Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 55
-------------------------------------------------
Trying to find an order 55 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^59 - 448528988354671499385957707735861027280365187411/265026570181444926006858105793526490839484691*t^57 + 6010681182132445756337019461032244336113700907363276/4505451693084563742116587798489950344271239747*t^55 - 2935080423068969369742081934350689808916362668517576420/4505451693084563742116587798489950344271239747*t^53 + 76620195192451437700330398377408924777837099422122215655/346573207160351057085891369114611564943941519*t^51 - 1130502035249904081228698011971560994054479066573356417575/20386659244726532769758315830271268526114207*t^49 + 217617190890825322842165920855793390976184289746220010339200/20386659244726532769758315830271268526114207*t^47 - 32951929935151157549548181954436713657191490096646514143063600/20386659244726532769758315830271268526114207*t^45 + 3991542598604251768589313680274933611984411118231481252256899875/20386659244726532769758315830271268526114207*t^43 - 391300492230270233690637013276949052319767671386497733792514227875/20386659244726532769758315830271268526114207*t^41 + 31290097474596621249390629373309092827244126731712979305516398069500/20386659244726532769758315830271268526114207*t^39 - 2051231000070230393680664203457365320210848643420510354573390057874500/20386659244726532769758315830271268526114207*t^37 + 110540544890706105553956862536075553578378720819738377482091963873662875/20386659244726532769758315830271268526114207*t^35 - 4900758311408655449968680492961253914729778420744052478303824473121436875/20386659244726532769758315830271268526114207*t^33 + 178566922909004787801267166372724503928149187289106102774776921325053180000/20386659244726532769758315830271268526114207*t^31 - 5332773695726748067426399197506983339505257453468141630212448147081771680000/20386659244726532769758315830271268526114207*t^29 + 129952577211871604254540128851067387900684996699596822188135488628733663758125/20386659244726532769758315830271268526114207*t^27 - 2567782615492994974974711404071502466442874408093662755526597293873488178118125/20386659244726532769758315830271268526114207*t^25 + 40797906964455090146785469294086570407241477406467680112686998470091699839312500/20386659244726532769758315830271268526114207*t^23 - 515634842114631661525056781925834984577416318515011076153422672312869440766437500/20386659244726532769758315830271268526114207*t^21 + 5113532039649187421839212308350267742675314571512466890563396329373960395552203125/20386659244726532769758315830271268526114207*t^19 - 39104362759487820255867521474183141721319820860824803958704199784655135516098453125/20386659244726532769758315830271268526114207*t^17 + 225534886595962796688041829278626561929192671203049036712343125874237435556104500000/20386659244726532769758315830271268526114207*t^15 - 953216144395200542881875225616295288431323446906847574822849147655026754326001250000/20386659244726532769758315830271268526114207*t^13 + 2841730910442647288490357702108627809707796787144544926399684050315032983116784140625/20386659244726532769758315830271268526114207*t^11 - 5670690586075684355461328693618230971060501202727727526104826677926013579745242140625/20386659244726532769758315830271268526114207*t^9 + 7022967482397135937781122767822822481930164173187433233313758517983135245671190812500/20386659244726532769758315830271268526114207*t^7 - 4798947773782147461704200208995306490231338752526120695940376152997349844824838687500/20386659244726532769758315830271268526114207*t^5 + 1470291696424456278486126902129484563058266893773482172984200597409498121224614765625/20386659244726532769758315830271268526114207*t^3 - 126203755067121776486065876571738567752339819636215213958997203034119699811201015625/20386659244726532769758315830271268526114207*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: 0
