Starting with polynomial:
P : t^18 - 153*t^16 + 9180*t^14 - 278460*t^12 + 4594590*t^10 - 41351310*t^8 + 192972780*t^6 - 413513100*t^4 + 310134825*t^2 - 34459425
Extension levels are: 18 33
-------------------------------------------------
Trying to find an order 33 Kronrod extension for:
P1 : t^18 - 153*t^16 + 9180*t^14 - 278460*t^12 + 4594590*t^10 - 41351310*t^8 + 192972780*t^6 - 413513100*t^4 + 310134825*t^2 - 34459425
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^51 - 71547698195435934369476187/72793935863433752742211*t^49 + 355668724156569551306571602772/800733294497771280164321*t^47 - 98210759565797506769764628219700/800733294497771280164321*t^45 + 18573948884674293101412429456759690/800733294497771280164321*t^43 - 48565546268582086174026600039343247310/15213932595457654323122099*t^41 + 5043529301737902490780374039920531303580/15213932595457654323122099*t^39 - 404558754112151559152421817251974048915580/15213932595457654323122099*t^37 + 25447801240960878065108769740237069867602725/15213932595457654323122099*t^35 - 115220424384835513586115970825959192326867175/1383084781405241302102009*t^33 + 4568890510001701328492401668629850877806882600/1383084781405241302102009*t^31 - 144573298593476428894708646510567626659403521000/1383084781405241302102009*t^29 + 125813414049307306851569504197663530205300741500/47692578669146251796621*t^27 - 132861295133014483470171570065093936547369760500/2510135719428750094559*t^25 + 40037178055338635657443030152567082978733320425000/47692578669146251796621*t^23 - 21638387377949779000295167896103834895655955095000/2073590376919402252027*t^21 + 208359344221314320511730958044492811027536216993125/2073590376919402252027*t^19 - 80540953807645341964665301576408244628937671369375/109136335627336960633*t^17 + 442095779148545398551956792518935280456796964862500/109136335627336960633*t^15 - 1765717528008318936910699042614995919712792787962500/109136335627336960633*t^13 + 4950136880158251658856969533949315580098320998356250/109136335627336960633*t^11 - 9268211260298658395768716090064565724272198190706250/109136335627336960633*t^9 + 10781439585503510265225161079773800957914025602862500/109136335627336960633*t^7 - 6958635884462991453414664474603037306884736286562500/109136335627336960633*t^5 + 2038130691576074271044873485498626291159256795640625/109136335627336960633*t^3 - 170915607399458308193589906631238400147868030265625/109136335627336960633*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:
| (8.1870960219037338458 - 1.4813744849408240929e-638j)  +/-  (2.89e-243, 2.89e-243j)
| (7.6105461560342129656 - 2.3735603917286840456e-637j)  +/-  (7.8e-243, 7.8e-243j)
| (-11.890626017948953904 + 3.7802916726700179009e-639j)  +/-  (8.89e-247, 8.89e-247j)
| (-8.1870960219037338458 + 1.7723928829218517903e-635j)  +/-  (3.07e-243, 3.07e-243j)
| (10.150292750654639305 + 3.0249045578619494426e-645j)  +/-  (9.55e-245, 9.55e-245j)
