Starting with polynomial:
P : 2*t
Extension levels are: 1 4 8 26
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : 2*t^5 - 10*t^3 + 15/2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P3 : 2*t^13 - 170/3*t^11 + 3251/6*t^9 - 2163*t^7 + 29631/8*t^5 - 20895/8*t^3 + 19215/32*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^39 - 5202701469556038537182507144760312538011811/9207890989550589640350126401413210598967*t^37 + 19654481193003794350865218132958327758101386293/276236729686517689210503792042396317969010*t^35 - 55550904541184988271681382475546863360251560857719/10496995728087672189999144097611060082822380*t^33 + 908901383362777614689791362066833759604075880204919/3498998576029224063333048032537020027607460*t^31 - 186973730925217262404689631822319990966829409112863061/20993991456175344379998288195222120165644760*t^29 + 1849336838778846198061100203783485031999440914172578323/8397596582470137751999315278088848066257904*t^27 - 12436811446970345568605204484135685356999509480396715961/3110220956470421389629376028921795580095520*t^25 + 4182077236050578121607122982803080428802167345816661975/77755523911760534740734400723044889502388*t^23 - 333947146466798301888553505784265968728232725837271166595/622044191294084277925875205784359116019104*t^21 + 172852813547600921304495011530592795220227252108852747405/43652223950462054591289488125218183580288*t^19 - 1865649646031604206276369541193201062735819979342511358675/87304447900924109182578976250436367160576*t^17 + 29004429740566637495235352237400950834489661535436759829445/349217791603696436730315905001745468642304*t^15 - 158801053076483206766447973105647421837976671435114960050325/698435583207392873460631810003490937284608*t^13 + 594386362926951322130932251464978255009459751031708193610375/1396871166414785746921263620006981874569216*t^11 - 1461719750550817466955285213908833356296429365944231650061675/2793742332829571493842527240013963749138432*t^9 + 4469581812378790930408519025237549274822750886334910652864875/11174969331318285975370108960055854996553728*t^7 - 3895080142787386768870158242531170359092874858701290916806575/22349938662636571950740217920111709993107456*t^5 + 1638433588839839559652210405068126022097703781388273519218875/44699877325273143901480435840223419986214912*t^3 - 218056402088079953964415313268933592554539604993378811144875/89399754650546287802960871680446839972429824*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:
| (5.9812862846389435919 - 4.0398082464495808295e-891j)  +/-  (3.98e-247, 3.98e-247j)
| (6.5713384751696814807 + 4.993186641758684477e-896j)  +/-  (9.55e-248, 9.55e-248j)
| (-7.2802506372026414171 + 1.0932119601774547252e-901j)  +/-  (1.01e-248, 1.01e-248j)
| (4.962593092700393863 - 4.5678196108977619259e-898j)  +/-  (1.62e-246, 1.62e-246j)
| (-5.4522831090801266746 + 7.0313601760299362969e-908j)  +/-  (9.97e-247, 9.97e-247j)
| (-6.5713384751696814807 + 3.4925138400504470605e-909j)  +/-  (9.44e-248, 9.44e-248j)
| (-5.9812862846389435919 - 8.3300274603233365703e-908j)  +/-  (3.57e-247, 3.57e-247j)
| (-4.0656929841242320401 - 8.5215034558881034425e-907j)  +/-  (2.25e-246, 2.25e-246j)
