Starting with polynomial:
P : 2097152*t^21 - 220200960*t^19 + 9413591040*t^17 - 213374730240*t^15 + 2800543334400*t^13 - 21844238008320*t^11 + 100119424204800*t^9 - 257449947955200*t^7 + 337903056691200*t^5 - 187723920384000*t^3 + 28158588057600*t
Extension levels are: 21 36
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P1 : 2097152*t^21 - 220200960*t^19 + 9413591040*t^17 - 213374730240*t^15 + 2800543334400*t^13 - 21844238008320*t^11 + 100119424204800*t^9 - 257449947955200*t^7 + 337903056691200*t^5 - 187723920384000*t^3 + 28158588057600*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2097152*t^57 - 431266610190358621801010908102656/343303287907604831431525*t^55 + 119695523318938213881198733280673792/343303287907604831431525*t^53 - 94157758587981571422999389646922973184/1579195124374982224585015*t^51 + 122426406211768399968828016372527804383232/17371146368124804470435165*t^49 - 2127297709596759005491257909683448246435840/3474229273624960894087033*t^47 + 705166860466398181330847361078586827116937216/17371146368124804470435165*t^45 - 36559564362032251686797569471487052856978931712/17371146368124804470435165*t^43 + 301416769071551832633596627755885962628472438784/3474229273624960894087033*t^41 - 9991970169011998867424708242917801979135606161408/3474229273624960894087033*t^39 + 268382885310822384765442243093486547561600789369856/3474229273624960894087033*t^37 - 5867947571248962690977655290122416379966945461912576/3474229273624960894087033*t^35 + 104669341206599698627812115697988389377952696250239232/3474229273624960894087033*t^33 - 138496422208591976104438874952644779415013843799418880/315839024874996444917003*t^31 + 1642018188674324804213902335265586271549232047597384960/315839024874996444917003*t^29 - 15801029888617261339523148975996104757449147974332476160/315839024874996444917003*t^27 + 122734042996850449768097612488091254938383457606970533600/315839024874996444917003*t^25 - 33203372638496982935419732111030376748660720475584676800/13732131516304193257261*t^23 + 163848945533061250632214607623974805426902899657242708500/13732131516304193257261*t^21 - 633032626364006323771606117357922774871781326106951924500/13732131516304193257261*t^19 + 1883554064605383073125954233400323381683561353087006199125/13732131516304193257261*t^17 - 4225935961086012916046843408472497994692689332411412555500/13732131516304193257261*t^15 + 13911046884005759060345008389438453321085391957338317647625/27464263032608386514522*t^13 - 16194514034912312179016122792061167994098073571257210596875/27464263032608386514522*t^11 + 25363922436958705080585678234558530636767013032373218753125/54928526065216773029044*t^9 - 3107600435397868832710666745003711675122961586633086225625/13732131516304193257261*t^7 + 54584908442380668654488506443791846519411910125964612309375/878856417043468368464704*t^5 - 6931255637463360129590431469199120113045897370906599596875/878856417043468368464704*t^3 + 1067583015073643668378398532684940793829042330432387321875/3515425668173873473858816*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
Positive weights:   57 out of 57
Indefinite weights: 0 out of 57
Negative weights:   0 out of 57
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-8.9128086440897306438 - 4.2343047555909995346e-617j)  +/-  (3.12e-246, 3.12e-246j)
