Starting with polynomial:
P : t
Extension levels are: 1 2 64
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 64 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^67 - 831261416000492318129199596114803363/387634576082751948649051473144961*t^65 + 837681295653300880907160240510341873200/387634576082751948649051473144961*t^63 - 17027865091987884770159010922287053226480/12504341163959740279001660424031*t^61 + 7532473511179826351379952983189544155460200/12504341163959740279001660424031*t^59 - 2489401909777671872865040628239890971545544760/12504341163959740279001660424031*t^57 + 638716908151875506764571117938197102202634015280/12504341163959740279001660424031*t^55 - 130521509832827441227193788816486580124516769962000/12504341163959740279001660424031*t^53 + 21624917804222849828526388537092646921640383243196100/12504341163959740279001660424031*t^51 - 2942063284796666161636391651327276392384639988562007500/12504341163959740279001660424031*t^49 + 331702153965823203073629683364211909774338540478137138000/12504341163959740279001660424031*t^47 - 663691482700894973399350299658520969408872601902890042000/266049811999143410191524689873*t^45 + 52290473086543168080691679063329405516390581081498200625000/266049811999143410191524689873*t^43 - 3461018320137464482531621033812480034158761751763476878835000/266049811999143410191524689873*t^41 + 192691796064115321596402196492577927030759510329621810010850000/266049811999143410191524689873*t^39 - 9023740157411135826696615239346989103231673831964140442797110000/266049811999143410191524689873*t^37 + 354999045152738324656851292082861165938861834407971604482798823750/266049811999143410191524689873*t^35 - 11703471718863334218460959118976636865949683594615255206195878031250/266049811999143410191524689873*t^33 + 322137987816504260835342275108225232438483287558577458161151385450000/266049811999143410191524689873*t^31 - 7365946022318583359845307024621481016643988063101313425124158532750000/266049811999143410191524689873*t^29 + 139014169769613854401550338574153598665058389419324276833083546800425000/266049811999143410191524689873*t^27 - 2147779618354396370284884358881923217856075296492850180418451574309275000/266049811999143410191524689873*t^25 + 26891409338798821205857775476307053258779005043192783382573143632493750000/266049811999143410191524689873*t^23 - 269444062700414610986138406646466689014726816476313707353841423768471250000/266049811999143410191524689873*t^21 + 2126972948397869151193611226718613181600240052928184478119559841320723437500/266049811999143410191524689873*t^19 - 12970762781463035520808217943719596986759883957950188275548169416724492312500/266049811999143410191524689873*t^17 + 59594313886165840863595783582654140551803120374097572385506259021495082250000/266049811999143410191524689873*t^15 - 199661625782298210652552173967201940800447142910319169017145747844070368750000/266049811999143410191524689873*t^13 + 466795419401245802375264932814705242767481230257149764633494217636481044375000/266049811999143410191524689873*t^11 - 715740784667213974897003899938418499618132938555113349738432182351354353125000/266049811999143410191524689873*t^9 + 655415894219167920553930547239426950026492804360827747447733156125741863750000/266049811999143410191524689873*t^7 - 306154831728750338576147893729283410023733797792448676754719405226678341250000/266049811999143410191524689873*t^5 + 52599453513911236492828910475681506763257525922927774822481923844893931640625/266049811999143410191524689873*t^3 - 865956555689817470964691287360177081281658185065030741737639414222807421875/266049811999143410191524689873*t
