Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 55
-------------------------------------------------
Trying to find an order 55 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^59 - 3588231906837371995087661661886888218242921499288/265026570181444926006858105793526490839484691*t^57 + 24042724728529783025348077844128977344454803629453104/4505451693084563742116587798489950344271239747*t^55 - 5870160846137938739484163868701379617832725337035152840/4505451693084563742116587798489950344271239747*t^53 + 76620195192451437700330398377408924777837099422122215655/346573207160351057085891369114611564943941519*t^51 - 1130502035249904081228698011971560994054479066573356417575/40773318489453065539516631660542537052228414*t^49 + 54404297722706330710541480213948347744046072436555002584800/20386659244726532769758315830271268526114207*t^47 - 4118991241893894693693522744304589207148936262080814267882950/20386659244726532769758315830271268526114207*t^45 + 3991542598604251768589313680274933611984411118231481252256899875/326186547915624524316133053284340296417827312*t^43 - 391300492230270233690637013276949052319767671386497733792514227875/652373095831249048632266106568680592835654624*t^41 + 7822524368649155312347657343327273206811031682928244826379099517375/326186547915624524316133053284340296417827312*t^39 - 512807750017557598420166050864341330052712160855127588643347514468625/652373095831249048632266106568680592835654624*t^37 + 110540544890706105553956862536075553578378720819738377482091963873662875/5218984766649992389058128852549444742685236992*t^35 - 4900758311408655449968680492961253914729778420744052478303824473121436875/10437969533299984778116257705098889485370473984*t^33 + 5580216340906399618789598949147640747754662102784565711711778791407911875/652373095831249048632266106568680592835654624*t^31 - 20831147248932609638384371865261653669942411927609928243017375574538170625/163093273957812262158066526642170148208913656*t^29 + 129952577211871604254540128851067387900684996699596822188135488628733663758125/83503756266399878224930061640791115882963791872*t^27 - 2567782615492994974974711404071502466442874408093662755526597293873488178118125/167007512532799756449860123281582231765927583744*t^25 + 10199476741113772536696367323521642601810369351616920028171749617522924959828125/83503756266399878224930061640791115882963791872*t^23 - 128908710528657915381264195481458746144354079628752769038355668078217360191609375/167007512532799756449860123281582231765927583744*t^21 + 5113532039649187421839212308350267742675314571512466890563396329373960395552203125/1336060100262398051598880986252657854127420669952*t^19 - 39104362759487820255867521474183141721319820860824803958704199784655135516098453125/2672120200524796103197761972505315708254841339904*t^17 + 7047965206123837396501307164957080060287270975095282397260722683569919861128265625/167007512532799756449860123281582231765927583744*t^15 - 