (1.04e-69, 1.54e-190j)
| (3.6344941673094908271e-16 - 4.0679630381248951335e-583j)  +/-  (1.5e-66, 2.23e-187j)
| (0.00026390939093280138295 - 5.5037549586938899907e-577j)  +/-  (2.27e-49, 3.36e-170j)
| (2.5569268492224240251e-35 - 9.5483050086831633444e-593j)  +/-  (4.24e-76, 6.28e-197j)
| (2.5569268492224240251e-35 + 5.8359668165725651634e-594j)  +/-  (1.41e-75, 2.09e-196j)
| (1.63649770516564983e-22 + 4.5287448654096208071e-586j)  +/-  (7.91e-71, 1.17e-191j)
| (4.9537141027212688695e-10 - 4.6309312506453717808e-580j)  +/-  (9.01e-63, 1.33e-183j)
| (0.001106092811178334554 + 1.2844799006835147951e-576j)  +/-  (6.77e-50, 1e-170j)
| (2.0315794925915575742e-14 + 5.1779989348344443276e-583j)  +/-  (1.78e-68, 2.64e-189j)
| (2.1242008979154163023e-40 + 1.464317824264514765e-595j)  +/-  (1.24e-78, 1.84e-199j)
| (0.010802827483325837587 + 3.54787534716807128e-576j)  +/-  (3.22e-48, 4.77e-169j)
| (4.2284251423534780272e-25 - 3.996407146447531262e-587j)  +/-  (3.01e-72, 4.45e-193j)
| (8.087035693122302921e-06 - 7.734594683749451445e-578j)  +/-  (9.3e-59, 1.38e-179j)
| (2.3563702597871332709e-31 + 2.1941487666452752214e-590j)  +/-  (5.61e-75, 8.3e-196j)
| (3.4634968105756981277e-20 - 4.4093504331077459053e-586j)  +/-  (7.81e-74, 1.16e-194j)
| (8.087035693122302921e-06 - 3.290923154719263466e-578j)  +/-  (6.16e-63, 9.12e-184j)
| (3.4634968105756981277e-20 - 5.0416718799650038815e-585j)  +/-  (5.61e-71, 8.31e-192j)
| (2.3068741671991718083e-11 + 2.3592756324503966608e-581j)  +/-  (9.61e-70, 1.42e-190j)
| (4.4163390840273052538e-18 + 4.892808358045587725e-584j)  +/-  (2.5e-70, 3.71e-191j)
| (2.1242008979154163023e-40 - 1.4105100195300580224e-596j)  +/-  (1.07e-82, 1.59e-203j)
| (1.63649770516564983e-22 + 2.6372984134635297224e-587j)  +/-  (4.35e-75, 6.44e-196j)
| (0.08246779985803168488 - 2.0820086711989281353e-575j)  +/-  (2.23e-55, 3.3e-176j)
| (4.4163390840273052538e-18 + 5.7283018218442351293e-585j)  +/-  (9.7e-74, 1.44e-194j)
| (0.025452857441524140212 - 9.9069475497615606808e-576j)  +/-  (1.27e-55, 1.87e-176j)
| (0.0038047044037198630931 - 2.7543918657062334908e-576j)  +/-  (2.31e-59, 3.43e-180j)
| (0.010802827483325837587 + 5.4399608186588739741e-576j)  +/-  (7.19e-58, 1.07e-178j)
| (0.050021063071589869888 + 1.2607360806657820432e-575j)  +/-  (9.5e-56, 1.41e-176j)
| (3.6344941673094908271e-16 - 5.9906287444049373764e-584j)  +/-  (1.7e-73, 2.51e-194j)
| (0.025452857441524140212 - 6.9766974740775361405e-576j)  +/-  (3.78e-58, 5.59e-179j)
| (2.3068741671991718083e-11 + 9.7219790956046411876e-581j)  +/-  (2.12e-71, 3.14e-192j)
| (1.0223058583117620957e-06 + 2.5164306266446782111e-578j)  +/-  (5.44e-68, 8.05e-189j)
| (1.0270224795096818556e-07 - 2.5763587196200306656e-579j)  +/-  (2.91e-71, 4.31e-192j)
| (0.001106092811178334554 + 7.1308447980018126718e-577j)  +/-  (4.45e-66, 6.59e-187j)
| (8.0211315907274814488e-13 - 1.7982502487998797772e-581j)  +/-  (1.18e-72, 1.75e-193j)
| (0.08246779985803168488 - 2.5530594713524837969e-575j)  +/-  (8.12e-62, 1.2e-182j)
| (8.1041464419636617817e-09 + 1.9583639973231649477e-579j)  +/-  (3.32e-70, 4.91e-191j)
| (0.00026390939093280138295 - 2.8066121168893280001e-577j)  +/-  (4.29e-68, 6.35e-189j)
| (0.1150418971539559788 + 3.0994349906763615096e-575j)  +/-  (1.17e-62, 1.73e-183j)
| (5.1347258120871911598e-05 + 1.0081867400487400607e-577j)  +/-  (3.09e-69, 4.57e-190j)
| (0.050021063071589869888 + 1.6617655915954724279e-575j)  +/-  (1.95e-63, 2.89e-184j)
| (0.0038047044037198630931 - 1.6595997119605473215e-576j)  +/-  (1.6e-66, 2.37e-187j)
| (2.0315794925915575742e-14 + 2.9062033996982718497e-582j)  +/-  (1.13e-74, 1.67e-195j)
| (1.0223058583117620957e-06 + 9.7121208065546871541e-579j)  +/-  (1.3e-71, 1.93e-192j)
| (8.1041464419636617817e-09 + 6.1022599206163484753e-580j)  +/-  (6.13e-74, 9.08e-195j)
| (1.0270224795096818556e-07 - 7.4026453862339878628e-579j)  +/-  (5.2e-73, 7.73e-194j)
| (0.1150418971539559788 + 3.5439427413754142735e-575j)  +/-  (1.23e-68, 1.8e-189j)
| (8.0211315907274814488e-13 - 3.7750984403427198931e-582j)  +/-  (1.29e-76, 1.92e-197j)
| (4.9537141027212688695e-10 - 1.2805568102126657866e-580j)  +/-  (4.85e-75, 7.18e-196j)
| (0.14594142450756708733 + 4.5604048433351825232e-575j)  +/-  (9.76e-70, 1.38e-190j)
| (0.13800756820662829823 - 4.0610076934724763466e-575j)  +/-  (1.02e-69, 1.51e-190j)
| (0.13800756820662829823 - 4.339234541194232957e-575j)  +/-  (6.54e-70, 8.59e-191j)
| (5.1347258120871911598e-05 + 2.1599363681851222699e-577j)  +/-  (7.38e-73, 1.35e-193j)