| (7.2802506372026414171 + 4.9488357696277959561e-908j)  +/-  (1e-248, 1e-248j)
| (2.7796084806380178827 + 2.836653231134699775e-908j)  +/-  (2.08e-247, 2.08e-247j)
| (0.95857246461381850711 + 2.4403175983532743564e-919j)  +/-  (3.76e-250, 3.76e-250j)
| (-3.1512629855004394848 - 1.140392314742181181e-913j)  +/-  (1.11e-246, 1.11e-246j)
| (-2.7796084806380178827 - 1.476547154288341627e-917j)  +/-  (2.2e-247, 2.2e-247j)
| (-2.396397951415888391 - 1.927202820883727723e-920j)  +/-  (4.54e-248, 4.54e-248j)
| (3.6658316928775966507 + 2.7026735999848341024e-921j)  +/-  (2.83e-246, 2.83e-246j)
| (0.98389775734140569999 + 3.7446279609651618323e-941j)  +/-  (4.53e-250, 4.53e-250j)
| (-3.6658316928775966507 + 1.7752963649837292836e-936j)  +/-  (2.75e-246, 2.75e-246j)
| (-3.4012099421432675636 - 1.7958259461916134522e-939j)  +/-  (2.93e-246, 2.93e-246j)
| (-0.66944416045059213743 + 1.7358309856010674545e-949j)  +/-  (3.8e-252, 3.8e-252j)
| (5.4522831090801266746 - 4.791697572044346236e-946j)  +/-  (9.43e-247, 9.43e-247j)
| (-4.962593092700393863 - 8.9027790058425059728e-953j)  +/-  (1.73e-246, 1.73e-246j)
| (1.3117288375389628728 - 1.8300756707947780492e-963j)  +/-  (3.46e-250, 3.46e-250j)
| (-4.5017229921952433534 - 1.9348134841808748102e-960j)  +/-  (2.15e-246, 2.15e-246j)
| (-2.0201828704560856329 - 1.5809793122655492067e-966j)  +/-  (9.33e-249, 9.33e-249j)
| (-0.98389775734140569999 - 1.4374353560166553683e-969j)  +/-  (4.56e-250, 4.56e-250j)
| (3.4012099421432675636 - 3.3347436233863071894e-967j)  +/-  (2.86e-246, 2.86e-246j)
| (2.0201828704560856329 - 1.0053000017497911723e-978j)  +/-  (8.3e-249, 8.3e-249j)
| (2.396397951415888391 - 1.2612890989082940317e-980j)  +/-  (4.7e-248, 4.7e-248j)
| (1.6566775594588798901 + 4.4865986738077064866e-987j)  +/-  (1.73e-249, 1.73e-249j)
| (-1.3117288375389628728 - 1.9598584283086560962e-991j)  +/-  (3.77e-250, 3.77e-250j)
| (-1.6566775594588798901 + 3.0400142904203325523e-991j)  +/-  (1.54e-249, 1.54e-249j)
| (-2.5561072781705553305e-999 - 5.4547960773131431765e-1001j)  +/-  (9.97e-998, 9.97e-998j)
| (0.66944416045059213743 - 2.7127732945662935002e-996j)  +/-  (3.83e-252, 3.83e-252j)
| (4.0656929841242320401 + 2.9376476645331140472e-989j)  +/-  (2.3e-246, 2.3e-246j)
| (-0.95857246461381850711 + 2.214287560916834875e-1010j)  +/-  (3.87e-250, 3.87e-250j)
| (-0.33971200374897154669 + 6.2069809932706453186e-1014j)  +/-  (1.06e-253, 1.06e-253j)
| (4.5017229921952433534 + 1.5712432758320523503e-1010j)  +/-  (2.1e-246, 2.1e-246j)
| (0.33971200374897154669 + 1.3206312989283302653e-1022j)  +/-  (1.06e-253, 1.06e-253j)
| (3.1512629855004394848 + 1.4569158563062280824e-1018j)  +/-  (1.2e-246, 1.2e-246j)
-------------------------------------------------
The weights are:
| (9.0784610612569895528e-17 + 2.6237687952967776116e-906j)  +/-  (1.87e-90, 4.62e-214j)
| (6.301532466544232253e-20 + 8.5618902144573332675e-909j)  +/-  (4.66e-92, 1.15e-215j)
| (4.415449909455768068e-24 + 1.6072334706192476853e-912j)  +/-  (2.03e-95, 5.01e-219j)
| (5.392340903189372648e-12 + 3.4731698719629504207e-904j)  +/-  (1.78e-88, 4.39e-212j)