59576009024700033930117201601018455526957715431677973426428071728439172145375078125/668030050131199025799440493126328927063710334976*t^13 + 2841730910442647288490357702108627809707796787144544926399684050315032983116784140625/21376961604198368825582095780042525666038730719232*t^11 - 5670690586075684355461328693618230971060501202727727526104826677926013579745242140625/42753923208396737651164191560085051332077461438464*t^9 + 1755741870599283984445280691955705620482541043296858308328439629495783811417797703125/21376961604198368825582095780042525666038730719232*t^7 - 1199736943445536865426050052248826622557834688131530173985094038249337461206209671875/42753923208396737651164191560085051332077461438464*t^5 + 1470291696424456278486126902129484563058266893773482172984200597409498121224614765625/342031385667173901209313532480680410656619691507712*t^3 - 126203755067121776486065876571738567752339819636215213958997203034119699811201015625/684062771334347802418627064961360821313239383015424*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: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   59 out of 59
Indefinite weights: 0 out of 59
Negative weights:   0 out of 59
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-9.4512595341625961944 + 9.3021770421363742193e-1407j)  +/-  (2.46e-499, 2.46e-499j)
| (-7.9654593771790612768 + 1.7005703217586542274e-1403j)  +/-  (3.44e-497, 3.44e-497j)
| (-8.4129786512806717972 + 1.2214691786901344688e-1404j)  +/-  (1.01e-497, 1.01e-497j)
| (-1.6506801238857845559 + 4.8411126835287910712e-1411j)  +/-  (1.17e-503, 1.17e-503j)
| (-2.2356303610261937372 + 4.4055559162530634464e-1409j)  +/-  (6.89e-502, 6.89e-502j)
| (-7.5460448210010119965 + 1.3831308874292048924e-1406j)  +/-  (7.73e-497, 7.73e-497j)
| (-8.9003938649805647039 - 2.8278587761433666565e-1405j)  +/-  (2.09e-498, 2.09e-498j)
| (2.2356303610261937372 + 1.2034586705616833725e-1411j)  +/-  (6.69e-502, 6.69e-502j)
| (-6.3980602238352289392 + 2.5967704354604351838e-1402j)  +/-  (2.4e-496, 2.4e-496j)
| (-1.0778939563830411966 - 1.6113602161386867015e-1413j)  +/-  (1.15e-505, 1.15e-505j)
| (-5.6936611765079729239 + 4.3870410665972093488e-1403j)  +/-  (1.9e-496, 1.9e-496j)
| (1.9418229195250896794 - 6.2724643765770301779e-1412j)  +/-  (9.79e-503, 9.79e-503j)
| (-4.3745394083996009294 - 3.027580585873878782e-1405j)  +/-  (1.44e-497, 1.44e-497j)
| (1.6506801238857845559 + 3.2685608869909673744e-1412j)  +/-  (1.26e-503, 1.26e-503j)
| (-10.130936268207998843 - 2.854966734038019261e-1409j)  +/-  (1.15e-500, 1.15e-500j)
| (-5.021848588524538907 - 3.1163183269291893466e-1404j)  +/-  (7.27e-497, 7.27e-497j)
| (-2.5320283539618639865 - 1.9901849804039059328e-1410j)  +/-  (4.67e-501, 4.67e-501j)
| (-5.3542634943473410187 + 2.062720733947034067e-1405j)  +/-  (1.25e-496, 1.25e-496j)
| (-2.8310832662859339258 - 1.1892124781615836533e-1411j)  +/-  (2.38e-500, 2.38e-500j)
| (0.79803935152875935819 - 2.4609462059751884082e-1417j)  +/-  (8.71e-507, 8.71e-507j)