  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:
| (-11.897748508596435405 - 1.7420715052667037793e-567j)  +/-  (2.77e-242, 2.77e-242j)
| (-12.587057714317804354 + 1.1169914018861278525e-575j)  +/-  (5.63e-243, 5.63e-243j)
| (11.897748508596435405 - 2.1816365482170444946e-588j)  +/-  (2.65e-242, 2.65e-242j)
| (11.264860681738575215 + 1.9386913544489538006e-606j)  +/-  (8.69e-242, 8.69e-242j)
| (-13.366099414720763988 + 5.0162032505275212418e-620j)  +/-  (6.4e-244, 6.4e-244j)
| (7.572072050225169207 - 9.6891501756100827632e-619j)  +/-  (3.37e-241, 3.37e-241j)
| (-14.327307470037223563 + 2.4055870088287377183e-633j)  +/-  (3.04e-245, 3.04e-245j)
| (13.366099414720763988 - 1.1349839602446158371e-635j)  +/-  (6.05e-244, 6.05e-244j)
| (-7.572072050225169207 + 6.8057689381012930714e-648j)  +/-  (3.44e-241, 3.44e-241j)
| (3.5808288384860917228 - 4.3599173324063071832e-657j)  +/-  (1.09e-245, 1.09e-245j)
| (12.587057714317804354 - 1.106121099402013694e-651j)  +/-  (5.55e-243, 5.55e-243j)
| (-4.8619263434309120869 + 1.0591399356412707758e-670j)  +/-  (1.21e-243, 1.21e-243j)
| (9.0482235414276210106 - 5.0771906366910956854e-668j)  +/-  (6.3e-241, 6.3e-241j)
| (-10.671718928134885542 + 8.5972804162152188046e-680j)  +/-  (2.2e-241, 2.2e-241j)
| (10.108501917808239966 - 8.2957284195953665091e-694j)  +/-  (4.03e-241, 4.03e-241j)
| (1.5243722519168902253 + 5.3629638221994507262e-719j)  +/-  (3.04e-250, 3.04e-250j)
| (8.0520528553747279046 + 1.4195474124557352376e-712j)  +/-  (5.16e-241, 5.16e-241j)
| (14.327307470037223563 - 1.182139892050482464e-726j)  +/-  (2.86e-245, 2.86e-245j)
| (4.0037563513890882771 + 1.5603918746051757221e-737j)  +/-  (6.67e-245, 6.67e-245j)
| (-5.7392742778162219494 - 6.377232225209326279e-733j)  +/-  (1.42e-242, 1.42e-242j)
| (-2.3344142183389772393 - 2.3162008078585031021e-742j)  +/-  (3.21e-248, 3.21e-248j)
| (9.5688197958512334588 + 9.5664729986075184958e-734j)  +/-  (5.9e-241, 5.9e-241j)
| (5.2979490914258546877 - 3.002041078050479758e-748j)  +/-  (4.58e-243, 4.58e-243j)
| (-2.7461523085193009407 + 8.7627775673122285948e-758j)  +/-  (2.59e-247, 2.59e-247j)
| (-3.5808288384860917228 + 4.3180184335457144115e-756j)  +/-  (1.1e-245, 1.1e-245j)
| (8.5434586026907656517 + 1.4304251209795609505e-749j)  +/-  (6.58e-241, 6.58e-241j)
| (1.1285980742394014482 + 2.476630062532939637e-767j)  +/-  (2.49e-251, 2.49e-251j)
| (-7.1019663820755873362 - 2.8055016509391594036e-756j)  +/-  (1.93e-241, 1.93e-241j)
| (-9.5688197958512334588 - 3.5926494488654516412e-761j)  +/-  (5.68e-241, 5.68e-241j)
| (-6.1865329604942913439 + 2.7279726907039228108e-767j)  +/-  (4.09e-242, 4.09e-242j)
| (-11.264860681738575215 + 2.7181247190220149997e-773j)  +/-  (9.08e-242, 9.08e-242j)
| (-1.5243722519168902253 - 4.4900026153349040401e-796j)  +/-  (3.19e-250, 3.19e-250j)
| (10.671718928134885542 + 1.7915214015497711282e-784j)  +/-  (2.06e-241, 2.06e-241j)
| (-8.5434586026907656517 - 2.1826345623846067551e-791j)  +/-  (6.37e-241, 6.37e-241j)
| (-4.4306747313425854721 + 2.3212353406091981379e-796j)  +/-  (3.04e-244, 3.04e-244j)
| (-1.9268550561874605799 - 4.8591872945100921527e-801j)  +/-  (3.9e-249, 3.9e-249j)
| (-10.108501917808239966 + 4.8616974654791400508e-794j)  +/-  (3.79e-241, 3.79e-241j)
