Starting with polynomial:
P : 2*t
Extension levels are: 1 52
-------------------------------------------------
Trying to find an order 52 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^53 - 1378*t^51 + 878475/2*t^49 - 86090550*t^47 + 46531942275/4*t^45 - 4606662285225/4*t^43 + 1386605347852725/16*t^41 - 40607728044258375/8*t^39 + 30090326480795455875/128*t^37 - 1113342079789431867375/128*t^35 + 132487707494942392217625/512*t^33 - 397463122484827176652875/64*t^31 + 61606783985148212381195625/512*t^29 - 962013626845006701029439375/512*t^27 + 48238111860371050294476174375/2048*t^25 - 241190559301855251472380871875/1024*t^23 + 61021211503369378622512360584375/32768*t^21 - 376895718109046162080223403609375/32768*t^19 + 7161018644071877079524244668578125/131072*t^17 - 6407227207853784755363797861359375/32768*t^15 + 134551771364929479862639755088546875/262144*t^13 - 249881861106297605459188116593015625/262144*t^11 + 1249409305531488027295940582965078125/1048576*t^9 - 488899293468843141115802836812421875/524288*t^7 + 3422295054281901987810619857686953125/8388608*t^5 - 684459010856380397562123971537390625/8388608*t^3 + 157952079428395476360490147277859375/33554432*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:
| (-7.3612580683690459931 + 1.2541978744224997818e-951j)  +/-  (3.82e-243, 3.82e-243j)
| (6.540532810875762839 + 4.5373797785399001581e-953j)  +/-  (1.17e-242, 1.17e-242j)
| (9.4852029643727302862 - 1.9531786447757169875e-958j)  +/-  (2.71e-246, 2.71e-246j)
| (-6.9409309282147529552 + 2.8320948571535236614e-953j)  +/-  (7.24e-243, 7.24e-243j)
| (-7.8078847487003961358 + 2.1265924035666385661e-960j)  +/-  (1.38e-243, 1.38e-243j)
| (8.8325166958454148505 + 2.5276326046277287772e-966j)  +/-  (4.4e-245, 4.4e-245j)
| (6.9409309282147529552 + 5.1690008528823468564e-964j)  +/-  (8.41e-243, 8.41e-243j)
| (-9.4852029643727302862 - 5.9339851058489811191e-967j)  +/-  (2.54e-246, 2.54e-246j)
| (8.2914303867830105436 - 8.977630954276569573e-967j)  +/-  (3.16e-244, 3.16e-244j)
| (-4.0544595295034731961 - 4.144455347855709774e-964j)  +/-  (7.91e-244, 7.91e-244j)
| (0.91229161088998862962 - 2.7343860290862040033e-973j)  +/-  (1.57e-251, 1.57e-251j)
| (3.4031434102599181484 + 3.2902688574698001732e-967j)  +/-  (7.28e-245, 7.28e-245j)
| (-8.8325166958454148505 - 6.8921189218428495267e-964j)  +/-  (3.91e-245, 3.91e-245j)
| (-3.7266776654942124268 - 5.020824790135284786e-966j)  +/-  (2.64e-244, 2.64e-244j)
| (7.3612580683690459931 - 9.0167090089152903705e-965j)  +/-  (3.46e-243, 3.46e-243j)
| (7.8078847487003961358 - 1.2232027501311216834e-965j)  +/-  (1.16e-243, 1.16e-243j)
| (4.7254265200961152685 + 2.543933069701007082e-964j)  +/-  (3.81e-243, 3.81e-243j)
| (6.1558623601311928748 + 3.4991602525930825388e-963j)  +/-  (1.57e-242, 1.57e-242j)
| (-2.4527991478588034831 + 3.6441349726824716924e-971j)  +/-  (6.48e-247, 6.48e-247j)
| (5.0702427937817158656 + 4.7290297355374137174e-965j)  +/-  (7.12e-243, 7.12e-243j)
| (4.387127257772072881 + 1.3392738519375684899e-970j)  +/-  (1.91e-243, 1.91e-243j)
| (2.4527991478588034831 - 1.7787734288987762779e-976j)  +/-  (7.64e-247, 7.64e-247j)
| (-6.1558623601311928748 - 1.3900802535873875341e-971j)  +/-  (1.79e-242, 1.79e-242j)
| (-5.7839619604859458629 - 1.9158819160181954564e-998j)  +/-  (1.28e-242, 1.28e-242j)
| (-6.540532810875762839 + 1.7605229433824556452e-1029j)  +/-  (1.26e-242, 1.26e-242j)
| (1.2176276482547365915 + 1.2455893289473634295e-1057j)  +/-  (1.75e-250, 1.75e-250j)
| (3.08330230893913567 + 2.3501493058196378419e-1052j)  +/-  (2e-245, 2e-245j)
