Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8 42
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P1 : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^50 - 130991759246428165486227056138977322338570461073/122749103214213163428429988486872850615280185*t^48 + 64052612704407332066230912715949943243487766364074/122749103214213163428429988486872850615280185*t^46 - 3812257941826205154866698203721127531750714650393310/24549820642842632685685997697374570123056037*t^44 + 13148790357670704677172786257651880666014268519729363712/417346950928324755656661960855367692091952629*t^42 - 1931072984605241120535598183299741933111107567942337698844/417346950928324755656661960855367692091952629*t^40 + 212760059639063435956518932015205541874425835835677981328174/417346950928324755656661960855367692091952629*t^38 - 486132989187291534170978405279191095834048387890830685534106/11279647322387155558288161104199126813296017*t^36 + 603632567865176765548011767193611077876796983379604098189925/212823534384663312420531341588662770062189*t^34 - 97262501074086957743856442519329959886267632105279207017411605/663508666022773856369891829658772165488001*t^32 + 3966062447380959315807294258890610061864378561986922244926163460/663508666022773856369891829658772165488001*t^30 - 127759646384505441634473759827191961255774841588994260460629744060/663508666022773856369891829658772165488001*t^28 + 3245774506780862138991554577906198066720938943888189592516491463080/663508666022773856369891829658772165488001*t^26 - 64743237334363703395658761644079607729866597806839443267359770940000/663508666022773856369891829658772165488001*t^24 + 1006599016001270100929820601919211994784051094022938861526442714779500/663508666022773856369891829658772165488001*t^22 - 12072895243253553613090504329902640727592255732273672260844735538376500/663508666022773856369891829658772165488001*t^20 + 110164004769635428767904641812725099839702642424260161366629334351995875/663508666022773856369891829658772165488001*t^18 - 751046361658732995204816423996874505270101364211310885979169523548013875/663508666022773856369891829658772165488001*t^16 + 3736249336971282327123914648396717738189372070357171784397922962631281250/663508666022773856369891829658772165488001*t^14 - 13147634508167428736095647882216196212502839168922642144023755772528198750/663508666022773856369891829658772165488001*t^12 + 31382187878989442031350470803455981092839027111567283504691562690267735000/663508666022773856369891829658772165488001*t^10 - 47893841565017354587142777288015819269303680384821029628820299844432472500/663508666022773856369891829658772165488001*t^8 + 42755198886194678540028162517084834573932383581846320298470905609531898750/663508666022773856369891829658772165488001*t^6 - 19241947922280145641690569666403275933075274038285707667192025296486531250/663508666022773856369891829658772165488001*t^4 + 3247398975199601167248431400156602164593303084321037179212261548160071875/663508666022773856369891829658772165488001*t^2 - 84159669392864016658268201230066290441059327904791805855537630959409375/663508666022773856369891829658772165488001