-------------------------------------------------
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: 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
-------------------------------------------------
The nodes are:
| (14.251654706260264837 + 1.5484112863963043087e-1218j)  +/-  (7.4e-498, 7.4e-498j)
| (12.258480159749387177 - 4.3731288572259636203e-1217j)  +/-  (1.58e-495, 1.58e-495j)
| (-13.517467868553004567 + 5.1187012181815269103e-1215j)  +/-  (7.43e-497, 7.43e-497j)
| (-15.138909876236824208 + 3.5287877403369947401e-1223j)  +/-  (3e-499, 3e-499j)
| (13.517467868553004567 + 1.578819500526175438e-1225j)  +/-  (7e-497, 7e-497j)
| (-14.251654706260264837 + 6.1236763148117887521e-1225j)  +/-  (7.21e-498, 7.21e-498j)
| (10.633588956058044741 - 5.6742196024986500122e-1229j)  +/-  (1.75e-494, 1.75e-494j)
| (8.2653743014132014537 + 9.357600211148062448e-1229j)  +/-  (1.86e-494, 1.86e-494j)
| (11.690976190683969114 + 1.5090870201827624753e-1231j)  +/-  (4.53e-495, 4.53e-495j)
| (9.6493374565077260007 + 4.1028117575840219762e-1229j)  +/-  (2.76e-494, 2.76e-494j)
| (15.138909876236824208 - 8.7863335429862495405e-1236j)  +/-  (2.88e-499, 2.88e-499j)
| (11.151257348604364279 - 4.1183909745447391827e-1231j)  +/-  (9.59e-495, 9.59e-495j)
| (12.862472493446085953 + 6.4157992013365343529e-1232j)  +/-  (3.88e-496, 3.88e-496j)
| (10.133939606135489568 - 7.0852020491693484273e-1230j)  +/-  (2.35e-494, 2.35e-494j)
| (3.689290707004242167 + 3.9249175929384774197e-1236j)  +/-  (6.3e-500, 6.3e-500j)
| (2.9018584708585793782 - 1.6615344610145838872e-1238j)  +/-  (1.27e-501, 1.27e-501j)
| (9.1775103367549721202 - 1.2653546622880315756e-1229j)  +/-  (2.9e-494, 2.9e-494j)
| (2.510731111209760529 - 4.8658865423821408669e-1239j)  +/-  (1.33e-502, 1.33e-502j)
| (3.2946101219049973046 + 4.3275816129997236097e-1237j)  +/-  (8.77e-501, 8.77e-501j)
| (5.2937294061147807023 - 7.1471678607189398397e-1233j)  +/-  (3.94e-497, 3.94e-497j)
| (8.7166698135074944257 - 7.6868215991341632474e-1231j)  +/-  (2.26e-494, 2.26e-494j)
| (-1.3436717508191779261 - 7.2938368860358799533e-1243j)  +/-  (8.86e-506, 8.86e-506j)
| (4.8880723725337388207 + 3.8522130394336213134e-1234j)  +/-  (9.36e-498, 9.36e-498j)
| (2.1209133977440349701 - 7.2869227175780706826e-1240j)  +/-  (1.36e-503, 1.36e-503j)
| (-0.95492570697610237186 + 7.2831288265292612382e-1244j)  +/-  (5.26e-507, 5.26e-507j)
| (3.4886929588565353955e-1266 + 1.4118780400052081968e-1265j)  +/-  (9.74e-1264, 9.74e-1264j)
| (6.9578283427532594384 - 3.414008969896981597e-1231j)  +/-  (2.75e-495, 2.75e-495j)
| (6.1165179489022495525 + 4.2660108542712059069e-1232j)  +/-  (4.19e-496, 4.19e-496j)
| (7.3868703662770951461 - 5.0962310761417157029e-1230j)  +/-  (5.66e-495, 5.66e-495j)