| (-10.150292750654639305 - 2.0001870733339530978e-641j)  +/-  (9.42e-245, 9.42e-245j)
| (-9.4460000696585672111 + 1.0104708008748053501e-649j)  +/-  (3.74e-244, 3.74e-244j)
| (6.5157037478316071685 - 2.9856185354183997915e-662j)  +/-  (6.01e-243, 6.01e-243j)
| (11.890626017948953904 - 1.2903461733300398101e-672j)  +/-  (8.98e-247, 8.98e-247j)
| (-8.7965219090344349579 + 8.6497719605926212561e-671j)  +/-  (1.25e-243, 1.25e-243j)
| (10.939024191809882418 - 8.9917203409592178534e-687j)  +/-  (1.31e-245, 1.31e-245j)
| (4.1880202316294037045 + 1.0932147699899242639e-684j)  +/-  (5.52e-245, 5.52e-245j)
| (4.6112192066757276621 + 3.348213459476441989e-683j)  +/-  (1.62e-244, 1.62e-244j)
| (-1.4670242498256063676 - 6.4325560971419540714e-697j)  +/-  (2.98e-250, 2.98e-250j)
| (7.1394648491464788756 - 1.5749102707187633182e-691j)  +/-  (3.94e-242, 3.94e-242j)
| (-6.5157037478316071685 + 1.1437107722763463817e-718j)  +/-  (6.28e-243, 6.28e-243j)
| (-10.939024191809882418 + 1.5754601219630895916e-738j)  +/-  (1.37e-245, 1.37e-245j)
| (8.7965219090344349579 - 1.2048497591996562727e-742j)  +/-  (1.22e-243, 1.22e-243j)
| (-2.5958336889112403291 + 1.3423613252031866275e-746j)  +/-  (1.48e-247, 1.48e-247j)
| (-4.6112192066757276621 + 3.4430684570676951165e-758j)  +/-  (1.69e-244, 1.69e-244j)
| (9.4460000696585672111 - 5.9299315610305378448e-775j)  +/-  (3.74e-244, 3.74e-244j)
| (3.7773911951558430068 + 8.064333374577414715e-785j)  +/-  (1.64e-245, 1.64e-245j)
| (-7.0219719120817213937 + 1.6075103521686010826e-801j)  +/-  (3.57e-242, 3.57e-242j)
| (-3.7773911951558430068 + 1.5697217569789289804e-826j)  +/-  (1.66e-245, 1.66e-245j)
| (-7.1394648491464788756 - 2.0602581405876450878e-837j)  +/-  (3.73e-242, 3.73e-242j)
| (5.5198209700352845941 + 1.601229739268027844e-855j)  +/-  (1.04e-243, 1.04e-243j)
| (2.5958336889112403291 - 6.3109071538057505344e-858j)  +/-  (1.51e-247, 1.51e-247j)
| (1.8397799215086454897 - 4.353707457740968947e-860j)  +/-  (2.45e-249, 2.45e-249j)
| (5.0540726854427398454 + 2.3587209066454206615e-854j)  +/-  (4.31e-244, 4.31e-244j)
| (-1.0983955180915012277 + 8.1741361655336795666e-861j)  +/-  (2.83e-251, 2.83e-251j)
| (7.0219719120817213937 - 3.4239714680970895823e-852j)  +/-  (3.74e-242, 3.74e-242j)
| (6.0077459113595975203 + 1.2588545099049193041e-853j)  +/-  (2.45e-243, 2.45e-243j)
| (1.4670242498256063676 + 2.5478557701953463466e-860j)  +/-  (3.08e-250, 3.08e-250j)
| (-6.0077459113595975203 - 1.9082250724641208832e-851j)  +/-  (2.4e-243, 2.4e-243j)
| (-7.6105461560342129656 - 2.3840823850030503531e-858j)  +/-  (8.6e-243, 8.6e-243j)
| (-0.36524575550769759592 - 4.4296776848097018822e-875j)  +/-  (9.63e-254, 9.63e-254j)
| (2.9807590889756190792 + 2.333108861199536694e-869j)  +/-  (7.73e-247, 7.73e-247j)
| (0.73150825738340078468 - 1.8408066474424913603e-874j)  +/-  (1.9e-252, 1.9e-252j)