-------------------------------------------------
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
Positive weights:   50 out of 50
Indefinite weights: 0 out of 50
Negative weights:   0 out of 50
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-10.030176613791951708 - 3.7733041679305039721e-511j)  +/-  (2.78e-244, 2.78e-244j)
| (-12.453196051025116045 - 6.4772417511360369691e-520j)  +/-  (9.29e-247, 9.29e-247j)
| (10.030176613791951708 + 8.8875173638520527733e-521j)  +/-  (2.86e-244, 2.86e-244j)
| (-6.0728340205957716754 - 1.0125906401783691424e-517j)  +/-  (5.01e-244, 5.01e-244j)
| (11.510804455271542834 - 7.9781779052328940395e-526j)  +/-  (1.55e-245, 1.55e-245j)
| (7.6411863952696656847 + 1.6313968111311283674e-522j)  +/-  (1.45e-243, 1.45e-243j)
| (6.0728340205957716754 - 1.1485028813486011105e-523j)  +/-  (5.22e-244, 5.22e-244j)
| (-10.729083355716344684 - 3.3108280315741136451e-527j)  +/-  (7.76e-245, 7.76e-245j)
| (-5.08928043799679413 + 1.7260770290547058609e-535j)  +/-  (1.01e-244, 1.01e-244j)
| (4.1445471861258943321 + 5.7637734649644743691e-540j)  +/-  (1.04e-245, 1.04e-245j)
| (8.197468565119909545 + 1.4645131541684321009e-547j)  +/-  (1.49e-243, 1.49e-243j)
| (12.453196051025116045 + 3.3901124049082563027e-556j)  +/-  (9.65e-247, 9.65e-247j)
| (-1.996358502499403779 - 1.102821554069100021e-567j)  +/-  (4.26e-249, 4.26e-249j)
| (-8.7765525606886408726 + 1.5359332842492142249e-563j)  +/-  (1.15e-243, 1.15e-243j)
| (8.7765525606886408726 + 3.1931969372371646486e-576j)  +/-  (1.16e-243, 1.16e-243j)
| (1.2810236051933793149 - 1.0018698987719100573e-584j)  +/-  (6.84e-251, 6.84e-251j)
| (-5.5758380632148015975 + 8.4168990477630347166e-577j)  +/-  (2.71e-244, 2.71e-244j)
| (-11.510804455271542834 - 3.1266430590667833294e-586j)  +/-  (1.37e-245, 1.37e-245j)
| (-2.8024858612875416991 - 4.077950661631457257e-592j)  +/-  (1.2e-247, 1.2e-247j)
| (-4.1445471861258943321 + 2.649534274012866835e-588j)  +/-  (9.45e-246, 9.45e-246j)
| (2.3855327770108876003 - 1.4420751732848917622e-601j)  +/-  (2.34e-248, 2.34e-248j)
| (4.6123230475785657265 - 6.7243162544663095562e-597j)  +/-  (3.33e-245, 3.33e-245j)
| (-8.197468565119909545 - 2.7996225466584718113e-619j)  +/-  (1.45e-243, 1.45e-243j)
| (10.729083355716344684 + 7.3268019903067467272e-639j)  +/-  (7.35e-245, 7.35e-245j)
| (-1.6365190424351079992 - 3.4822284261621375092e-650j)  +/-  (6.26e-250, 6.26e-250j)
| (-9.3844161198607385433 - 3.6330383011899348526e-646j)  +/-  (6.22e-244, 6.22e-244j)
| (9.3844161198607385433 - 2.7339914173066054734e-656j)  +/-  (6.33e-244, 6.33e-244j)
| (2.8024858612875416991 + 8.6031742165405115898e-662j)  +/-  (1.21e-247, 1.21e-247j)
| (-3.6860724786691113679 - 1.8971258732477725718e-657j)  +/-  (2.59e-246, 2.59e-246j)
| (-1.2810236051933793149 + 1.6674866305282069714e-669j)  +/-  (7.51e-251, 7.51e-251j)
| (-3.2378685733586539787 - 2.1686175825838783701e-661j)  +/-  (5.42e-247, 5.42e-247j)