| (4.0862094247820806458 - 8.0364700672799138423e-1238j)  +/-  (3.53e-499, 3.53e-499j)
| (1.7320508075688772935 + 6.9195255322567001186e-1242j)  +/-  (1.24e-504, 1.24e-504j)
| (7.8224383604935480496 - 2.1920623533035801127e-1231j)  +/-  (1.09e-494, 1.09e-494j)
| (0.95492570697610237186 + 5.6938342337683513857e-1247j)  +/-  (5.62e-507, 5.62e-507j)
| (4.4856889645288570446 - 2.33088147992986671e-1239j)  +/-  (1.89e-498, 1.89e-498j)
| (-0.56321340438818642218 - 1.6194895388266834277e-1248j)  +/-  (2.76e-508, 2.76e-508j)
| (-0.1354513001123270514 + 3.029900427211629301e-1265j)  +/-  (1.32e-509, 1.32e-509j)
| (1.3436717508191779261 + 1.9243660119111906337e-1245j)  +/-  (8.58e-506, 8.58e-506j)
| (0.56321340438818642218 - 1.5383985852520116566e-1247j)  +/-  (2.89e-508, 2.89e-508j)
| (6.5345878286524225028 + 6.1432515791773052816e-1234j)  +/-  (1.13e-495, 1.13e-495j)
| (5.7030632157620226046 - 2.0349301132363427849e-1235j)  +/-  (1.26e-496, 1.26e-496j)
| (0.1354513001123270514 + 8.2658145334315273452e-1257j)  +/-  (2.08e-509, 2.08e-509j)
| (-11.690976190683969114 - 1.3610954420070280757e-1250j)  +/-  (4.13e-495, 4.13e-495j)
| (-8.7166698135074944257 + 5.2015967722575743784e-1313j)  +/-  (2.46e-494, 2.46e-494j)
| (-12.258480159749387177 + 3.3246722461118446582e-1402j)  +/-  (1.55e-495, 1.55e-495j)
| (-7.3868703662770951461 + 5.5964680782223232996e-1471j)  +/-  (5.94e-495, 5.94e-495j)
| (-8.2653743014132014537 + 9.6619048854314630319e-1523j)  +/-  (1.79e-494, 1.79e-494j)
| (-2.9018584708585793782 - 1.3125211330567050005e-1562j)  +/-  (1.18e-501, 1.18e-501j)
| (-10.133939606135489568 + 1.0480534059363605134e-1566j)  +/-  (2.31e-494, 2.31e-494j)
| (-9.1775103367549721202 - 3.9103419625701503792e-1603j)  +/-  (2.95e-494, 2.95e-494j)
| (-2.1209133977440349701 + 1.6792687840068099123e-1632j)  +/-  (1.55e-503, 1.55e-503j)
| (-7.8224383604935480496 + 2.1082162299530601814e-1622j)  +/-  (1.14e-494, 1.14e-494j)
| (-4.4856889645288570446 - 4.4622097917915106318e-1632j)  +/-  (1.9e-498, 1.9e-498j)
| (-10.633588956058044741 - 2.8075421434556746822e-1627j)  +/-  (1.74e-494, 1.74e-494j)
| (-11.151257348604364279 + 3.9157249842144550444e-1629j)  +/-  (1e-494, 1e-494j)
| (-6.1165179489022495525 - 7.2684102982743662061e-1636j)  +/-  (4.37e-496, 4.37e-496j)
| (-12.862472493446085953 - 4.6790682792867423409e-1640j)  +/-  (3.92e-496, 3.92e-496j)
| (-4.0862094247820806458 - 6.3967208418957171811e-1650j)  +/-  (3.83e-499, 3.83e-499j)
| (-9.6493374565077260007 + 4.8495432250270847005e-1643j)  +/-  (2.82e-494, 2.82e-494j)
| (-5.2937294061147807023 + 4.7137065938768093942e-1650j)  +/-  (3.7e-497, 3.7e-497j)
| (-2.510731111209760529 + 1.7577275565435369602e-1662j)  +/-  (1.38e-502, 1.38e-502j)
| (-3.689290707004242167 - 2.7466851061952712191e-1659j)  +/-  (5.58e-500, 5.58e-500j)
| (-4.8880723725337388207 + 7.0527963170388783603e-1656j)  +/-  (8.82e-498, 8.82e-498j)
| (-5.7030632157620226046 - 3.2703402117807820618e-1657j)  +/-  (1.39e-496, 1.39e-496j)
| (-6.9578283427532594384 - 1.0069743157491958127e-1677j)  +/-  (2.81e-495, 2.81e-495j)
| (-3.2946101219049973046 - 7.2452423834543459751e-1708j)  +/-  (9.05e-501, 9.05e-501j)
