Starting with polynomial:
P : t
Extension levels are: 1 2 10 26
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P2 : t^3 - 3/5*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P3 : t^13 - 124943/42780*t^11 + 576433/179676*t^9 - 310453/189658*t^7 + 10439/27094*t^5 - 97669/2763588*t^3 + 3421/4605980*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 3189268649727806706148217532503789540996578918504609895242606216498470312696897712229/326709098717516490345022306317451218140670640696168101751564365827461218826575283340*t^37 + 362053604428936295809194895816122255930082184346298408366715746930109348876889473549597/8233069287681415556694562119199770697144900145543436164139422018852022714429697140168*t^35 - 2537295540237583350702753314868915917397368624191530287005653363624282870239580747283521719651/20925885178599114062048331509062507583914129816225859633723035132829941056970673635102183416*t^33 + 10035776092198633666335305005769425938035235581755959160494975877899421776381595388561364157/43855755382827071954420700448802498843809806022922908439530373431264795480295174213946747*t^31 - 1121529524682451922646552160609112233616144585064075018316722283362713083315817767772359771292/3580908053694910647714693967205871947190738541698525357525185482902916483928413944773074539*t^29 + 1625392153533765844526715361480222701343445380848631767626886196089167348461553277119290399300579/5058421854980332475836974217152990415835960661729786472434490275631119850558007350681617033570*t^27 - 11506883704713101763609293531600386780358456016029149578219536206036498792620126633375642932872291/45675675860896483615150159783033298643733600345545257110352915896254334058001562670228823436458*t^25 + 2574210412274732422852996403918464635328396228750574570072598396136552531257000754879948350340505/16880141079026961336033754702425349498771113171179768932086947179050514760565794899867173878691*t^23 - 354982974609733735522755729276561169471052794587523453581180032488751493863792721329544763215227095/4962761477233926632793923882513052752638707272326852066033562470640851339606343700560949120335154*t^21 + 645361058134531448117623468174809815689833498273822516921500827961546184782920897499404654290265/24875997379618679863628691140416304524504798357528080531496553737548127015570645115593729926492*t^19 - 2814443304681649556164217423210210330683738761961553726072013160838693350835161260773172410138093/389723958947359317863516161199855437550575174267939928326779341888253989910606773477635102181708*t^17 + 1125609785738369864525126771904144791156486428445382414200392754179239456714105985100725672923995/739329275061902235358729188158549285941532315890650746384625516229187716153945202626690120315299*t^15 - 7220864909186383201079497827814697004321986470305104381473151464156143449778572351186282513107810/30312500277537991649707896714500520723602824951516680601769646165396696362311753307694294932927259*t^13 + 1628360240733785100732114211566670568271133490555082060549349619083809615981741025801086503773345/60625000555075983299415793429001041447205649903033361203539292330793392724623506615388589865854518*t^11 - 1140939962799502292705525540744172922936307239972416822774239606657603197594311538230225082093325/545625004995683849694742140861009373024850849127300250831853630977140534521611559538497308792690662*t^9 + 1315760386381324681402324170769301539664013934020081776460611658606971084159799111948903186076/12481617761339173032232663353029626180307045568271574365434560185751580855069545479638827325322989*t^7 - 19806986320883464980261857972635738190882566163090352103172393727450660970548718980729500075/6381579005797471926254294045158004362863752621371932758267293929557199234170895433198798933247844*t^5 + 142432116596925072257887238050383132471452535894900714365213305152585324392209561250559309085/3221785743784037969626096450798341059765785966275487195388088106722163156222849208703507918585411528*t^3 - 1468590127671433240339249055362483873734540012021200409005972233254725131227934176231931265/7517500068829421929127558385196129139453500587976136789238872249018380697853314820308185143365960232*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:
