Starting with polynomial:
P : t
Extension levels are: 1 4 14 32
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P2 : t^5 - 10*t^3 + 15*t
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P3 : t^19 - 10067/33*t^17 + 4654486/165*t^15 - 13098722/11*t^13 + 26061308*t^11 - 305527040*t^9 + 1871898210*t^7 - 5508762714*t^5 + 6473363715*t^3 - 1927283085*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^51 - 91214001897741174196706706436901730314473441311201869922067362781851886351747401051114582450993520784466907/87745432851566710976812014670979861123532323561578632873722248162267583652943548832103083537299186737097*t^49 + 104244869410590565928623772137048990764693172557328977996224563884137905585523817468233756930664445281948932997082/211905220336533607009001015430416364613330561401212398390039229311876214521858670429528946742577535970089255*t^47 - 29865733193241724452774161908185364331324527636415223835624398801750484052021528463845160305313928992982903575858754/211905220336533607009001015430416364613330561401212398390039229311876214521858670429528946742577535970089255*t^45 + 4260431270272415622835699581694101328099434908412301347943488162047535156076760101135552757137632433352226222255266632/155397161580124645139934077982305334049775745027555758819362101495375890649363024981654560944556859711398787*t^43 - 256336294163073537077173873966725087663864481579610285851855486522028677456190817836016188833564844780473417882855885004/66598783534339133631400319135273714592761033583238182351155186355161095992584153563566240404810082733456623*t^41 + 39381343406078301533049087994299714734679625441592776891599800815389658498895305312886464542545787480856388034049216379570/97336683627111041461277389505400044404804587544732728051688349288312371066084532131366043668568582456590449*t^39 - 1057870773026573844514376972320229943899883824722001971312624744298090243894308536768072312656892597616687639705360272904222/32445561209037013820425796501800014801601529181577576017229449762770790355361510710455347889522860818863483*t^37 + 199124845866541242925118575943555937344495760290113276778839932383968942131331371385061965978746259042105424864376260954280217/97336683627111041461277389505400044404804587544732728051688349288312371066084532131366043668568582456590449*t^35 - 3530125776103452256869600338891658870547845088648255544017543166182018409755303697972009194368607859312351232466751352718865/34975452255519598081666327526194769818470926174894979537078098917826938938585890093915215116266109398703*t^33 + 11616481322521507178668262564049108221936923369776021772711922816124634552279658721150611619701508560369329219104397148439421820/2949596473548819438220526954709092254691048107416143274293586342070071850487410064586849808138441892623953*t^31 - 359351834705616911286435601122654365572835878376731922455585290538858958834237900990206546992954323602589670597621513186091393900/2949596473548819438220526954709092254691048107416143274293586342070071850487410064586849808138441892623953*t^29 + 8808826464918053147508944930147158613198291776261014995663473364137447024346035173567650021402552051370076066670337605535887495800/2949596473548819438220526954709092254691048107416143274293586342070071850487410064586849808138441892623953*t^27 - 18951293373119823416902783301613412836344743527623395034828017298679946191870138405989847035621876597725191284192324678796957487200/327732941505424382024502994967676917187894234157349252699287371341119094498601118287427756459826876958217*t^25 + 12527553674752203132188034949514183399217963982961115919368777260419513099470918605188560665647320397645575622926484245987049477500/14249258326322799218456651955116387703821488441623880552142929188744308456460918186409902454775081606879*t^23 - 