| (-6.5345878286524225028 + 3.7263236467730797384e-1700j)  +/-  (1.27e-495, 1.27e-495j)
| (-1.7320508075688772935 - 3.1002139255957411143e-1722j)  +/-  (1.17e-504, 1.17e-504j)
-------------------------------------------------
The weights are:
| (2.4786682123243914031e-45 + 2.186814967621857829e-1256j)  +/-  (1.34e-146, 1.76e-393j)
| (5.451267299338619871e-34 + 1.4810118749704918484e-1249j)  +/-  (2.31e-142, 3.04e-389j)
| (5.7666695760752750078e-41 + 2.2894829225370628022e-1254j)  +/-  (1.33e-146, 1.75e-393j)
| (6.991078929377198477e-51 + 7.3179351833439307505e-1261j)  +/-  (3.44e-150, 4.54e-397j)
| (5.7666695760752750078e-41 - 5.5735991100358193501e-1254j)  +/-  (4.02e-146, 5.29e-393j)
| (2.4786682123243914031e-45 + 8.5181733792458568467e-1258j)  +/-  (2.49e-148, 3.28e-395j)
| (5.6664981537576829792e-26 - 1.7296783301947128423e-1246j)  +/-  (9.31e-141, 1.23e-387j)
| (2.6087651000451208041e-16 + 6.0378815476926127137e-1242j)  +/-  (1.32e-135, 1.74e-382j)
| (4.610674065130485141e-31 - 1.2822598656188755438e-1248j)  +/-  (4.95e-143, 6.52e-390j)
| (1.1526918323900694185e-21 - 1.6972249567183707927e-1244j)  +/-  (2.01e-139, 2.65e-386j)
| (6.991078929377198477e-51 - 2.3894262962779049928e-1259j)  +/-  (5.67e-152, 7.47e-399j)
| (2.0945541006895244756e-28 + 1.4700834986216372493e-1247j)  +/-  (2.54e-142, 3.35e-389j)
| (2.9661340877963275079e-37 + 8.765547605862726421e-1252j)  +/-  (3.12e-146, 4.11e-393j)
| (9.8241788492863328706e-24 + 1.829814491992570506e-1245j)  +/-  (9.74e-141, 1.28e-387j)
| (0.0001748904041694437834 - 5.3267903083664772264e-1236j)  +/-  (4.08e-124, 5.38e-371j)
| (0.0023201866108183870627 - 2.2685873164314461768e-1235j)  +/-  (1.94e-119, 2.56e-366j)
| (9.5447590006175433949e-20 + 1.3777568431471689917e-1243j)  +/-  (4.54e-140, 5.99e-387j)
| (0.0066618321792893248316 + 4.2731066128961570969e-1235j)  +/-  (2.7e-117, 3.56e-364j)
| (0.00069027489932066374605 + 1.1354698186319955383e-1235j)  +/-  (2.83e-122, 3.74e-369j)
| (1.3357239204764073974e-07 - 1.2448655037161919987e-1237j)  +/-  (8.73e-133, 1.15e-379j)
| (5.7651937798019884231e-18 - 9.8490804625143148182e-1243j)  +/-  (4.98e-140, 6.56e-387j)
| (0.062819767088282610268 - 1.7969562471213658356e-1234j)  +/-  (8.49e-112, 1.12e-358j)
| (1.0444569249825067748e-06 + 3.5461574593023110402e-1237j)  +/-  (1.34e-131, 1.77e-378j)
| (0.016382461408902248736 - 7.6428237887622411804e-1235j)  +/-  (4.4e-118, 5.8e-365j)
| (0.098484621188864707533 + 3.2536267264747892347e-1234j)  +/-  (8.05e-114, 1.06e-360j)
| (-0.19235722887536643744 - 7.6202229465084531516e-1233j)  +/-  (2.33e-114, 3.07e-361j)
| (5.2233926704025249807e-12 - 7.8810681553728611852e-1240j)  +/-  (2.46e-138, 3.24e-385j)
| (1.2468001771060783606e-09 - 1.2208748791911854779e-1238j)  +/-  (1.45e-136, 1.92e-383j)
| (2.4419990414027584415e-13 + 1.7820600735868487624e-1240j)  +/-  (1.94e-139, 2.56e-386j)
| (3.7602721219311726615e-05 + 2.3298624945918619133e-1236j)  +/-  (6.86e-131, 9.05e-378j)
| (0.034584984313738162516 + 1.3123114290415800416e-1234j)  +/-  (1.19e-120, 1.57e-367j)
| (9.038920306494231361e-15 - 3.3807535692621731721e-1241j)  +/-  (2e-140, 2.64e-387j)
