Starting with polynomial:
P : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Extension levels are: 3 28
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P1 : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -1/6*t^31 + 17694833258112594148144259583071558749770837774895662089592190790891/121237738599720803700319730735352471616669226031815139541047685842*t^30 - 1206349592142792952576026375543821429833322052369666526717108110827565/20206289766620133950053288455892078602778204338635856590174614307*t^29 + 450911501735356992693217834038914593635328109190306174140190946332694519/29715132009735491103019541846900115592320888733288024397315609275*t^28 - 1358604173472146501958421363242341745956060314950331352869074309374165414732/505157244165503348751332211397301965069455108465896414754365357675*t^27 + 178627750273779836895355267646927605716593256339236222004232173499632857121564/505157244165503348751332211397301965069455108465896414754365357675*t^26 - 1392064643375242404726970037075671763546382477006581072786725207538542695724776/38858249551192565288564016261330920389958085266607416519566565975*t^25 + 4457374800181555200305382805247943473565523711284963425828514732953985337488600/1554329982047702611542560650453236815598323410664296660782662639*t^24 - 286860435045475908465736259123348591254349168671360182566298421630101694062198720/1554329982047702611542560650453236815598323410664296660782662639*t^23 + 883772448992192879192922021097514836928471762204695764043131558190419228176149440/91431175414570741855444744144308047976371965333193921222509567*t^22 - 645887882956517499243893615612022896806320118151517456363938142881882025839259941760/1554329982047702611542560650453236815598323410664296660782662639*t^21 + 22925514656010104702532680962254745646553543591325403716164627711156723892758358139520/1554329982047702611542560650453236815598323410664296660782662639*t^20 - 674361441084853628322151701918474238002221101019468167017468575074401878073562379712000/1554329982047702611542560650453236815598323410664296660782662639*t^19 + 16471217010216607929730921493983925122372510005990842251633073087121853841066992050163200/1554329982047702611542560650453236815598323410664296660782662639*t^18 - 334189821460761330797078808913448605741081146963790254586314957399587085783439145210188800/1554329982047702611542560650453236815598323410664296660782662639*t^17 + 330980930721580466794450972590738121220946677893787703229612704092097600100567328461900800/91431175414570741855444744144308047976371965333193921222509567*t^16 - 4613273623234903402010365681278998455396288501839321540168368151125709719083018180751769600/91431175414570741855444744144308047976371965333193921222509567*t^15 + 53028039578836387448467647024763360599724839324627870286088262512870439160720028223805440000/91431175414570741855444744144308047976371965333193921222509567*t^14 - 500003834122951046438184586300051539445251153645027445921923859084669566108661888069103616000/91431175414570741855444744144308047976371965333193921222509567*t^13 + 3840126717167618191579152250573370920962889933704823653209078336615931344731333766893522944000/91431175414570741855444744144308047976371965333193921222509567*t^12 - 23805056997491735552721886440974192602871925764628614818706661819167151401754750734513553408000/91431175414570741855444744144308047976371965333193921222509567*t^11 + 117732900106059605408257254246391889587484603048404959359086804973823144433103579020373016576000/91431175414570741855444744144308047976371965333193921222509567*t^10 - 