148242219662961870328951772304219188574570832329489392359741202080212770039850273660165252178604065114761335154569489059394723587500/14249258326322799218456651955116387703821488441623880552142929188744308456460918186409902454775081606879*t^21 + 70989539468764148941305034038429465822977650016253173774664313699953004517516543743214350635505001985167949227962500662933883939375/749960964543305222024034313427178300201130970611783186954891009933910971392679904547889602882899031941*t^19 - 488697517246311774721733036523319972126698854315125143720403800550834581700766303942402006366459125198945303393596079145670993067125/749960964543305222024034313427178300201130970611783186954891009933910971392679904547889602882899031941*t^17 + 2492248854063568461340362032759211008796880586407720214494909993861001074616721055808853368233602222959313725241561298731566497911750/749960964543305222024034313427178300201130970611783186954891009933910971392679904547889602882899031941*t^15 - 9158696627360625365983352865963340280001967243717623529675931212809796901536162525481485652280930785035630966766053715076911945238750/749960964543305222024034313427178300201130970611783186954891009933910971392679904547889602882899031941*t^13 + 2125434282988656787304059934763635460455242804309170812024733264774140431704134182894009474239276538173214753977186101055349051410000/68178269503936838365821301220652572745557360964707562450444637266719179217516354958899054807536275631*t^11 - 3587534274037109392472540316095752102709076589421897833340317407238884510095043056122632732664491220431478008681584272946650211812500/68178269503936838365821301220652572745557360964707562450444637266719179217516354958899054807536275631*t^9 + 3746007474731968033415951257432775161674963049642010608059030380596976623721070289206273094359505484382665291986772145786496186713750/68178269503936838365821301220652572745557360964707562450444637266719179217516354958899054807536275631*t^7 - 2219310648906916213752359931061841966738562452272968828659954339608998834883307913580768811551632749025955833327504948139057224708750/68178269503936838365821301220652572745557360964707562450444637266719179217516354958899054807536275631*t^5 + 670507374594183255728158314758949414630309045933833808293058810642897214501074999360767931853605591411520612283255919151341897028125/68178269503936838365821301220652572745557360964707562450444637266719179217516354958899054807536275631*t^3 - 79678458941391570434768471026367654053172733616464304519083624029612598960238255597343453992703801589737820348969847674287371771875/68178269503936838365821301220652572745557360964707562450444637266719179217516354958899054807536275631*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:
| (10.528536651510974909 - 4.6085185809170258474e-950j)  +/-  (1.69e-245, 1.69e-245j)
| (13.487781287282568426 - 6.8665116778747349845e-954j)  +/-  (3.41e-248, 3.41e-248j)
| (11.453088854513091478 + 7.2203010842203290768e-952j)  +/-  (2.15e-246, 2.15e-246j)
| (-2.4307394697464519038 + 3.9800630117057734646e-953j)  +/-  (6.24e-248, 6.24e-248j)
| (4.5389269600723963503 - 1.5310827434039127191e-947j)  +/-  (8.15e-245, 8.15e-245j)
| (9.0497703877789551539 - 4.0084138303879951668e-948j)  +/-  (2.2e-244, 2.2e-244j)
| (-7.784887716314096031 - 2.1706291130820089254e-952j)  +/-  (6.4e-244, 6.4e-244j)
| (9.7505644839236065873 + 3.472093557573159962e-952j)  +/-  (8.31e-245, 8.31e-245j)
| (-5.0244993395557398136 + 8.3018219417473772264e-953j)  +/-  (3.06e-244, 3.06e-244j)
| (-10.528536651510974909 + 2.2197026246069087566e-957j)  +/-  (1.67e-245, 1.67e-245j)
| (3.6693753049455151439 + 1.0066421922493743922e-956j)  +/-  (7.64e-246, 7.64e-246j)
| (8.3991802765217112718 - 4.0530269738018642024e-954j)  +/-  (3.79e-244, 3.79e-244j)
| (-3.6693753049455151439 - 7.79548050368465155e-962j)  +/-  (7.63e-246, 7.63e-246j)
| (-13.487781287282568426 + 3.6891288272545702284e-964j)  +/-  (3.8e-248, 3.8e-248j)
| (-11.453088854513091478 + 2.6446200773188652851e-962j)  +/-  (2.09e-246, 2.09e-246j)