| (0.098484621188864707533 + 3.7606922646926334319e-1234j)  +/-  (5.66e-119, 7.46e-366j)
| (6.8329526812277292295e-06 - 9.4636817845757573078e-1237j)  +/-  (1.12e-132, 1.48e-379j)
| (0.13472953211233735204 - 6.6580233089888856269e-1234j)  +/-  (1.48e-118, 1.94e-365j)
| (0.23928443498361862096 + 4.2373334473949294977e-1233j)  +/-  (4.23e-118, 5.58e-365j)
| (0.062819767088282610268 - 2.2039183932121431947e-1234j)  +/-  (8.52e-121, 1.12e-367j)
| (0.13472953211233735204 - 7.2510595740918964458e-1234j)  +/-  (2.38e-119, 3.14e-366j)
| (8.9611884850271102454e-11 + 3.1938400701651705393e-1239j)  +/-  (3.02e-138, 3.98e-385j)
| (1.4203235167447204253e-08 + 4.1728483764303345923e-1238j)  +/-  (2.42e-136, 3.19e-383j)
| (0.23928443498361862096 + 4.3251329104800602038e-1233j)  +/-  (4.11e-120, 5.41e-367j)
| (4.610674065130485141e-31 - 4.7041692286665852953e-1250j)  +/-  (3.96e-168, 5.22e-415j)
| (5.7651937798019884231e-18 - 1.9440419412587078266e-1243j)  +/-  (4.25e-163, 5.6e-410j)
| (5.451267299338619871e-34 + 1.7665956125770051538e-1251j)  +/-  (3.68e-169, 4.85e-416j)
| (2.4419990414027584415e-13 + 4.8324258395109801933e-1241j)  +/-  (7.69e-161, 1.01e-407j)
| (2.6087651000451208041e-16 + 1.3863644452014168142e-1242j)  +/-  (1.62e-162, 2.14e-409j)
| (0.0023201866108183870627 - 1.4516118463319732957e-1235j)  +/-  (1.99e-147, 2.63e-394j)
| (9.8241788492863328706e-24 + 2.2079200634927532717e-1246j)  +/-  (5.13e-167, 6.76e-414j)
| (9.5447590006175433949e-20 + 2.3717633727313039056e-1244j)  +/-  (5.79e-165, 7.63e-412j)
| (0.016382461408902248736 - 5.5282432250772879538e-1235j)  +/-  (1.17e-145, 1.54e-392j)
| (9.038920306494231361e-15 - 8.6913642305380499209e-1242j)  +/-  (1.51e-162, 1.99e-409j)
| (6.8329526812277292295e-06 - 4.6917220158813674075e-1237j)  +/-  (3.25e-157, 4.28e-404j)
| (5.6664981537576829792e-26 - 1.6309978724525668981e-1247j)  +/-  (1.88e-168, 2.47e-415j)
| (2.0945541006895244756e-28 + 9.8163434294007946888e-1249j)  +/-  (1.36e-169, 1.79e-416j)
| (1.2468001771060783606e-09 - 4.3392012385965789699e-1239j)  +/-  (8.24e-163, 1.09e-409j)
| (2.9661340877963275079e-37 - 5.5049133546534864502e-1253j)  +/-  (9.61e-174, 1.27e-420j)
| (3.7602721219311726615e-05 + 1.2319212317057905436e-1236j)  +/-  (4.91e-159, 6.47e-406j)
| (1.1526918323900694185e-21 - 2.4867365945466833214e-1245j)  +/-  (5.64e-167, 7.43e-414j)
| (1.3357239204764073974e-07 - 5.3605363426096091609e-1238j)  +/-  (4.79e-162, 6.31e-409j)
| (0.0066618321792893248316 + 2.9083521822851681971e-1235j)  +/-  (3.08e-156, 4.06e-403j)
| (0.0001748904041694437834 - 3.0028408076759890823e-1236j)  +/-  (2.82e-159, 3.72e-406j)
| (1.0444569249825067748e-06 + 1.6523379435466202578e-1237j)  +/-  (1.78e-161, 2.34e-408j)
| (1.4203235167447204253e-08 + 1.5956123777253395749e-1238j)  +/-  (3.05e-163, 4.02e-410j)
| (5.2233926704025249807e-12 - 2.4010338129196015048e-1240j)  +/-  (9.41e-166, 1.24e-412j)
| (0.00069027489932066374605 + 6.8226898759706910496e-1236j)  +/-  (3.99e-161, 5.26e-408j)
| (8.9611884850271102454e-11 + 1.0731084079200305538e-1239j)  +/-  (3.78e-165, 4.98e-412j)
| (0.034584984313738162516 + 1.0080704903321917297e-1234j)  +/-  (9.1e-160, 1.2e-406j)