| (-7.1477902537194271455 - 3.9938621560959427494e-1405j)  +/-  (1.46e-496, 1.46e-496j)
| (-4.0582797609333758206 - 1.4689642720097144599e-1409j)  +/-  (5.18e-498, 5.18e-498j)
| (-1.9418229195250896794 + 5.6998289483285858536e-1415j)  +/-  (9.38e-503, 9.38e-503j)
| (0.52464762327529031788 - 2.4028639902337023341e-1419j)  +/-  (6.5e-508, 6.5e-508j)
| (-3.132960147764226824 + 1.2316079957498623646e-1411j)  +/-  (1.09e-499, 1.09e-499j)
| (-0.79803935152875935819 + 2.3382308314190558963e-1418j)  +/-  (9.19e-507, 9.19e-507j)
| (1.0778939563830411966 + 1.5230426754600350409e-1417j)  +/-  (1.1e-505, 1.1e-505j)
| (1.3624922765937394238 + 1.7707799456391593605e-1418j)  +/-  (1.33e-504, 1.33e-504j)
| (-6.7661773655984824903 - 4.6491338038663026325e-1407j)  +/-  (2.18e-496, 2.18e-496j)
| (-0.25915969448246283046 + 3.8592821980935913598e-1455j)  +/-  (4.25e-509, 4.25e-509j)
| (-0.52464762327529031788 + 3.2745242133257868534e-1421j)  +/-  (7.44e-508, 7.44e-508j)
| (0.25915969448246283046 - 7.3825337243942388668e-1454j)  +/-  (4.25e-509, 4.25e-509j)
| (-3.7462157289283300958 - 3.302497295638319711e-1412j)  +/-  (1.69e-498, 1.69e-498j)
| (-4.6955213615549712748 - 8.9377483933657979418e-1409j)  +/-  (3.66e-497, 3.66e-497j)
| (2.5320283539618639865 + 7.2606890848361410992e-1420j)  +/-  (4.34e-501, 4.34e-501j)
| (-1.6070733672135034552e-1439 + 2.2421110972596304776e-1439j)  +/-  (1.63e-1437, 1.63e-1437j)
| (-1.3624922765937394238 - 1.4446522987496312736e-1422j)  +/-  (1.43e-504, 1.43e-504j)
| (-3.4379010870695130648 + 1.8315895355658146189e-1414j)  +/-  (4.54e-499, 4.54e-499j)
| (-6.0411375127491862905 - 2.0621048451539379956e-1430j)  +/-  (2.2e-496, 2.2e-496j)
| (8.4129786512806717972 + 8.9944708912001352791e-1474j)  +/-  (1e-497, 1e-497j)
| (8.9003938649805647039 + 5.155565209138445858e-1509j)  +/-  (2.27e-498, 2.27e-498j)
| (7.9654593771790612768 + 6.8802926945819853624e-1535j)  +/-  (3.55e-497, 3.55e-497j)
| (9.4512595341625961944 + 2.7527742386823132113e-1560j)  +/-  (2.46e-499, 2.46e-499j)
| (4.6955213615549712748 + 2.1696100793741122202e-1593j)  +/-  (3.38e-497, 3.38e-497j)
| (7.1477902537194271455 + 1.4172741972383336994e-1630j)  +/-  (1.41e-496, 1.41e-496j)
| (5.3542634943473410187 + 1.3579225440987063507e-1660j)  +/-  (1.28e-496, 1.28e-496j)
| (10.130936268207998843 + 6.6045063489284552389e-1678j)  +/-  (1.18e-500, 1.18e-500j)
| (2.8310832662859339258 + 4.0876703552146727563e-1687j)  +/-  (2.51e-500, 2.51e-500j)
| (4.0582797609333758206 - 1.1875743748800384363e-1705j)  +/-  (5.36e-498, 5.36e-498j)
| (6.3980602238352289392 + 1.2744193023834043063e-1747j)  +/-  (2.41e-496, 2.41e-496j)
| (7.5460448210010119965 + 9.2379027294604222365e-1779j)  +/-  (8.05e-497, 8.05e-497j)
| (5.021848588524538907 + 4.601606036836393296e-1798j)  +/-  (7.3e-497, 7.3e-497j)
| (3.7462157289283300958 - 1.082874808961786295e-1808j)  +/-  (1.65e-498, 1.65e-498j)