| (-5.422647016161452581 + 3.8540537405173437377e-1056j)  +/-  (1.19e-242, 1.19e-242j)
| (-1.5240438405087579033 + 4.2894570615863980398e-1073j)  +/-  (1.63e-249, 1.63e-249j)
| (-0.60775496588729694722 - 3.089365784786925183e-1076j)  +/-  (9.41e-253, 9.41e-253j)
| (-3.4031434102599181484 - 2.4545055973997859239e-1068j)  +/-  (6.9e-245, 6.9e-245j)
| (3.7266776654942124268 - 1.7888025170581598613e-1067j)  +/-  (2.55e-244, 2.55e-244j)
| (-2.7666660769675387289 + 3.7258139421848894893e-1070j)  +/-  (3.93e-246, 3.93e-246j)
| (-2.1413081984302372101 - 2.7505590875513847859e-1071j)  +/-  (1.28e-247, 1.28e-247j)
| (5.422647016161452581 - 1.6207900402009622256e-1065j)  +/-  (1.14e-242, 1.14e-242j)
| (-1.4610072867631912904e-1091 - 1.5558270999872561125e-1091j)  +/-  (1.13e-1089, 1.13e-1089j)
| (-8.2914303867830105436 - 1.8232389037016950246e-1066j)  +/-  (3.27e-244, 3.27e-244j)
| (1.5240438405087579033 + 1.485232552227149436e-1076j)  +/-  (1.53e-249, 1.53e-249j)
| (2.7666660769675387289 - 1.4883138311285288287e-1072j)  +/-  (4.13e-246, 4.13e-246j)
| (4.0544595295034731961 + 2.7687976971343039188e-1071j)  +/-  (8.39e-244, 8.39e-244j)
| (-1.2176276482547365915 + 5.856245654956901116e-1079j)  +/-  (1.66e-250, 1.66e-250j)
| (-3.08330230893913567 - 1.8738505256012743363e-1071j)  +/-  (1.79e-245, 1.79e-245j)
| (0.30374624334991530216 + 2.7202196408448647088e-1080j)  +/-  (7.75e-254, 7.75e-254j)
| (1.8318338313140425143 - 4.4343854582489640091e-1076j)  +/-  (1.63e-248, 1.63e-248j)
| (-5.0702427937817158656 + 1.9434267180044218102e-1068j)  +/-  (7.04e-243, 7.04e-243j)
| (-0.30374624334991530216 - 5.5083464985330564154e-1083j)  +/-  (5.6e-254, 5.6e-254j)
| (-1.8318338313140425143 + 3.6457813378714022035e-1078j)  +/-  (1.57e-248, 1.57e-248j)
| (-4.7254265200961152685 - 6.3771260624777562718e-1072j)  +/-  (3.83e-243, 3.83e-243j)
| (0.60775496588729694722 - 5.1904544451992719095e-1083j)  +/-  (8.47e-253, 8.47e-253j)
| (5.7839619604859458629 + 6.4063969631957668866e-1075j)  +/-  (1.26e-242, 1.26e-242j)
| (-4.387127257772072881 - 3.2915404892953854689e-1082j)  +/-  (2.12e-243, 2.12e-243j)
| (-0.91229161088998862962 - 1.3157614128051532486e-1092j)  +/-  (1.09e-251, 1.09e-251j)
| (2.1413081984302372101 + 6.0703292838297827642e-1088j)  +/-  (1.16e-247, 1.16e-247j)
-------------------------------------------------
The weights are:
| (7.1362429170911497344e-25 + 6.8679870953995305215e-975j)  +/-  (8.21e-75, 1.88e-194j)
| (5.8367133295093192977e-20 - 1.7311563067620968789e-971j)  +/-  (8.82e-73, 2.02e-192j)
| (3.5930201153507351423e-40 + 7.1213122811769713196e-983j)  +/-  (2.6e-81, 5.93e-201j)
| (2.7599847130640565545e-22 + 2.5886617201263479959e-974j)  +/-  (4.27e-74, 9.76e-194j)
| (8.7273196309986530628e-28 + 7.6617809148592280985e-977j)  +/-  (1.04e-76, 2.37e-196j)
| (4.3226896508794229272e-35 - 3.167929539102322214e-980j)  +/-  (3.42e-80, 7.82e-200j)
| (2.7599847130640565545e-22 - 4.5549927288902460453e-973j)  +/-  (1.85e-75, 4.22e-195j)
| (3.5930201153507351423e-40 - 1.8916260006739222022e-983j)  +/-  (1.77e-83, 4.05e-203j)
| (3.981523339099432814e-31 + 3.9737327681064748352e-978j)  +/-  (2.58e-79, 5.9e-199j)
| (1.3516762957947920342e-08 + 1.0196591651397656464e-967j)  +/-  (6.82e-68, 1.56e-187j)
| (0.074836935768288671733 + 5.1416760521607220417e-964j)  +/-  (1.02e-63, 2.34e-183j)
| (1.6943815671498184467e-06 + 4.4791391946216746835e-966j)  +/-  (2.76e-65, 6.32e-185j)
| (4.3226896508794229272e-35 + 7.7875702294246174888e-981j)  +/-  (8.18e-82, 1.87e-201j)