| (-8.2500741360717875294 - 4.7480999189797580657e-616j)  +/-  (5.61e-245, 5.61e-245j)
| (-6.758289792505396377 + 7.703004609953614627e-612j)  +/-  (6.38e-243, 6.38e-243j)
| (5.5503518732646782452 + 7.1277528489527160287e-619j)  +/-  (6.93e-242, 6.93e-242j)
| (-5.2054519962411742646 + 1.1467630517662442498e-616j)  +/-  (1.63e-241, 1.63e-241j)
| (8.2500741360717875294 - 1.0442990281374850562e-630j)  +/-  (5.99e-245, 5.99e-245j)
| (7.7008830012768287984 + 5.5958136583792288311e-631j)  +/-  (4.13e-244, 4.13e-244j)
| (8.9128086440897306438 - 1.548631161434426762e-632j)  +/-  (3.39e-246, 3.39e-246j)
| (7.2105173677836218421 - 3.4269019826867957637e-629j)  +/-  (2.13e-243, 2.13e-243j)
| (-5.9316775157219176688 - 1.6397197769214048251e-625j)  +/-  (3.37e-242, 3.37e-242j)
| (-3.5319728771376777392 + 1.7642891352428101717e-631j)  +/-  (3.63e-243, 3.63e-243j)
| (5.0126191454912253572 + 3.898408959475344563e-637j)  +/-  (1.87e-241, 1.87e-241j)
| (-7.7008830012768287984 - 5.9157947962884262766e-636j)  +/-  (4.23e-244, 4.23e-244j)
| (-1.9449629491862538419 - 5.6173932290515027758e-646j)  +/-  (1.14e-246, 1.14e-246j)
| (-5.5503518732646782452 + 2.4986340656218604937e-640j)  +/-  (6.81e-242, 6.81e-242j)
| (2.453552124512838002 - 7.2203512947954247181e-659j)  +/-  (3.2e-245, 3.2e-245j)
| (2.7083990604665901444 + 4.007809660154530661e-658j)  +/-  (1.26e-244, 1.26e-244j)
| (3.8166254275818267497 + 1.1823413913789218356e-656j)  +/-  (8.38e-243, 8.38e-243j)
| (-0.25399276721860891489 + 1.1993567163858602977e-666j)  +/-  (9.08e-254, 9.08e-254j)
| (1.4489342506507319627 - 5.4040904752252776367e-662j)  +/-  (2.38e-248, 2.38e-248j)
| (3.2567949642606884947 + 2.1152771767082342319e-657j)  +/-  (1.39e-243, 1.39e-243j)
| (4.1219955474918400208 + 2.1765976305746396571e-656j)  +/-  (1.8e-242, 1.8e-242j)
| (5.9316775157219176688 - 1.8509469761799986625e-655j)  +/-  (3.41e-242, 3.41e-242j)
| (-6.3338546971234726891 - 9.233405142930001941e-655j)  +/-  (1.5e-242, 1.5e-242j)
| (4.7739923434112194297 - 1.61042456451644654e-665j)  +/-  (1.04e-241, 1.04e-241j)
| (-7.2105173677836218421 + 1.0745681673719331471e-664j)  +/-  (2.04e-243, 2.04e-243j)
| (2.9799912077045980025 + 2.8299906838268756199e-675j)  +/-  (4.38e-244, 4.38e-244j)
| (6.3338546971234726891 - 3.3096688592455414488e-673j)  +/-  (1.51e-242, 1.51e-242j)
| (-2.7083990604665901444 - 8.8191924409541848014e-673j)  +/-  (1.21e-244, 1.21e-244j)
| (-0.70652016452900442722 - 5.595155466151340407e-693j)  +/-  (1.56e-251, 1.56e-251j)
| (-5.0126191454912253572 + 1.5353766179243088332e-694j)  +/-  (1.89e-241, 1.89e-241j)
| (-1.4489342506507319627 + 1.0822897863932254375e-717j)  +/-  (2.37e-248, 2.37e-248j)
| (2.2047777267849041498 + 2.8454817662643766399e-719j)  +/-  (6.86e-246, 6.86e-246j)
| (-3.2567949642606884947 + 5.9480376385540196065e-721j)  +/-  (1.38e-243, 1.38e-243j)
| (-2.2047777267849041498 + 5.0696103141724100586e-733j)  +/-  (6.21e-246, 6.21e-246j)
| (-0.96149963441836906428 - 4.6139044159169784665e-745j)  +/-  (2.08e-250, 2.08e-250j)
| (3.5319728771376777392 - 1.1464673218023000751e-734j)  +/-  (3.75e-243, 3.75e-243j)
| (1.2159367692289765319 + 4.2279143652252068964e-745j)  +/-  (2.67e-249, 2.67e-249j)
| (6.758289792505396377 - 3.3726309931221123571e-736j)  +/-  (6.72e-243, 6.72e-243j)
| (-4.1219955474918400208 + 2.8269887748436869694e-753j)  +/-  (1.73e-242, 1.73e-242j)