| (6.7661773655984824903 - 1.3791642244187594294e-1815j)  +/-  (2.06e-496, 2.06e-496j)
| (4.3745394083996009294 + 3.4558524774890933995e-1831j)  +/-  (1.49e-497, 1.49e-497j)
| (5.6936611765079729239 + 1.7134628023978384716e-1861j)  +/-  (1.93e-496, 1.93e-496j)
| (6.0411375127491862905 + 3.2954280479112931485e-1893j)  +/-  (2.35e-496, 2.35e-496j)
| (3.4379010870695130648 + 1.3669324175338860321e-1904j)  +/-  (4.9e-499, 4.9e-499j)
| (3.132960147764226824 + 2.2016232497221983289e-1905j)  +/-  (1.25e-499, 1.25e-499j)
-------------------------------------------------
The weights are:
| (5.414487958085262583e-40 - 4.5001095048719514828e-1430j)  +/-  (1.19e-170, 2.54e-417j)
| (6.7854766079506279142e-29 + 1.9801649458970739704e-1424j)  +/-  (9.53e-167, 2.04e-413j)
| (4.7883667195755142077e-32 - 4.7749184555142708051e-1426j)  +/-  (3.81e-168, 8.16e-415j)
| (0.010717352057101371106 + 1.3492849009882488349e-1410j)  +/-  (1.01e-131, 2.17e-378j)
| (0.0011240198351338999769 + 4.4808589520920298761e-1411j)  +/-  (5.23e-139, 1.12e-385j)
| (4.2861550518233605312e-26 - 5.5523161659971409073e-1423j)  +/-  (3.64e-166, 7.79e-413j)
| (1.1441785997033715224e-35 + 6.8326780688265888021e-1428j)  +/-  (6.29e-170, 1.35e-416j)
| (0.0011240198351338999769 + 1.1622461311020479876e-1411j)  +/-  (6.45e-144, 1.38e-390j)
| (3.4075378638053462783e-19 + 2.9630770281083931616e-1419j)  +/-  (7.46e-164, 1.6e-410j)
| (0.04986673473126993747 + 2.9883387808653531452e-1410j)  +/-  (7.95e-129, 1.7e-375j)
| (1.6149316991561729495e-15 + 9.0716004523160193936e-1417j)  +/-  (5.33e-162, 1.14e-408j)
| (0.0038016343497984697535 - 2.5137690244862819853e-1411j)  +/-  (4.77e-143, 1.02e-389j)
| (8.783180775702018458e-10 - 1.3784992295634141351e-1413j)  +/-  (7.47e-158, 1.6e-404j)
| (0.010717352057101371106 + 5.057314911532000116e-1411j)  +/-  (1.64e-140, 3.52e-387j)
| (1.2061784411611091255e-45 + 7.0219371180198152107e-1433j)  +/-  (6.93e-176, 1.48e-422j)
| (2.0724100920911970628e-12 - 1.0938033188748444496e-1415j)  +/-  (1.86e-160, 3.99e-407j)
| (0.00027598038539036464737 - 8.9211599258900221607e-1412j)  +/-  (4.41e-149, 9.43e-396j)
| (6.7145538513928920378e-14 - 6.8146114374276910107e-1416j)  +/-  (1.62e-161, 3.48e-408j)
| (5.6012653331283798341e-05 + 6.2770138653535278127e-1412j)  +/-  (8.24e-152, 1.76e-398j)
| (0.082646867235076161906 - 2.729721496042268654e-1410j)  +/-  (2.1e-138, 4.51e-385j)
| (1.4230874738506256124e-23 + 1.1329136387144187449e-1421j)  +/-  (1.5e-167, 3.22e-414j)
| (1.2467964355773940813e-08 + 3.7613218211144462005e-1413j)  +/-  (3.59e-158, 7.69e-405j)
| (0.0038016343497984697535 - 9.2340974868905639391e-1411j)  +/-  (1.2e-147, 2.58e-394j)
| (0.11548480218584978775 + 4.0970034495020245794e-1410j)  +/-  (2.64e-141, 5.65e-388j)
| (9.3453640517088967934e-06 - 3.2379329081765437962e-1412j)  +/-  (1.4e-154, 3e-401j)
| (0.082646867235076161906 - 4.1504374708645135133e-1410j)  +/-  (1.72e-142, 3.68e-389j)