| (0.9116454620945159471 + 3.6128424253858798165e-670j)  +/-  (5.75e-252, 5.75e-252j)
| (3.6860724786691113679 - 2.1516799120993921625e-661j)  +/-  (2.52e-246, 2.52e-246j)
| (-4.6123230475785657265 - 5.4448225541952696926e-679j)  +/-  (3.6e-245, 3.6e-245j)
| (0.17705030206024984203 + 1.3721126788703770442e-708j)  +/-  (2.35e-254, 2.35e-254j)
| (-7.1035402833887368944 + 2.652847348296802303e-708j)  +/-  (1.27e-243, 1.27e-243j)
| (7.1035402833887368944 - 7.4371876880540349531e-726j)  +/-  (1.34e-243, 1.34e-243j)
| (-7.6411863952696656847 - 6.4718045299053343646e-734j)  +/-  (1.48e-243, 1.48e-243j)
| (6.5815061536566790652 - 3.3202100778152044828e-744j)  +/-  (8.37e-244, 8.37e-244j)
| (5.5758380632148015975 - 1.2322036938410850669e-745j)  +/-  (2.3e-244, 2.3e-244j)
| (-0.53907981135137510807 - 1.5279264021481921628e-755j)  +/-  (3.86e-253, 3.86e-253j)
| (-0.17705030206024984203 - 3.3757621914833241669e-756j)  +/-  (2.35e-254, 2.35e-254j)
| (5.08928043799679413 + 1.0713149414776068337e-746j)  +/-  (9.76e-245, 9.76e-245j)
| (1.996358502499403779 + 1.5816397887736915616e-751j)  +/-  (4.35e-249, 4.35e-249j)
| (-6.5815061536566790652 + 5.5253247506960800862e-745j)  +/-  (8.59e-244, 8.59e-244j)
| (-0.9116454620945159471 - 5.215992313902257357e-766j)  +/-  (6.02e-252, 6.02e-252j)
| (-2.3855327770108876003 + 1.5802400465096698049e-762j)  +/-  (2.25e-248, 2.25e-248j)
| (3.2378685733586539787 + 2.1984318595081968904e-761j)  +/-  (5.57e-247, 5.57e-247j)
| (0.53907981135137510807 - 1.1078146702721815934e-767j)  +/-  (3.56e-253, 3.56e-253j)
| (1.6365190424351079992 - 1.8650610273659842714e-764j)  +/-  (6.46e-250, 6.46e-250j)
-------------------------------------------------
The weights are:
| (3.8051762651812559463e-23 - 7.863597221604834144e-533j)  +/-  (3.1e-83, 3.17e-204j)
| (9.1568834223350436502e-35 - 3.5055572181342749007e-540j)  +/-  (6.88e-88, 7.03e-209j)
| (3.8051762651812559463e-23 + 4.7488674709882259687e-535j)  +/-  (1.28e-84, 1.31e-205j)
| (1.9673674300850110069e-09 - 5.4604057173631845362e-526j)  +/-  (2.43e-74, 2.48e-195j)
| (5.6750472010489540615e-30 + 9.9950841543303164472e-539j)  +/-  (1.16e-87, 1.18e-208j)
| (4.5674219644248845079e-14 + 5.3487718604583441284e-530j)  +/-  (6.82e-80, 6.97e-201j)
| (1.9673674300850110069e-09 - 2.9394273286625050943e-527j)  +/-  (4.61e-76, 4.71e-197j)
| (2.9492126766511512868e-26 - 4.2057203660286230739e-535j)  +/-  (1.01e-86, 1.03e-207j)
| (4.5641559187500385847e-07 - 1.6094635300539689886e-525j)  +/-  (1.64e-73, 1.67e-194j)
| (3.4409822861989880078e-05 - 1.881232531005973461e-524j)  +/-  (2.07e-70, 2.12e-191j)
| (5.7866155594665462081e-16 - 4.4516784388046108097e-531j)  +/-  (1.62e-81, 1.65e-202j)
| (9.1568834223350436502e-35 - 2.8296799355197160063e-541j)  +/-  (1.03e-90, 1.05e-211j)
| (0.020269537834162212408 - 8.6634467546756974788e-522j)  +/-  (5.09e-61, 5.21e-182j)
| (4.4365380739013591032e-18 - 7.4465224754055259349e-531j)  +/-  (1.13e-84, 1.16e-205j)
| (4.4365380739013591032e-18 + 2.9020642973693446082e-532j)  +/-  (2.59e-83, 2.65e-204j)