| (-3.8166254275818267497 + 6.2246858089575034634e-790j)  +/-  (8.54e-243, 8.54e-243j)
| (4.4455887171102480025 - 2.156196129361656037e-808j)  +/-  (3.65e-242, 3.65e-242j)
| (-4.4455887171102480025 - 3.5886973022270003656e-826j)  +/-  (4.04e-242, 4.04e-242j)
| (0.47945070707910757629 + 4.5251751202999294224e-852j)  +/-  (1.61e-252, 1.61e-252j)
| (5.2054519962411742646 + 2.157757766368443596e-840j)  +/-  (1.68e-241, 1.68e-241j)
| (-1.6861175292124962944 + 5.8900245591115297312e-847j)  +/-  (1.77e-247, 1.77e-247j)
| (-2.9799912077045980025 + 1.5628844140344811544e-841j)  +/-  (4.34e-244, 4.34e-244j)
| (1.9449629491862538419 + 9.2923687957566902231e-850j)  +/-  (1.09e-246, 1.09e-246j)
| (0.70652016452900442722 + 1.6768045850630309197e-854j)  +/-  (1.61e-251, 1.61e-251j)
| (5.8896061413692829083e-864 - 6.3763545944560498017e-864j)  +/-  (4.95e-862, 4.95e-862j)
| (-1.2159367692289765319 + 3.4008645940206550805e-852j)  +/-  (3.07e-249, 3.07e-249j)
| (1.6861175292124962944 + 1.0866668877930528565e-850j)  +/-  (1.7e-247, 1.7e-247j)
| (-2.453552124512838002 - 3.1270346576949844356e-845j)  +/-  (2.9e-245, 2.9e-245j)
| (0.96149963441836906428 - 1.923506555939889367e-855j)  +/-  (1.93e-250, 1.93e-250j)
| (0.25399276721860891489 + 1.4575147873886994216e-858j)  +/-  (9.08e-254, 9.08e-254j)
| (-4.7739923434112194297 + 7.493042038558943906e-846j)  +/-  (1.06e-241, 1.06e-241j)
| (-0.47945070707910757629 + 2.9512557871822462563e-867j)  +/-  (1.66e-252, 1.66e-252j)
-------------------------------------------------
The weights are:
| (1.3666205686196882208e-35 - 2.6538659661160757103e-641j)  +/-  (1.95e-77, 2.35e-198j)
| (9.1916590611313630988e-31 + 2.4431361445756346452e-638j)  +/-  (1.2e-75, 1.45e-196j)
| (3.5960371222482020332e-21 + 2.4246253264613690922e-631j)  +/-  (1.81e-71, 2.19e-192j)
| (8.7063871547914068407e-15 - 7.9600549800438375844e-629j)  +/-  (4.03e-69, 4.87e-190j)
| (2.8766025649151689143e-13 + 1.8379599492472243901e-626j)  +/-  (2.17e-66, 2.63e-187j)
| (9.1916590611313630988e-31 - 2.4301079735567133658e-639j)  +/-  (7.17e-79, 8.67e-200j)
| (5.1041831453043359049e-27 + 4.3018075427715739074e-637j)  +/-  (2.11e-77, 2.55e-198j)
| (1.3666205686196882208e-35 + 3.6508004295237008572e-642j)  +/-  (1.94e-81, 2.34e-202j)
| (6.9656295539997935373e-24 - 3.7400820665248901488e-635j)  +/-  (2.85e-76, 3.45e-197j)
| (1.159124739321132802e-16 + 4.0899513131180524098e-629j)  +/-  (7.62e-73, 9.21e-194j)
| (5.9736432055733178668e-07 + 1.1730459102273396225e-622j)  +/-  (3.94e-64, 4.77e-185j)
| (9.7277553912787685335e-13 - 1.187391385184953809e-626j)  +/-  (4.7e-71, 5.69e-192j)
| (5.1041831453043359049e-27 - 6.5933827917536316237e-636j)  +/-  (9.21e-79, 1.11e-199j)
| (0.0033810482934625535454 + 7.1980450159004275154e-620j)  +/-  (1.43e-54, 1.73e-175j)
| (8.7063871547914068407e-15 - 8.060934665888166985e-628j)  +/-  (1.41e-71, 1.7e-192j)
| (0.00033945244053444271211 + 6.6593756560419713829e-621j)  +/-  (3.23e-60, 3.9e-181j)
| (9.7149904192476607592e-05 - 2.1690574843990142389e-621j)  +/-  (4.76e-62, 5.76e-183j)
| (7.8370880420068144389e-08 - 7.3145249672026835488e-624j)  +/-  (1.19e-68, 1.43e-189j)
| (0.12776104646666279793 - 1.2337936044199362087e-618j)  +/-  (5.26e-54, 6.37e-175j)