| (2.2164049320365272931 - 1.2117944337622450773e-870j)  +/-  (1.98e-248, 1.98e-248j)
| (-1.8397799215086454897 - 1.5110121530617086624e-870j)  +/-  (2.77e-249, 2.77e-249j)
| (-2.2164049320365272931 - 3.4239922661977853672e-870j)  +/-  (1.98e-248, 1.98e-248j)
| (-4.1880202316294037045 + 1.8649282565746782374e-865j)  +/-  (5.2e-245, 5.2e-245j)
| (-0.73150825738340078468 + 3.7467507750619998502e-874j)  +/-  (1.9e-252, 1.9e-252j)
| (1.0983955180915012277 + 1.5774327583177030775e-874j)  +/-  (2.74e-251, 2.74e-251j)
| (-5.0540726854427398454 + 9.9386274144242742221e-864j)  +/-  (4.4e-244, 4.4e-244j)
| (-6.9285075019069811474e-903 - 1.8060408386782497628e-902j)  +/-  (9.87e-901, 9.87e-901j)
| (-3.3747365357780909953 - 2.1221451308276126212e-873j)  +/-  (4.15e-246, 4.15e-246j)
| (-5.5198209700352845941 - 1.6426103109625827271e-871j)  +/-  (1e-243, 1e-243j)
| (0.36524575550769759592 - 6.2139017034861445416e-893j)  +/-  (1.14e-253, 1.14e-253j)
| (3.3747365357780909953 - 2.8021293697030551241e-885j)  +/-  (3.88e-246, 3.88e-246j)
| (-2.9807590889756190792 - 2.5871129293797360961e-883j)  +/-  (8.01e-247, 8.01e-247j)
-------------------------------------------------
The weights are:
| (6.5835605101707188902e-16 + 1.4296317215317777933e-651j)  +/-  (8.43e-68, 5.19e-188j)
| (5.9126819259484427532e-14 + 6.8438630079062607966e-650j)  +/-  (3.09e-66, 1.9e-186j)
| (8.7084604756626214984e-32 + 4.1211799287478058193e-661j)  +/-  (1.46e-77, 8.98e-198j)
| (6.5835605101707188902e-16 + 7.0184038764046504155e-650j)  +/-  (4.6e-70, 2.83e-190j)
| (1.2517680139793147187e-23 - 6.7380282134076043006e-657j)  +/-  (1.53e-74, 9.42e-195j)
| (1.2517680139793147187e-23 + 5.1471152676439028026e-656j)  +/-  (1.18e-74, 7.26e-195j)
| (1.1322520533550885221e-20 - 5.5845913451714337041e-654j)  +/-  (3.48e-73, 2.14e-193j)
| (1.245228662890601536e-10 + 2.3344826145651570596e-648j)  +/-  (7.29e-67, 4.48e-187j)
| (8.7084604756626214984e-32 - 8.6751773554545187376e-662j)  +/-  (1.55e-79, 9.52e-200j)
| (3.9451901444990510484e-18 + 5.2912665435478998884e-652j)  +/-  (6.65e-73, 4.09e-193j)
| (3.5109490643464595678e-27 + 4.5533031522304296687e-659j)  +/-  (2.55e-77, 1.57e-197j)
| (2.5764212637389215706e-05 - 1.2312019211500608135e-644j)  +/-  (7.38e-62, 4.54e-182j)
| (4.160588052861373373e-06 + 2.9042993843758088232e-645j)  +/-  (2.41e-63, 1.48e-183j)
| (0.050382511326072748808 + 1.0265334631999634013e-641j)  +/-  (1.11e-47, 6.83e-168j)
| (5.0463251604301211878e-13 - 5.3134640080511883308e-650j)  +/-  (1.74e-69, 1.07e-189j)
| (1.245228662890601536e-10 + 3.5859284374110061758e-647j)  +/-  (1.18e-71, 7.28e-192j)
| (3.5109490643464595678e-27 - 2.6919502014803479738e-658j)  +/-  (1.25e-79, 7.67e-200j)
| (3.9451901444990510484e-18 - 2.7356538889769525957e-653j)  +/-  (4.4e-74, 2.7e-194j)