457703189028720719908800388993037040816056122033452099057716381933623470480065763926578790400000/91431175414570741855444744144308047976371965333193921222509567*t^9 + 1372211891255621989276454665655116947826922269755109603524514054102658964543703979157076869120000/91431175414570741855444744144308047976371965333193921222509567*t^8 - 3094199298790022424041451799000372271077116615466049525487680166254498761166776283253622702080000/91431175414570741855444744144308047976371965333193921222509567*t^7 + 5075173969305435627352275568714228163317564039610998896686517538920313250316462077499884175360000/91431175414570741855444744144308047976371965333193921222509567*t^6 - 5782660656446225062753959604403356191780212678218365275174332136920358545104045608661111275520000/91431175414570741855444744144308047976371965333193921222509567*t^5 + 4283139299582315045495794938599502334552706027448383974655022775521476004474093020943286272000000/91431175414570741855444744144308047976371965333193921222509567*t^4 - 1861731639821596748449996584736571517496431349565260311569071181534471453885669877387551047680000/91431175414570741855444744144308047976371965333193921222509567*t^3 + 397935501484882796210241731873267489070155662970556164769194802710265526218265677917973381120000/91431175414570741855444744144308047976371965333193921222509567*t^2 - 28509537785313929327781102306876166805187472495924460556533868609821121529009124166850314240000/91431175414570741855444744144308047976371965333193921222509567*t + 82652741226836650112039942608612585864619801988375052242960071203366479070701431637934080000/91431175414570741855444744144308047976371965333193921222509567
-------------------------------------------------
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: 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:
| (102.22608982603566836 - 3.880152903383948757e-570j)  +/-  (4.38e-244, 4.38e-244j)
| (47.025595131021783467 + 2.628437287901667504e-575j)  +/-  (5.85e-240, 5.85e-240j)
| (79.958137246129270831 + 7.332614659435327487e-586j)  +/-  (6.73e-242, 6.73e-242j)
| (89.707320548045816039 - 6.0235814884915054476e-600j)  +/-  (8.05e-243, 8.05e-243j)
| (71.727366311668661716 + 6.3104442323277554463e-621j)  +/-  (3.18e-241, 3.18e-241j)
| (12.739514992267032547 - 2.5766788566163823686e-637j)  +/-  (2.12e-242, 2.12e-242j)
| (37.749757996951597714 - 1.1724562714813233884e-660j)  +/-  (6.49e-240, 6.49e-240j)
| (42.191496399687205667 - 4.0440488831693176791e-682j)  +/-  (6.74e-240, 6.74e-240j)
| (6.1158075622247380276 + 6.6058042570321591534e-698j)  +/-  (2.15e-243, 2.15e-243j)
| (64.528198593988761291 + 3.1297917526803671309e-694j)  +/-  (9.85e-241, 9.85e-241j)
| (4.4376801255037770793 - 6.6034712441483322138e-720j)  +/-  (5.41e-246, 5.41e-246j)
| (26.405793730719192607 - 5.3409740596563503442e-715j)  +/-  (1.99e-240, 1.99e-240j)
| (33.658925672986243396 - 1.7636485966915456972e-731j)  +/-  (4.99e-240, 4.99e-240j)
| (3.2687482192458845516 - 1.0609887263969010921e-756j)  +/-  (3.26e-247, 3.26e-247j)
| (52.3061153495492127 - 1.3557424300820765921e-749j)  +/-  (4.08e-240, 4.08e-240j)
| (1.4974057585773198175 - 5.9635504279952733337e-771j)  +/-  (9.66e-250, 9.66e-250j)
| (2.2942803602790417198 + 1.7283975542505781736e-769j)  +/-  (1.7e-248, 1.7e-248j)
| (8.751321848982299842 - 5.6510643930149004066e-765j)  +/-  (1.92e-243, 1.92e-243j)
| (29.886356971308497769 + 4.7456823227241450989e-761j)  +/-  (3.69e-240, 3.69e-240j)
| (23.195733900445337114 + 7.6684046718885980299e-774j)  +/-  (1.03e-240, 1.03e-240j)
| (6.7889256736657545994 - 4.3423919709262492085e-789j)  +/-  (2.1e-243, 2.1e-243j)
| (0.87226329595066717682 - 8.627692674243515052e-800j)  +/-  (4.61e-251, 4.61e-251j)