| (-4.081684574563255551 + 3.7545179839102948872e-962j)  +/-  (2.72e-245, 2.72e-245j)
| (-9.7505644839236065873 + 9.578152856247940412e-961j)  +/-  (7.37e-245, 7.37e-245j)
| (-8.3991802765217112718 + 3.634612398551030191e-960j)  +/-  (3.85e-244, 3.85e-244j)
| (7.784887716314096031 + 2.2092058758750963923e-958j)  +/-  (6.61e-244, 6.61e-244j)
| (-2.0872695419014224088 - 1.0647289831176633356e-968j)  +/-  (1.38e-248, 1.38e-248j)
| (-6.1013838828954408496 + 4.1994552432304913909e-963j)  +/-  (1.67e-243, 1.67e-243j)
| (1.3556261799742658658 + 1.4061253279173199925e-972j)  +/-  (1.19e-250, 1.19e-250j)
| (-6.6367905724765826016 + 1.3212849367121614953e-964j)  +/-  (1.18e-243, 1.18e-243j)
| (5.0244993395557398136 + 2.5891384132088607735e-965j)  +/-  (3.08e-244, 3.08e-244j)
| (5.4983291699947363701 - 7.7668091530432893558e-979j)  +/-  (1.64e-243, 1.64e-243j)
| (1.785645923770438526 + 3.7574176222315160689e-1005j)  +/-  (2.23e-249, 2.23e-249j)
| (-9.0497703877789551539 + 2.1567155409073617419e-998j)  +/-  (2.15e-244, 2.15e-244j)
| (6.6367905724765826016 + 7.1269645813252754465e-1001j)  +/-  (1.13e-243, 1.13e-243j)
| (-7.1988479063141652686 - 3.8301166461645707859e-1013j)  +/-  (9.25e-244, 9.25e-244j)
| (-0.66248171638301031012 + 3.1314156609906413383e-1020j)  +/-  (3.46e-251, 3.46e-251j)
| (-5.704698183934789073 - 9.7262194595940878851e-1012j)  +/-  (2.48e-243, 2.48e-243j)
| (3.2762053826306548692 - 1.8591225046698912069e-1019j)  +/-  (1.94e-246, 1.94e-246j)
| (7.1988479063141652686 - 5.8142323054812281073e-1026j)  +/-  (9.71e-244, 9.71e-244j)
| (-0.77866737369365059888 - 4.1273095556513629297e-1059j)  +/-  (2.03e-251, 2.03e-251j)
| (-1.3556261799742658658 + 3.7735652815096995712e-1057j)  +/-  (1.15e-250, 1.15e-250j)
| (5.704698183934789073 + 9.4879979715904583813e-1049j)  +/-  (2.47e-243, 2.47e-243j)
| (-4.5389269600723963503 + 1.6679343006529744515e-1063j)  +/-  (8.27e-245, 8.27e-245j)
| (2.0872695419014224088 + 2.9170103318910093756e-1066j)  +/-  (1.48e-248, 1.48e-248j)
| (2.8569700138728056542 + 1.4615335779863477428e-1064j)  +/-  (3.46e-247, 3.46e-247j)
| (-1.785645923770438526 + 8.974267932136443059e-1068j)  +/-  (2.14e-249, 2.14e-249j)
| (-0.62203438278647062188 - 1.2895484416661173045e-1069j)  +/-  (1.7e-251, 1.7e-251j)
| (6.1013838828954408496 - 1.4310653625574289408e-1063j)  +/-  (1.68e-243, 1.68e-243j)
| (-2.8569700138728056542 + 4.2778945048311586148e-1073j)  +/-  (3.25e-247, 3.25e-247j)
| (0.77866737369365059888 - 1.4025775965217324339e-1077j)  +/-  (2e-251, 2e-251j)
| (4.081684574563255551 - 3.4616183051748089027e-1072j)  +/-  (2.51e-245, 2.51e-245j)
| (-5.4983291699947363701 + 2.4945028170715093767e-1073j)  +/-  (1.72e-243, 1.72e-243j)
| (-3.2762053826306548692 + 3.4356190058631155114e-1080j)  +/-  (1.89e-246, 1.89e-246j)
| (2.4307394697464519038 + 1.626223307700992595e-1082j)  +/-  (6.15e-248, 6.15e-248j)
| (0.62203438278647062188 + 2.2827356750054979455e-1086j)  +/-  (1.64e-251, 1.64e-251j)
| (0.66248171638301031012 - 1.0874587886565214873e-1085j)  +/-  (3.17e-251, 3.17e-251j)
| (-4.0578358729932044703e-1218 - 1.2354914258440482386e-1217j)  +/-  (6.63e-1216, 6.63e-1216j)
-------------------------------------------------
The weights are:
| (2.8220200211641973062e-25 + 2.0134158197297348404e-966j)  +/-  (2.28e-75, 5.02e-197j)
| (6.366950444489051525e-39 + 8.2524827520494592835e-974j)  +/-  (2.69e-81, 5.94e-203j)
| (1.3807186620701763181e-29 - 6.6541855458589685709e-969j)  +/-  (1.93e-77, 4.25e-199j)
| (0.0084624235657974872881 - 7.5089964655675023108e-951j)  +/-  (2.28e-48, 5.03e-170j)
| (6.3663171728239859856e-06 + 3.2075075838234966692e-952j)  +/-  (1.4e-60, 3.09e-182j)
| (4.4127607752859155258e-19 + 1.1858862783995916413e-962j)  +/-  (1.81e-73, 3.99e-195j)
| (1.6533235907327201917e-14 - 3.5816619573779577143e-960j)  +/-  (3.23e-74, 7.13e-196j)