| (0.0052371189577844843129 - 1.9835117510655687438e-642j)  +/-  (8.04e-60, 4.94e-180j)
| (4.160588052861373373e-06 + 1.1916552007630868719e-644j)  +/-  (4.9e-68, 3.01e-188j)
| (1.1322520533550885221e-20 + 5.1742382588192037124e-655j)  +/-  (9.23e-76, 5.68e-196j)
| (0.00012925932431832978677 + 4.4653472213532605713e-644j)  +/-  (2.71e-64, 1.67e-184j)
| (3.2127452343085761126e-12 - 2.5339987399902753152e-647j)  +/-  (2.87e-73, 1.76e-193j)
| (0.00012925932431832978677 + 1.328532146914413132e-643j)  +/-  (1.62e-67, 9.95e-188j)
| (5.0463251604301211878e-13 + 1.6836146610286546823e-647j)  +/-  (1.61e-73, 9.92e-194j)
| (4.6069018916750686408e-08 + 1.0036581146151931483e-646j)  +/-  (5.77e-71, 3.55e-191j)
| (0.0052371189577844843129 - 9.7518328213876302519e-643j)  +/-  (5.11e-65, 3.15e-185j)
| (0.027538474110044164258 - 4.0370439860622691845e-642j)  +/-  (3.1e-62, 1.91e-182j)
| (5.1453703021809113241e-07 - 5.8027408661860786205e-646j)  +/-  (4.16e-70, 2.56e-190j)
| (0.080164979428248538625 - 1.4272746109558380641e-641j)  +/-  (1.24e-59, 7.64e-180j)
| (3.2127452343085761126e-12 - 3.3156173071977506865e-649j)  +/-  (2.59e-73, 1.6e-193j)
| (2.8905490725589162093e-09 - 1.5650747085801986757e-647j)  +/-  (3.11e-72, 1.91e-192j)
| (0.050382511326072748808 + 6.9522271039040078417e-642j)  +/-  (5.54e-64, 3.41e-184j)
| (2.8905490725589162093e-09 - 1.4137963569613371493e-646j)  +/-  (1.21e-76, 7.44e-197j)
| (5.9126819259484427532e-14 - 7.4742556743512167463e-649j)  +/-  (1.79e-78, 1.1e-198j)
| (0.13649793429595449916 - 1.9832786648940640968e-641j)  +/-  (1.27e-64, 7.81e-185j)
| (0.0018267877961908283237 + 3.975244016798063844e-643j)  +/-  (6.51e-69, 4e-189j)
| (0.11192865268880192005 + 1.4637834899056301251e-641j)  +/-  (9.6e-66, 5.9e-186j)
| (0.012930968236990281532 + 2.1014195008448020074e-642j)  +/-  (2.88e-67, 1.77e-187j)
| (0.027538474110044164258 - 6.6060166836832060657e-642j)  +/-  (6.33e-69, 3.89e-189j)
| (0.012930968236990281532 + 3.8253807379291766306e-642j)  +/-  (3.81e-70, 2.34e-190j)
| (2.5764212637389215706e-05 - 4.2588582867983881171e-644j)  +/-  (6.13e-75, 3.77e-195j)
| (0.11192865268880192005 + 1.7743979917942803047e-641j)  +/-  (2.65e-68, 1.63e-188j)
| (0.080164979428248538625 - 1.0678531560367930709e-641j)  +/-  (3.55e-69, 2.17e-189j)
| (5.1453703021809113241e-07 - 2.9137933170277693515e-645j)  +/-  (1.05e-76, 6.45e-197j)
| (0.14559539990261382202 + 1.9948318994168879231e-641j)  +/-  (1.21e-69, 7.31e-190j)
| (0.00053512545869880297209 - 3.6802939743804638228e-643j)  +/-  (2.03e-74, 1.22e-194j)
| (4.6069018916750686408e-08 + 6.4781580970072336393e-646j)  +/-  (1.29e-77, 8.12e-198j)
| (0.13649793429595449916 - 1.8019969658361254854e-641j)  +/-  (1.26e-71, 9.01e-192j)
| (0.00053512545869880297209 - 1.4186320329595460875e-643j)  +/-  (2.39e-74, 1.72e-194j)
| (0.0018267877961908283237 + 9.0910937498106589322e-643j)  +/-  (5.48e-74, 3.2e-194j)