| (1.7081206861240522041e-07 - 3.8122435440137170861e-967j)  +/-  (1.22e-66, 2.78e-186j)
| (7.1362429170911497344e-25 + 1.1316050684310930522e-974j)  +/-  (1.65e-77, 3.76e-197j)
| (8.7273196309986530628e-28 - 2.566455466794782946e-976j)  +/-  (1.13e-78, 2.59e-198j)
| (3.8640067341278044573e-11 + 3.7246754035322448391e-968j)  +/-  (9.05e-73, 2.07e-192j)
| (7.4358676868981614665e-18 + 7.7592319537553413972e-971j)  +/-  (5.24e-76, 1.2e-195j)
| (0.00043015419958156174976 - 2.2977058997446966152e-965j)  +/-  (4.56e-66, 1.04e-185j)
| (1.3457193312052334084e-12 - 8.5955271358237214363e-969j)  +/-  (5.68e-74, 1.3e-193j)
| (8.2814361174072158743e-10 - 1.4509255544035298119e-967j)  +/-  (2.3e-72, 5.26e-192j)
| (0.00043015419958156174976 - 5.4418024856220505996e-965j)  +/-  (1.42e-66, 3.25e-186j)
| (7.4358676868981614665e-18 + 1.5918539086298854709e-972j)  +/-  (3.53e-81, 8.06e-201j)
| (6.1132455633269240964e-16 - 1.543882881466671154e-971j)  +/-  (1.12e-80, 2.56e-200j)
| (5.8367133295093192977e-20 - 1.744726111512549772e-973j)  +/-  (3.2e-82, 7.32e-202j)
| (0.039175127473033394679 - 3.9457928337875426992e-964j)  +/-  (9.85e-64, 2.25e-183j)
| (1.3345751808167237821e-05 - 1.1384160475767268728e-965j)  +/-  (1.03e-72, 2.35e-192j)
| (3.4131103516925490931e-14 + 1.2557365603465522531e-970j)  +/-  (2.42e-80, 5.54e-200j)
| (0.016978459001015047059 + 1.647802619020998579e-964j)  +/-  (5.15e-68, 1.18e-187j)
| (0.11863440402280581893 - 4.997415045508691549e-964j)  +/-  (1.83e-66, 4.17e-186j)
| (1.6943815671498184467e-06 + 1.2595817161537124003e-966j)  +/-  (1.24e-75, 2.84e-195j)
| (1.7081206861240522041e-07 - 1.588811800332957758e-966j)  +/-  (1.41e-75, 3.23e-195j)
| (8.4276409796202008582e-05 + 9.7299192188945077814e-966j)  +/-  (4.7e-74, 1.07e-193j)
| (0.0017867124559233027839 + 4.8934049497703967146e-965j)  +/-  (4.74e-72, 1.08e-191j)
| (3.4131103516925490931e-14 + 1.8033385341803090323e-969j)  +/-  (2.36e-80, 5.4e-200j)
| (0.1713458405552413235 - 6.6224261218726475199e-964j)  +/-  (1.17e-69, 2.67e-189j)
| (3.981523339099432814e-31 - 9.6525205247301479102e-979j)  +/-  (7.5e-89, 1.72e-208j)
| (0.016978459001015047059 + 2.7643740041747422936e-964j)  +/-  (1.55e-71, 3.54e-191j)
| (8.4276409796202008582e-05 + 2.6150377561395191364e-965j)  +/-  (1.11e-74, 2.54e-194j)
| (1.3516762957947920342e-08 + 5.0682287412549766778e-967j)  +/-  (5.13e-77, 1.17e-196j)
| (0.039175127473033394679 - 2.6179790268391866911e-964j)  +/-  (5.57e-72, 1.27e-191j)
| (1.3345751808167237821e-05 - 3.7017733159615511139e-966j)  +/-  (8.51e-77, 1.94e-196j)
| (0.15631190842787289344 + 6.6592643247655000641e-964j)  +/-  (3.34e-72, 7.63e-192j)
| (0.0060738766336914101327 - 1.7663229063074115772e-964j)  +/-  (2.99e-74, 6.83e-194j)
| (1.3457193312052334084e-12 - 8.505747364209717072e-970j)  +/-  (2.79e-82, 6.38e-202j)
| (0.15631190842787289344 + 6.0189281484703251696e-964j)  +/-  (1.32e-73, 3.01e-193j)
| (0.0060738766336914101327 - 9.4283098088440177361e-965j)  +/-  (1.09e-75, 2.5e-195j)
| (3.8640067341278044573e-11 + 4.8702967974444574855e-969j)  +/-  (5.74e-82, 1.31e-201j)
| (0.11863440402280581893 - 6.1208067926680728427e-964j)  +/-  (1.45e-75, 3.32e-195j)
| (6.1132455633269240964e-16 - 3.5716258369920594537e-970j)  +/-  (2.18e-84, 4.98e-204j)
| (8.2814361174072158743e-10 - 2.3922147401751823684e-968j)  +/-  (2.5e-81, 5.71e-201j)
| (0.074836935768288671733 + 3.7877307542651684695e-964j)  +/-  (9.04e-77, 2.06e-196j)
| (0.0017867124559233027839 + 1.0280370447834367248e-964j)  +/-  (5.23e-78, 1.2e-197j)