| (6.6239383250146396002e-22 - 2.0799003860384780359e-964j)  +/-  (1.11e-74, 2.45e-196j)
| (6.4744261851706348721e-07 - 2.4071896099692988781e-954j)  +/-  (7.57e-66, 1.67e-187j)
| (2.8220200211641973062e-25 - 8.0047007085392436476e-967j)  +/-  (6.27e-81, 1.38e-202j)
| (0.00018681089838043865055 + 1.9812730978468458008e-951j)  +/-  (3.76e-60, 8.29e-182j)
| (1.2073606619639542245e-16 - 4.5775478753855297522e-961j)  +/-  (2.88e-73, 6.36e-195j)
| (0.00018681089838043865055 + 2.0989030596975521843e-952j)  +/-  (1.39e-61, 3.05e-183j)
| (6.366950444489051525e-39 - 4.0969218352142361145e-974j)  +/-  (5.08e-87, 1.12e-208j)
| (1.3807186620701763181e-29 + 2.8771791211260586191e-969j)  +/-  (3.5e-83, 7.72e-205j)
| (4.1946790102371706182e-05 - 5.2103017145370583142e-953j)  +/-  (5.53e-65, 1.22e-186j)
| (6.6239383250146396002e-22 + 7.5875689719206290386e-965j)  +/-  (3.56e-80, 7.85e-202j)
| (1.2073606619639542245e-16 + 1.3654944867536181165e-961j)  +/-  (1.15e-77, 2.54e-199j)
| (1.6533235907327201917e-14 + 1.359946405444139676e-959j)  +/-  (4.25e-77, 9.36e-199j)
| (0.012434556872160757104 + 2.0896679699046999265e-950j)  +/-  (1.2e-58, 2.64e-180j)
| (1.6915511092934892332e-09 + 3.5035961257840331793e-956j)  +/-  (2.68e-73, 5.91e-195j)
| (0.074824231588132128754 + 9.7901291613243981976e-950j)  +/-  (1.62e-56, 3.56e-178j)
| (5.9826712725258947294e-11 - 1.5643199710861491739e-957j)  +/-  (1.4e-74, 3.08e-196j)
| (6.4744261851706348721e-07 + 4.7412905583272428103e-953j)  +/-  (6.95e-73, 1.53e-194j)
| (4.3626772630732944057e-08 - 9.9185948353379844857e-954j)  +/-  (2.05e-74, 4.51e-196j)
| (0.030177139354607017545 - 7.6038976165297945929e-950j)  +/-  (1.83e-62, 4.03e-184j)
| (4.4127607752859155258e-19 - 3.9333453354207820732e-963j)  +/-  (7.74e-81, 1.71e-202j)
| (5.9826712725258947294e-11 + 8.3335974472376527215e-957j)  +/-  (1.28e-77, 2.81e-199j)
| (1.2771591026282451032e-12 + 7.7975931582606843382e-959j)  +/-  (3.07e-77, 6.76e-199j)
| (-1.9646922144713575335 + 4.5531573986773650807e-948j)  +/-  (4.22e-63, 9.3e-185j)
| (6.0540673341354600682e-09 - 4.4163024251071984585e-955j)  +/-  (1.61e-74, 3.55e-196j)
| (0.00075153343381923663835 - 4.1014610220233182018e-951j)  +/-  (3.46e-71, 7.62e-193j)
| (1.2771591026282451032e-12 - 3.441094351964268672e-958j)  +/-  (5.24e-79, 1.16e-200j)
| (0.57130799583326748052 - 1.1131005046893851224e-948j)  +/-  (9.13e-65, 2.01e-186j)
| (0.074824231588132128754 + 5.2868737409691016456e-950j)  +/-  (3.51e-66, 7.73e-188j)
| (6.0540673341354600682e-09 + 3.8805247798501322374e-954j)  +/-  (4.8e-76, 1.06e-197j)
| (6.3663171728239859856e-06 + 1.0737107887489922009e-953j)  +/-  (2.19e-74, 4.83e-196j)
| (0.012434556872160757104 + 5.6485842056582353047e-950j)  +/-  (5.49e-70, 1.21e-191j)
| (0.0029040265481560061617 + 9.0152126113901649412e-951j)  +/-  (4.93e-72, 1.09e-193j)
| (0.030177139354607017545 - 3.3099813287769394956e-950j)  +/-  (8.32e-70, 1.83e-191j)
| (1.6613920131082570847 - 3.5503984748420232475e-948j)  +/-  (1.44e-66, 3.17e-188j)
| (1.6915511092934892332e-09 - 2.3859443988870017663e-955j)  +/-  (2.47e-77, 5.44e-199j)
| (0.0029040265481560061617 + 2.0504120828875862641e-951j)  +/-  (7.34e-73, 1.62e-194j)
| (0.57130799583326748052 - 1.57412537525860883e-948j)  +/-  (3.93e-70, 8.66e-192j)
| (4.1946790102371706182e-05 - 9.8232892287638801689e-952j)  +/-  (1.06e-74, 2.35e-196j)
| (4.3626772630732944057e-08 + 9.4809620327153579285e-955j)  +/-  (9.01e-77, 1.99e-198j)
| (0.00075153343381923663835 - 6.6271379823513147844e-952j)  +/-  (8.59e-74, 1.89e-195j)
| (0.0084624235657974872881 - 2.4828838044240154451e-950j)  +/-  (3.88e-73, 8.55e-195j)
| (1.6613920131082570847 - 4.6781258145511135198e-948j)  +/-  (4.54e-72, 1e-193j)
| (-1.9646922144713575335 + 6.1095084353393440374e-948j)  +/-  (5.83e-72, 1.28e-193j)
| (0.20440494257074916588 + 1.5857946223839995585e-949j)  +/-  (1.42e-73, 3.68e-195j)