| (0.04986673473126993747 + 1.67157404907129956e-1410j)  +/-  (2.29e-143, 4.91e-390j)
| (0.025257271048821821541 - 9.5160297302922351516e-1411j)  +/-  (1.07e-146, 2.3e-393j)
| (2.7687562139817395659e-21 - 1.7145800106083714333e-1420j)  +/-  (5.4e-167, 1.16e-413j)
| (0.13802168683463135272 - 6.2791951565915964997e-1410j)  +/-  (1.69e-143, 3.61e-390j)
| (0.11548480218584978775 + 5.3736181632322446002e-1410j)  +/-  (1.52e-143, 3.26e-390j)
| (0.13802168683463135272 - 5.4978410476969281069e-1410j)  +/-  (4.32e-144, 9.26e-391j)
| (1.406080376422516638e-07 - 7.0081395753380907635e-1413j)  +/-  (8.95e-158, 1.92e-404j)
| (4.8536113038653002607e-11 - 1.0022770850691851585e-1414j)  +/-  (8.14e-161, 1.74e-407j)
| (0.00027598038539036464737 - 4.9668936842876926317e-1412j)  +/-  (1.93e-161, 4.12e-408j)
| (0.1454737318686120152 + 6.3700446255154819545e-1410j)  +/-  (7.68e-146, 1.64e-392j)
| (0.025257271048821821541 - 2.0524345946657200413e-1410j)  +/-  (8.25e-149, 1.77e-395j)
| (1.2733802404452325302e-06 + 1.516362608970389587e-1412j)  +/-  (5.56e-157, 1.19e-403j)
| (2.8065525016295445852e-17 - 2.1129095162035143447e-1418j)  +/-  (2.31e-165, 4.94e-412j)
| (4.7883667195755142077e-32 + 1.6000588429172430468e-1426j)  +/-  (3.54e-189, 7.59e-436j)
| (1.1441785997033715224e-35 - 2.450797033958130562e-1428j)  +/-  (1.19e-190, 2.56e-437j)
| (6.7854766079506279142e-29 - 6.1876538726633856441e-1425j)  +/-  (1.4e-188, 3e-435j)
| (5.414487958085262583e-40 + 1.7270099335982267301e-1430j)  +/-  (1.32e-192, 2.82e-439j)
| (4.8536113038653002607e-11 + 9.3222231657663876781e-1416j)  +/-  (1.31e-180, 2.81e-427j)
| (1.4230874738506256124e-23 - 3.0863719865534455298e-1422j)  +/-  (1.18e-187, 2.53e-434j)
| (6.7145538513928920378e-14 + 2.9337388467588556962e-1417j)  +/-  (2.33e-183, 5e-430j)
| (1.2061784411611091255e-45 - 2.8958208250626813792e-1433j)  +/-  (1.17e-195, 2.5e-442j)
| (5.6012653331283798341e-05 + 1.9385344256159534973e-1412j)  +/-  (6.48e-174, 1.39e-420j)
| (1.2467964355773940813e-08 + 1.8074091109532730274e-1414j)  +/-  (1.01e-179, 2.16e-426j)
| (3.4075378638053462783e-19 - 5.3504551773032731637e-1420j)  +/-  (8.77e-187, 1.88e-433j)
| (4.2861550518233605312e-26 + 1.6161147335198046552e-1423j)  +/-  (4.82e-189, 1.03e-435j)
| (2.0724100920911970628e-12 - 1.7670693406607957834e-1416j)  +/-  (2.72e-183, 5.83e-430j)
| (1.406080376422516638e-07 - 6.7423926108734533758e-1414j)  +/-  (1.58e-180, 3.39e-427j)
| (2.7687562139817395659e-21 + 4.543092011386782413e-1421j)  +/-  (6.91e-188, 1.48e-434j)
| (8.783180775702018458e-10 - 4.3480588208459540974e-1415j)  +/-  (2.74e-182, 5.87e-429j)
| (1.6149316991561729495e-15 - 4.2185516737343165728e-1418j)  +/-  (6.2e-186, 1.33e-432j)
| (2.8065525016295445852e-17 + 5.1830343986590198512e-1419j)  +/-  (8.03e-187, 1.72e-433j)
| (1.2733802404452325302e-06 + 2.2710421080680612222e-1413j)  +/-  (4.52e-182, 9.71e-429j)
| (9.3453640517088967934e-06 - 6.9452881341734897481e-1413j)  +/-  (1.43e-181, 3.05e-428j)