| (0.015745609191231479077 + 1.9099866093144661501e-619j)  +/-  (5.26e-54, 6.37e-175j)
| (3.8481470530696591627e-06 - 1.5441309154364487822e-622j)  +/-  (3.94e-66, 4.76e-187j)
| (7.4419352076693854537e-09 + 1.2210487566996756524e-624j)  +/-  (3.33e-70, 4.03e-191j)
| (1.159124739321132802e-16 + 2.6707585393782941988e-630j)  +/-  (2.23e-77, 2.7e-198j)
| (8.7930585961622805778e-19 - 2.5274665591960426752e-630j)  +/-  (1.28e-79, 1.55e-200j)
| (2.2629725709190284589e-11 + 3.97882688410966635e-626j)  +/-  (2.05e-73, 2.48e-194j)
| (6.9656295539997935373e-24 + 1.1541067179630383196e-633j)  +/-  (1.54e-82, 1.87e-203j)
| (2.1705181247982230308e-05 + 5.9674872828319712655e-622j)  +/-  (9.33e-67, 1.13e-187j)
| (8.7930585961622805778e-19 - 8.2075489440685793512e-632j)  +/-  (3.17e-79, 3.84e-200j)
| (9.7149904192476607592e-05 - 5.0726600386464474359e-621j)  +/-  (3.43e-70, 4.15e-191j)
| (0.083416084601191154637 - 9.2489824834146169165e-619j)  +/-  (1.21e-61, 1.46e-182j)
| (9.7277553912787685335e-13 - 8.0798916910340412906e-626j)  +/-  (4.32e-77, 5.23e-198j)
| (0.015745609191231479077 + 2.9530681452908393384e-619j)  +/-  (6.83e-64, 8.25e-185j)
| (0.0011084559936726233891 - 1.6806897056011572649e-620j)  +/-  (2.9e-66, 3.51e-187j)
| (3.8481470530696591627e-06 - 4.4196516495671312222e-622j)  +/-  (9.84e-73, 1.19e-193j)
| (0.0011084559936726233891 - 3.3094016380292725906e-620j)  +/-  (8.83e-69, 1.07e-189j)
| (0.058286584596755699589 + 6.1914298816956287162e-619j)  +/-  (6.49e-63, 7.84e-184j)
| (5.9736432055733178668e-07 + 3.674726134210768421e-623j)  +/-  (6.46e-71, 7.8e-192j)
| (0.031382609092297685342 - 3.0720660498627181218e-619j)  +/-  (2.94e-64, 3.55e-185j)
| (3.5960371222482020332e-21 + 2.0519424724932691746e-633j)  +/-  (5.16e-82, 6.23e-203j)
| (7.4419352076693854537e-09 + 5.0466923196254943078e-624j)  +/-  (2.53e-76, 3.06e-197j)
| (7.8370880420068144389e-08 - 2.6323140675604646857e-623j)  +/-  (2.28e-75, 2.75e-196j)
| (4.8584998398930693206e-10 - 1.9660884580902374727e-625j)  +/-  (1.44e-75, 1.73e-196j)
| (4.8584998398930693206e-10 - 9.5452401466529368673e-625j)  +/-  (1.62e-77, 1.96e-198j)
| (0.096788196948057060527 + 1.0548140550910627859e-618j)  +/-  (1.26e-68, 1.51e-189j)
| (2.8766025649151689143e-13 + 2.3409408488351303659e-627j)  +/-  (1.07e-77, 1.27e-198j)
| (0.0082140871186210557627 - 1.5716384934677736279e-619j)  +/-  (9.42e-71, 1.13e-191j)
| (2.1705181247982230308e-05 + 1.5389629859473630923e-621j)  +/-  (7.24e-74, 8.65e-195j)
| (0.0033810482934625535454 + 3.9797029699694979081e-620j)  +/-  (1.44e-71, 1.71e-192j)
| (0.083416084601191154637 - 7.4975084917504403961e-619j)  +/-  (3.79e-70, 4.45e-191j)
| (0.1469068766762695305 + 1.1353310073787709406e-618j)  +/-  (4.22e-70, 4.96e-191j)
| (0.031382609092297685342 - 4.4207660374386178486e-619j)  +/-  (6.68e-71, 7.93e-192j)
| (0.0082140871186210557627 - 9.4378076036486966617e-620j)  +/-  (1.57e-71, 1.88e-192j)
| (0.00033945244053444271211 + 1.4256454077557325613e-620j)  +/-  (1.9e-73, 2.26e-194j)
| (0.058286584596755699589 + 4.6485434951483184484e-619j)  +/-  (3.5e-71, 4.01e-192j)
| (0.12776104646666279793 - 1.1443769580270398333e-618j)  +/-  (6.67e-71, 7.68e-192j)
| (2.2629725709190284589e-11 + 2.3215681223978853001e-625j)  +/-  (2.04e-79, 2.96e-200j)
| (0.096788196948057060527 + 1.2159811764282008312e-618j)  +/-  (3.39e-71, 3.49e-192j)