| (0.063655950379407154906 + 2.5725421552789745918e-521j)  +/-  (2.34e-56, 2.39e-177j)
| (3.4787607596833944254e-08 + 1.3780022310780065802e-525j)  +/-  (4.61e-77, 4.71e-198j)
| (5.6750472010489540615e-30 + 2.0135046418039826203e-537j)  +/-  (1.17e-89, 1.2e-210j)
| (0.0033600259224627139357 - 1.0461117900877491095e-522j)  +/-  (5.46e-69, 5.59e-190j)
| (3.4409822861989880078e-05 + 1.2716657901219275414e-524j)  +/-  (5.39e-74, 5.51e-195j)
| (0.0093836970148778189131 - 2.7586425483774353903e-522j)  +/-  (1.71e-68, 1.75e-189j)
| (4.5255737919822916923e-06 + 4.4096947114824211219e-525j)  +/-  (1.39e-76, 1.42e-197j)
| (5.7866155594665462081e-16 + 8.3351300670417757438e-530j)  +/-  (2.42e-84, 2.48e-205j)
| (2.9492126766511512868e-26 - 9.8324013591562528545e-537j)  +/-  (2.73e-89, 2.79e-210j)
| (0.036803971371404488365 + 1.7869516238558745093e-521j)  +/-  (3.51e-66, 3.59e-187j)
| (1.8757502407213474686e-20 + 6.7558090530481828469e-532j)  +/-  (2.47e-86, 2.53e-207j)
| (1.8757502407213474686e-20 - 1.410389720154224281e-533j)  +/-  (1.5e-86, 1.54e-207j)
| (0.0033600259224627139357 + 8.9100766413779835543e-523j)  +/-  (2.38e-73, 2.44e-194j)
| (0.00020284920416327232747 - 7.2153558948214621551e-524j)  +/-  (2.83e-75, 2.9e-196j)
| (0.063655950379407154906 - 2.883621352631937484e-521j)  +/-  (3.47e-67, 3.55e-188j)
| (0.0009337011368799464257 + 2.9695238548028461502e-523j)  +/-  (3.2e-74, 3.27e-195j)
| (0.098436480249617272465 - 3.6893317675980684815e-521j)  +/-  (4.28e-68, 4.38e-189j)
| (0.00020284920416327232747 + 7.3416058392897414776e-524j)  +/-  (1.53e-77, 1.56e-198j)
| (4.5255737919822916923e-06 + 3.908654743815652251e-527j)  +/-  (9.43e-78, 9.65e-199j)
| (0.13972320017484240286 - 5.8814325933098532617e-521j)  +/-  (9.57e-70, 9.79e-191j)
| (2.3301844922793745216e-12 + 8.3181988123992130759e-528j)  +/-  (4.87e-84, 4.98e-205j)
| (2.3301844922793745216e-12 - 5.216477478760347533e-529j)  +/-  (2.59e-85, 2.65e-206j)
| (4.5674219644248845079e-14 - 8.5662178525622630459e-529j)  +/-  (3.19e-85, 3.27e-206j)
| (8.0676022158143127239e-11 + 4.2425085919530885134e-528j)  +/-  (9.52e-85, 9.73e-206j)
| (3.4787607596833944254e-08 + 1.7660901633008588395e-526j)  +/-  (8.89e-84, 9.09e-205j)
| (0.12719115806190937931 - 5.1622486873354091398e-521j)  +/-  (2.47e-76, 2.53e-197j)
| (0.13972320017484240286 + 5.9807961826647999806e-521j)  +/-  (3.78e-76, 3.87e-197j)
| (4.5641559187500385847e-07 - 9.3417952350791779494e-526j)  +/-  (4.02e-83, 4.11e-204j)
| (0.020269537834162212408 + 7.3930647123895415118e-522j)  +/-  (2.7e-79, 2.76e-200j)
| (8.0676022158143127239e-11 - 8.9651671866636564315e-527j)  +/-  (1.94e-85, 1.99e-206j)
| (0.098436480249617272465 + 4.0120540861294476388e-521j)  +/-  (1.57e-77, 1.61e-198j)
| (0.0093836970148778189131 + 3.2662709116694853657e-522j)  +/-  (3.22e-79, 3.31e-200j)
| (0.0009337011368799464257 - 2.6502744809173455946e-523j)  +/-  (3.21e-81, 3.3e-202j)
| (0.12719115806190937931 + 4.9077332870295759455e-521j)  +/-  (8.74e-79, 9.93e-200j)
| (0.036803971371404488365 - 1.5546469276502039476e-521j)  +/-  (2.15e-79, 2.15e-200j)