| (0.96375229857121199904 - 3.2390573342623564546e-937j)  +/-  (7.75e-242, 7.75e-242j)
| (0.99304762120002015918 + 1.1967064902727554231e-937j)  +/-  (1.24e-241, 1.24e-241j)
| (-0.93829919215080213815 - 1.7125904019924308312e-935j)  +/-  (3.86e-242, 3.86e-242j)
| (0.98189373966174310941 + 1.1800836029925965684e-947j)  +/-  (1.14e-241, 1.14e-241j)
| (0.90591989788431806766 - 9.3819711435073829349e-950j)  +/-  (1.79e-242, 1.79e-242j)
| (0.82336249839555119204 - 2.7618712145584282867e-951j)  +/-  (2.01e-243, 2.01e-243j)
| (-0.99867860805739849386 - 3.1140181976326927912e-946j)  +/-  (4.48e-242, 4.48e-242j)
| (-0.90591989788431806766 + 1.5016197527086263219e-971j)  +/-  (1.77e-242, 1.77e-242j)
| (-0.98189373966174310941 - 2.3927216902671014902e-991j)  +/-  (1.14e-241, 1.14e-241j)
| (0.99867860805739849386 + 2.2081721050469925266e-1014j)  +/-  (4.65e-242, 4.65e-242j)
| (0.86732662484779688767 - 4.2974246076063197814e-1018j)  +/-  (6.6e-243, 6.6e-243j)
| (-0.96375229857121199904 + 4.1805805232740844758e-1014j)  +/-  (7.87e-242, 7.87e-242j)
| (-0.86732662484779688767 + 4.6097917810510298543e-1024j)  +/-  (6.7e-243, 6.7e-243j)
| (-0.82336249839555119204 - 1.3261651467711250623e-1032j)  +/-  (2.31e-243, 2.31e-243j)
| (-0.99304762120002015918 - 9.0860998820114584031e-1046j)  +/-  (1.12e-241, 1.12e-241j)
| (0.77459666924148337704 - 1.0795643386596669584e-1057j)  +/-  (5.75e-244, 5.75e-244j)
| (0.93829919215080213815 + 1.8950607645259350186e-1060j)  +/-  (4.04e-242, 4.04e-242j)
| (-0.32118908219889955262 - 4.0794161430080515593e-1068j)  +/-  (2.43e-250, 2.43e-250j)
| (-0.77459666924148337704 + 1.6054161638200589838e-1064j)  +/-  (5.57e-244, 5.57e-244j)
| (-0.7208837691772378803 + 2.6416289174784988339e-1064j)  +/-  (1.18e-244, 1.18e-244j)
| (0.25033726097206800803 + 6.3919265292926538818e-1072j)  +/-  (1.98e-251, 1.98e-251j)
| (0.7208837691772378803 + 3.6781250337990900897e-1066j)  +/-  (1.11e-244, 1.11e-244j)
| (0.17101852249474448773 + 6.4860945054541162842e-1074j)  +/-  (6.94e-253, 6.94e-253j)
| (-0.59706738604131558719 + 5.8199842842296373393e-1065j)  +/-  (2.38e-246, 2.38e-246j)
| (-0.52800882982846544973 - 7.2522021702275265106e-1067j)  +/-  (2.34e-247, 2.34e-247j)
| (-0.086566243049470393435 + 4.6680003034629272147e-1076j)  +/-  (2.48e-254, 2.48e-254j)
| (0.66169949263036031332 + 1.2721620567701564378e-1066j)  +/-  (1.96e-245, 1.96e-245j)
| (0.32118908219889955262 - 1.0391915182189332057e-1071j)  +/-  (2.79e-250, 2.79e-250j)
| (-0.17101852249474448773 + 2.0283483496067259214e-1074j)  +/-  (5.9e-253, 5.9e-253j)
| (-0.66169949263036031332 - 2.5063913477049461846e-1068j)  +/-  (1.72e-245, 1.72e-245j)
| (-0.25033726097206800803 + 3.218820200715565885e-1075j)  +/-  (1.8e-251, 1.8e-251j)
| (0.38736385932378655649 + 2.188697945074530971e-1072j)  +/-  (2.91e-249, 2.91e-249j)
| (0.59706738604131558719 - 1.663217746977520679e-1070j)  +/-  (2.28e-246, 2.28e-246j)
| (-6.618367788460309385e-1090 - 1.5814523788963914313e-1091j)  +/-  (2.58e-1088, 2.58e-1088j)
| (-0.45679321179984000061 - 5.2132407022325139154e-1074j)  +/-  (2.53e-248, 2.53e-248j)
| (-0.38736385932378655649 - 4.3173356334734998208e-1076j)  +/-  (2.87e-249, 2.87e-249j)