| (2.3344142183389772393 - 5.6492040246361643726e-801j)  +/-  (3.22e-248, 3.22e-248j)
| (-3.161658777016302039 - 2.9321320909822919536e-799j)  +/-  (1.82e-246, 1.82e-246j)
| (-5.2979490914258546877 + 2.0339884775110698664e-795j)  +/-  (4.64e-243, 4.64e-243j)
| (3.161658777016302039 - 7.6606220299638813266e-798j)  +/-  (1.85e-246, 1.85e-246j)
| (-6.6404699919236215569 - 1.3294260622274486043e-793j)  +/-  (9.66e-242, 9.66e-242j)
| (2.7461523085193009407 + 1.2935019996924472929e-798j)  +/-  (2.61e-247, 2.61e-247j)
| (7.1019663820755873362 + 1.2208795498087477077e-791j)  +/-  (1.94e-241, 1.94e-241j)
| (4.4306747313425854721 - 3.1126515652010404333e-800j)  +/-  (3.2e-244, 3.2e-244j)
| (-0.74196378430272585765 + 2.679373039938034759e-809j)  +/-  (1.78e-252, 1.78e-252j)
| (-4.0037563513890882771 + 1.3053954803891943037e-801j)  +/-  (6.5e-245, 6.5e-245j)
| (4.8619263434309120869 - 1.6026894133628591457e-798j)  +/-  (1.28e-243, 1.28e-243j)
| (1.9268550561874605799 + 3.0969911185363403941e-805j)  +/-  (3.54e-249, 3.54e-249j)
| (6.1865329604942913439 - 1.3359113943634618633e-796j)  +/-  (3.97e-242, 3.97e-242j)
| (-3.6756017869744938606e-836 - 2.6036194424547510773e-836j)  +/-  (2.66e-834, 2.66e-834j)
| (-1.1285980742394014482 - 2.2787087160973418951e-809j)  +/-  (2.58e-251, 2.58e-251j)
| (-9.0482235414276210106 + 8.306289228479348951e-798j)  +/-  (6.13e-241, 6.13e-241j)
| (0.74196378430272585765 + 5.1392806347141248373e-813j)  +/-  (1.73e-252, 1.73e-252j)
| (0.36650715475756670485 + 1.4461613385778278592e-812j)  +/-  (1.17e-253, 1.17e-253j)
| (-8.0520528553747279046 + 6.0677516262416335319e-799j)  +/-  (5.17e-241, 5.17e-241j)
| (-0.36650715475756670485 + 1.7778181708868678625e-813j)  +/-  (1.17e-253, 1.17e-253j)
| (5.7392742778162219494 - 1.6548715089602863724e-800j)  +/-  (1.44e-242, 1.44e-242j)
| (6.6404699919236215569 - 2.1380896032995367154e-806j)  +/-  (9.03e-242, 9.03e-242j)
-------------------------------------------------
The weights are:
| (4.7883667195755142077e-32 - 4.9402876520730487471e-598j)  +/-  (3.1e-66, 5.39e-185j)
| (1.1441785997033715224e-35 - 1.9253053010598617037e-600j)  +/-  (1.09e-67, 1.89e-186j)
| (4.7883667195755142077e-32 - 3.5055696519780692059e-600j)  +/-  (3.41e-68, 5.92e-187j)
| (6.7854766079506279142e-29 + 1.3432009354170492841e-598j)  +/-  (5.85e-67, 1.02e-185j)
| (5.414487958085262583e-40 + 6.6371084303216545323e-603j)  +/-  (1.66e-70, 2.88e-189j)
| (6.7145538513928920378e-14 - 5.9453392871096636391e-591j)  +/-  (3.65e-59, 6.34e-178j)
| (1.2061784411611091255e-45 - 7.0611764837467128475e-606j)  +/-  (7.92e-73, 1.38e-191j)
| (5.414487958085262583e-40 - 3.857529623529045695e-604j)  +/-  (2.76e-72, 4.8e-191j)
| (6.7145538513928920378e-14 - 2.675990453612687546e-590j)  +/-  (1.1e-60, 1.91e-179j)
| (0.00027598038539036464737 + 8.850995584554392396e-586j)  +/-  (3.57e-45, 6.21e-164j)
| (1.1441785997033715224e-35 + 5.4202212442926114135e-602j)  +/-  (2.08e-70, 3.62e-189j)
| (1.2733802404452325302e-06 - 1.0157753351908230695e-586j)  +/-  (5.73e-53, 9.96e-172j)
| (3.4075378638053462783e-19 + 1.1185019017758026412e-593j)  +/-  (1.99e-64, 3.46e-183j)
| (4.2861550518233605312e-26 - 6.3989213084201850376e-596j)  +/-  (6.56e-69, 1.14e-187j)
| (1.4230874738506256124e-23 + 6.5769168848907137951e-596j)  +/-  (1.04e-66, 1.8e-185j)
| (0.04986673473126993747 - 2.7058676622164949438e-584j)  +/-  (4.95e-34, 8.6e-153j)
| (1.6149316991561729495e-15 + 8.6413158851271651806e-592j)  +/-  (7.2e-63, 1.25e-181j)
| (1.2061784411611091255e-45 + 6.5416617671597021911e-607j)  +/-  (3.11e-76, 5.41e-195j)