| (3.5152970549159768276e-14 - 1.2256905984561700878e-906j)  +/-  (2.56e-91, 6.32e-215j)
| (6.301532466544232253e-20 - 4.0246599200485760943e-910j)  +/-  (3.17e-94, 7.82e-218j)
| (9.0784610612569895528e-17 + 3.0658574916650215142e-908j)  +/-  (8.29e-93, 2.05e-216j)
| (1.5799791123029346269e-08 + 1.1124967244880823606e-902j)  +/-  (8.46e-89, 2.09e-212j)
| (4.415449909455768068e-24 - 1.640870283703631243e-911j)  +/-  (1.09e-97, 2.69e-221j)
| (9.5468374134305835354e-05 + 1.773314393671339655e-899j)  +/-  (1.73e-85, 4.27e-209j)
| (-0.010624589031155796859 + 8.7107034430972820941e-896j)  +/-  (3.35e-77, 8.27e-201j)
| (9.3857732794847224399e-06 - 2.3592217524360359581e-900j)  +/-  (2.03e-86, 5.01e-210j)
| (9.5468374134305835354e-05 + 6.4805805439036596959e-900j)  +/-  (2.23e-85, 5.5e-209j)
| (0.00068885302369623366666 - 2.3275658444599206565e-899j)  +/-  (2.55e-84, 6.29e-208j)
| (2.9793604210330615951e-07 - 7.5213070588810622179e-901j)  +/-  (3.27e-91, 8.07e-215j)
| (0.077961477910997863706 - 8.244053984701241303e-896j)  +/-  (3.35e-77, 8.27e-201j)
| (2.9793604210330615951e-07 - 1.8052195124488740125e-901j)  +/-  (8.55e-89, 2.11e-212j)
| (9.7051807783394716021e-07 + 9.5741058280309633862e-901j)  +/-  (6.93e-88, 1.71e-211j)
| (0.11641895568228426778 - 8.8804713869710177283e-897j)  +/-  (7.11e-82, 1.75e-205j)
| (3.5152970549159768276e-14 - 2.6490959751390478422e-905j)  +/-  (1.04e-96, 2.57e-220j)
| (5.392340903189372648e-12 + 3.2328191034911692358e-905j)  +/-  (1.49e-93, 3.67e-217j)
| (0.033735525739097379752 + 3.0940250983532988431e-897j)  +/-  (7.85e-85, 1.94e-208j)
| (3.99813371666542753e-10 - 6.4746278403300867376e-904j)  +/-  (3.07e-92, 7.57e-216j)
| (0.0035326639345381737741 + 9.261524932119831738e-899j)  +/-  (4.39e-87, 1.08e-210j)
| (0.077961477910997863706 - 5.9149502665218666662e-896j)  +/-  (2.43e-84, 5.99e-208j)
| (9.7051807783394716021e-07 + 3.4816542082602009891e-900j)  +/-  (3.3e-93, 8.14e-217j)
| (0.0035326639345381737741 + 1.870839987313220028e-898j)  +/-  (5.65e-90, 1.4e-213j)
| (0.00068885302369623366666 - 5.4394011895920088323e-899j)  +/-  (3.84e-91, 9.47e-215j)
| (0.012881457083391772776 - 7.0100703940931475162e-898j)  +/-  (7.09e-89, 1.75e-212j)
| (0.033735525739097379752 + 1.9810347707111115106e-897j)  +/-  (2.21e-88, 5.46e-212j)
| (0.012881457083391772776 - 3.9690918374983371624e-898j)  +/-  (4.51e-89, 1.11e-212j)
| (0.1926980008508464659 - 5.9276035233830053303e-897j)  +/-  (1.8e-88, 4.43e-212j)
| (0.11641895568228426778 - 1.1118862826439931545e-896j)  +/-  (2.56e-88, 6.31e-212j)
| (1.5799791123029346269e-08 + 5.8349075839113569466e-902j)  +/-  (7.28e-97, 1.79e-220j)
| (-0.010624589031155796859 + 6.30435687307545939e-896j)  +/-  (1.71e-88, 4.28e-212j)
| (0.16895051642516106523 + 6.2107120562780955408e-897j)  +/-  (1.48e-89, 3.71e-213j)
| (3.99813371666542753e-10 - 4.5874730657074585733e-903j)  +/-  (3.94e-98, 9.73e-222j)
| (0.16895051642516106523 + 6.9586795834841120425e-897j)  +/-  (5.2e-91, 1.83e-214j)
| (9.3857732794847224399e-06 - 7.6132846422964928515e-900j)  +/-  (1.6e-94, 3.86e-218j)