| (0.086566243049470393435 - 9.1474526489783068195e-1081j)  +/-  (2.48e-254, 2.48e-254j)
| (0.52800882982846544973 + 2.5705859842481278752e-1073j)  +/-  (2.38e-247, 2.38e-247j)
| (0.45679321179984000061 + 6.3153789656161044545e-1075j)  +/-  (2.48e-248, 2.48e-248j)
-------------------------------------------------
The weights are:
| (0.021823435693470710474 + 1.6046974964544296713e-937j)  +/-  (2.01e-75, 5.76e-192j)
| (0.0080889452218144191237 - 3.0080071556225100922e-938j)  +/-  (7.32e-76, 2.09e-192j)
| (0.029013522492023410914 + 3.8118886052819419849e-937j)  +/-  (2.04e-77, 5.83e-194j)
| (0.014497483784523056894 + 2.5715276313389540685e-937j)  +/-  (1.02e-75, 2.92e-192j)
| (0.03562415192215433077 + 4.2986657316069886591e-937j)  +/-  (7.29e-77, 2.08e-193j)
| (0.046408024535635607134 + 4.9076735965060749922e-937j)  +/-  (7.09e-78, 2.03e-194j)
| (0.0033638987648373596611 + 1.7033750939900631375e-936j)  +/-  (3.24e-78, 9.26e-195j)
| (0.03562415192215433077 + 1.7193326204546837171e-935j)  +/-  (4.73e-78, 1.35e-194j)
| (0.014497483784523056894 + 9.2732875114026990046e-936j)  +/-  (3.12e-78, 8.92e-195j)
| (0.0033638987648373596611 - 6.8617911347184368317e-938j)  +/-  (1.32e-76, 3.77e-193j)
| (0.04141504755300938605 - 4.4153973728905961295e-937j)  +/-  (1.45e-77, 4.14e-194j)
| (0.021823435693470710474 - 1.7877696669450096077e-935j)  +/-  (2.45e-78, 7e-195j)
| (0.04141504755300938605 - 9.0437671314065061286e-936j)  +/-  (9.53e-80, 2.73e-196j)
| (0.046408024535635607134 + 6.4891574735742930372e-936j)  +/-  (1.42e-80, 4.06e-197j)
| (0.0080889452218144191237 - 5.2723014156062695702e-936j)  +/-  (1.15e-78, 3.28e-195j)
| (0.051153668076297212724 - 5.5118687243507250067e-937j)  +/-  (1.73e-81, 4.96e-198j)
| (0.029013522492023410914 - 5.3755494989006553267e-937j)  +/-  (1.99e-79, 5.7e-196j)
| (0.066868108968248686495 + 3.4424264632091715169e-936j)  +/-  (2.09e-84, 5.98e-201j)
| (0.051153668076297212724 - 5.1814206803010641785e-936j)  +/-  (3.43e-82, 9.81e-199j)
| (0.05637934702210069885 + 4.2805402030461358602e-936j)  +/-  (4.75e-83, 1.36e-199j)
| (0.075425207461675871559 - 1.5401861595555651418e-936j)  +/-  (1.41e-86, 4.04e-203j)
| (0.05637934702210069885 + 6.0800465016139401392e-937j)  +/-  (4.94e-85, 1.41e-201j)
| (0.082507702795443379948 + 1.3002907548425939948e-936j)  +/-  (1.08e-86, 3.09e-203j)
| (0.067104387432734046401 + 3.2353923748421561314e-936j)  +/-  (8.51e-86, 2.43e-202j)
| (0.070648986453011913131 - 3.1474441979767261834e-936j)  +/-  (2.45e-86, 7.01e-203j)
| (0.08590554850508040981 - 1.4259981751692822186e-936j)  +/-  (3.52e-88, 1.01e-204j)
| (0.061991183484075968989 - 6.6665481712210338185e-937j)  +/-  (1.5e-87, 4.28e-204j)
| (0.066868108968248686495 + 1.7173240509222244571e-936j)  +/-  (2.42e-88, 6.93e-205j)
| (0.082507702795443379948 + 1.8634501079537380866e-936j)  +/-  (2.03e-88, 5.8e-205j)
| (0.061991183484075968989 - 3.6247725293897665996e-936j)  +/-  (2.01e-87, 5.75e-204j)
| (0.075425207461675871559 - 2.6257040114485945844e-936j)  +/-  (2.1e-88, 6e-205j)
| (0.067244471959443786073 - 1.5606074341266883512e-936j)  +/-  (1.44e-89, 4.12e-206j)
| (0.067104387432734046401 + 7.54455951887081287e-937j)  +/-  (1.18e-89, 3.39e-206j)
| (0.08688977029913479832 + 1.2261212305064515747e-936j)  +/-  (1.22e-89, 3.5e-206j)
| (0.071091992724852345841 + 3.3667141988905253002e-936j)  +/-  (2.07e-89, 5.92e-206j)
| (0.067244471959443786073 - 3.6697344037973839072e-936j)  +/-  (1.64e-89, 4.69e-206j)
| (0.08590554850508040981 - 1.1902717093556725858e-936j)  +/-  (3.42e-90, 9.77e-207j)
| (0.070648986453011913131 - 9.1433346169866376725e-937j)  +/-  (2.77e-91, 7.97e-208j)
| (0.071091992724852345841 + 1.1965607630277862802e-936j)  +/-  (3.54e-91, 1.01e-207j)