| (5.6012653331283798341e-05 - 3.5232209938502223596e-586j)  +/-  (1.76e-52, 3.06e-171j)
| (1.2467964355773940813e-08 - 9.9973013945695179399e-588j)  +/-  (7.7e-61, 1.34e-179j)
| (0.010717352057101371106 - 1.2815174820784945669e-584j)  +/-  (3.69e-46, 6.42e-165j)
| (2.7687562139817395659e-21 - 9.5898568055833581814e-595j)  +/-  (6.3e-66, 1.09e-184j)
| (1.406080376422516638e-07 + 1.2845478331835026318e-587j)  +/-  (2.55e-58, 4.42e-177j)
| (0.0038016343497984697535 + 6.9743099530675363925e-585j)  +/-  (1.4e-49, 2.43e-168j)
| (0.00027598038539036464737 + 1.6472543343916433689e-585j)  +/-  (3.8e-54, 6.61e-173j)
| (2.8065525016295445852e-17 - 1.0727284855506167316e-592j)  +/-  (2.55e-64, 4.43e-183j)
| (0.082646867235076161906 + 4.3000619445335617002e-584j)  +/-  (6.6e-39, 1.15e-157j)
| (2.0724100920911970628e-12 + 1.4029395741794174858e-589j)  +/-  (1.13e-65, 1.96e-184j)
| (2.7687562139817395659e-21 - 8.8393137590012225756e-594j)  +/-  (1.16e-71, 2.02e-190j)
| (8.783180775702018458e-10 + 2.6937436334093092684e-588j)  +/-  (5.38e-64, 9.35e-183j)
| (6.7854766079506279142e-29 + 4.9158850920148226782e-597j)  +/-  (1.73e-74, 3e-193j)
| (0.04986673473126993747 - 3.5011245736704742753e-584j)  +/-  (1.02e-48, 1.77e-167j)
| (4.2861550518233605312e-26 - 3.4760531365708596082e-597j)  +/-  (6.45e-72, 1.12e-190j)
| (2.8065525016295445852e-17 - 6.5372599751797328725e-592j)  +/-  (3.17e-70, 5.5e-189j)
| (9.3453640517088967934e-06 + 2.8075999044481834522e-586j)  +/-  (2.41e-61, 4.19e-180j)
| (0.025257271048821821541 + 2.1930735923627072172e-584j)  +/-  (3.31e-53, 5.75e-172j)
| (1.4230874738506256124e-23 + 8.0890627789512126963e-595j)  +/-  (8.34e-73, 1.45e-191j)
| (0.010717352057101371106 - 8.6111860263907098315e-585j)  +/-  (3.81e-58, 6.61e-177j)
| (0.0011240198351338999769 - 3.523950581103604502e-585j)  +/-  (2.06e-58, 3.57e-177j)
| (1.406080376422516638e-07 + 3.3468738511356035708e-587j)  +/-  (1.99e-63, 3.46e-182j)
| (0.0011240198351338999769 - 2.0442735827772981796e-585j)  +/-  (7.8e-62, 1.35e-180j)
| (4.8536113038653002607e-11 - 6.5109565784742015536e-589j)  +/-  (2.33e-66, 4.05e-185j)
| (0.0038016343497984697535 + 4.3585427996212286792e-585j)  +/-  (6.97e-61, 1.21e-179j)
| (2.0724100920911970628e-12 + 3.5412071040078559402e-590j)  +/-  (1.18e-70, 2.05e-189j)
| (9.3453640517088967934e-06 + 1.2839301943334843847e-586j)  +/-  (3.94e-66, 6.84e-185j)
| (0.11548480218584978775 - 7.1040530087809775093e-584j)  +/-  (1.83e-58, 3.17e-177j)
| (5.6012653331283798341e-05 - 7.0971081096339695379e-586j)  +/-  (1.09e-63, 1.9e-182j)
| (1.2733802404452325302e-06 - 4.2642919276764697328e-587j)  +/-  (2.38e-67, 4.14e-186j)
| (0.025257271048821821541 + 1.581738168498310989e-584j)  +/-  (2.63e-62, 4.57e-181j)
| (8.783180775702018458e-10 + 8.5071395001944187952e-589j)  +/-  (1.74e-70, 3.03e-189j)
| (0.1454737318686120152 - 9.140089021179698726e-584j)  +/-  (6e-62, 1.04e-180j)
| (0.082646867235076161906 + 5.2013478276244426928e-584j)  +/-  (4.8e-62, 8.35e-181j)
| (3.4075378638053462783e-19 + 8.221759711550961565e-593j)  +/-  (1.71e-74, 2.98e-193j)
| (0.11548480218584978775 - 6.2700229403562818575e-584j)  +/-  (3.7e-63, 6.44e-182j)
| (0.13802168683463135272 + 8.1577238428794905593e-584j)  +/-  (4.78e-63, 8.31e-182j)
| (1.6149316991561729495e-15 + 4.482739950708941323e-591j)  +/-  (1.4e-72, 2.44e-191j)
| (0.13802168683463135272 + 8.676291456407238335e-584j)  +/-  (1.15e-63, 2e-182j)
| (1.2467964355773940813e-08 - 3.4908455787449909764e-588j)  +/-  (2.65e-70, 4.57e-189j)
| (4.8536113038653002607e-11 - 1.846451002954011956e-589j)  +/-  (1.23e-71, 2.14e-190j)