| (0.1261228766299679159 - 2.4715930760735153219e-801j)  +/-  (5.05e-254, 5.05e-254j)
| (0.0030250600793372693843 - 1.4033502769669692903e-803j)  +/-  (3.42e-256, 3.42e-256j)
| (58.105999005893008277 + 1.3837743546351138697e-786j)  +/-  (2.29e-240, 2.29e-240j)
| (10.656157305266601798 - 3.6154639882214808839e-796j)  +/-  (6.17e-243, 6.17e-243j)
| (0.41577455678347908331 - 7.4604155093922904713e-805j)  +/-  (2.1e-252, 2.1e-252j)
| (6.2899450829374791969 - 6.9091848286429177124e-797j)  +/-  (3.51e-243, 3.51e-243j)
| (17.518316495677815827 - 2.0294933476624982178e-793j)  +/-  (1.82e-241, 1.82e-241j)
| (20.238286994480191252 + 4.9884834041088317589e-801j)  +/-  (4.73e-241, 4.73e-241j)
| (15.022707988238170922 - 3.6906070177352197225e-808j)  +/-  (6.41e-242, 6.41e-242j)
-------------------------------------------------
The weights are:
| (5.9967145564343748194e-44 - 6.8257374819531677337e-609j)  +/-  (2.6e-100, 1.86e-217j)
| (1.905794862547527701e-20 - 2.6278898463575960322e-595j)  +/-  (5.9e-91, 4.21e-208j)
| (1.6705957758932897463e-34 - 7.8665768475436959319e-604j)  +/-  (1.48e-97, 1.06e-214j)
| (1.1855376894297696889e-38 + 4.5149040031726367549e-606j)  +/-  (4.51e-99, 3.22e-216j)
| (5.4129483299837508735e-31 + 6.7218495841482991346e-602j)  +/-  (1.26e-96, 8.96e-214j)
| (6.396538734171001011e-06 - 1.7124606340683405668e-588j)  +/-  (3.6e-80, 2.57e-197j)
| (1.7175892550238547761e-16 - 6.6429638833994696545e-594j)  +/-  (6.2e-91, 4.43e-208j)
| (2.1981524139971259419e-18 + 1.263129610040781687e-594j)  +/-  (7.75e-92, 5.53e-209j)
| (0.018251454998517099502 + 2.486211108660691921e-585j)  +/-  (5.34e-76, 3.81e-193j)
| (6.410897780878611255e-28 - 3.6690428993407116111e-600j)  +/-  (1.57e-96, 1.12e-213j)
| (0.015161303454094054188 - 2.1996883750568700666e-586j)  +/-  (2.93e-74, 2.09e-191j)
| (1.1379518072235902678e-11 + 1.205037822342136438e-591j)  +/-  (2.02e-89, 1.44e-206j)
| (9.4658448773747418902e-15 + 3.9355692220209812064e-593j)  +/-  (5.9e-91, 4.21e-208j)
| (0.040598397617634577757 + 2.1830549133278791225e-586j)  +/-  (3.4e-75, 2.42e-192j)
| (1.062077189396233183e-22 - 6.2673545727632580294e-597j)  +/-  (4.71e-95, 3.36e-212j)
| (0.15891215464410540849 + 2.6436145852991912336e-586j)  +/-  (4.2e-72, 2.99e-189j)
| (0.089166982402344902313 - 2.4090143450915511856e-586j)  +/-  (2.42e-74, 1.72e-191j)
| (0.00028995621888811626496 - 2.7805062778982915621e-587j)  +/-  (4.6e-83, 3.28e-200j)
| (3.7979052021013728672e-13 - 2.2562570162271997693e-592j)  +/-  (1.31e-90, 9.33e-208j)
| (2.5996578125371880985e-10 - 5.9355396463399261476e-591j)  +/-  (8.15e-90, 5.82e-207j)
| (0.0042698872611536688947 + 6.6532334473829080049e-586j)  +/-  (1.65e-82, 1.18e-199j)
| (0.22590179811850040966 - 2.7560280967441536946e-586j)  +/-  (9e-77, 6.42e-194j)
| (0.18211736866135139222 - 2.1424267329644394852e-586j)  +/-  (4.59e-77, 3.28e-194j)
| (0.036538301050709246367 + 8.9633408538611613878e-587j)  +/-  (3.57e-77, 2.55e-194j)
| (3.5444002154232171524e-25 + 1.5319478784923206072e-598j)  +/-  (7.06e-97, 5.04e-214j)
| (4.6845780562539973305e-05 + 6.5029336232906399765e-588j)  +/-  (5.73e-86, 4.09e-203j)
| (0.24601512337402212488 + 2.629418108020075191e-586j)  +/-  (1.18e-79, 8.41e-197j)
| (-0.017276753170292224036 - 3.0134053700890263395e-585j)  +/-  (3.71e-82, 2.65e-199j)
| (6.4242454546196725773e-08 - 1.1378765360265862373e-589j)  +/-  (1.5e-89, 1.07e-206j)
| (4.606677475293284905e-09 + 2.6973178924105560622e-590j)  +/-  (2.8e-90, 2e-207j)
| (7.1392880776136286778e-07 + 4.5082915743248257602e-589j)  +/-  (7.47e-89, 5.33e-206j)
