Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 6 33
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 33 Kronrod extension for:
P2 : 3/2*t^8 - 161/52*t^6 + 105/52*t^4 - 245/572*t^2 + 25/1716
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^41 - 288186070490653111244297565045552446671359502050992690057/18603692508983255765793489431098235947874776060032661972*t^39 + 29459632650961661304738599608623426942015174882264560912604907/397579512609481158970772662632000400442031839178958019003612*t^37 - 2857738734687905542007287827630021427327249962577798159791864005/13120123916112878246035497866856013214587050692905614627119196*t^35 + 3814457136863553361730413873137776683229937295598172011134524019235/8664904694884262304488872376925049870147990764757522345881720444*t^33 - 553348309869726862646577557049124040042547383384554712708145078703/853361826011328863320873794697164002363059696529149928003502771*t^31 + 49432340519941600369028515823804082200756902999720051082325645807/68661296345739103945357661642300551914269170985104017195684131*t^29 - 9929822360863409323577580639718931026012096402829894702327998219397/16155022154490329171143438389267001286114474944638045188755966251*t^27 + 1107972839721182036033279732545697877748344341152379722030638727850/2715516544486978407685079387369666882851151059070212724035903159*t^25 - 8042233808326839771592236180407586538548390512864686620199172728075/38017231622817697707591111423175336359916114826982978136502644226*t^23 + 6334241034304734941211667238400377386069280784175209181954251845/74011482718009794369093662731684626268493409786469133296241358*t^21 - 336107858679530678303704949841602165010452066280339741529578744905/12514989291983465704983409350486290851400957054845328206426336298*t^19 + 80872217213767415417356403713858652769251224687072295433869597755/12514989291983465704983409350486290851400957054845328206426336298*t^17 - 18258512281241281405036206088757940129558404019264936835416290525/15590706999335334395191196394249870806406277009002230901226029117*t^15 + 10720141869482012611835006865584898342244567032485664131493076775/68832441105909061377408751427674599682705263801649305135344849639*t^13 - 7052283425141978515149482391696111274183973319992052317535110155/481827087741363429641861259993722197778936846611545135947413947473*t^11 + 10258500280796162962202026680002179164878188393032882881194130599445/11154121871362475627689218401123762070510468385658502062587742915291778*t^9 - 87937840322518114473757098112063257926555423075959876498341792485/2478693749191661250597604089138613793446770752368556013908387314509284*t^7 + 3349300606451558359285521304346691595958225565221948025436676975/4603288391355942322538407594114568473544002825827318311544147869802956*t^5 - 82279582293286562482463236246363915434292583099780531701272275/13809865174067826967615222782343705420632008477481954934632443609408868*t^3 + 263314437147095479538277960938569783289620964629807716264625/32223018739491596257768853158801979314808019780791228180809035088620692*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:
| (0.98219129046748981137 + 9.4050117856571759126e-862j)  +/-  (1.16e-240, 1.16e-240j)
| (-0.99856127064094102005 - 4.8659649059292208528e-884j)  +/-  (3.21e-241, 3.21e-241j)
| (-0.94755615828187897822 - 1.2164991100010039147e-883j)  +/-  (5.48e-241, 5.48e-241j)
| (0.99856127064094102005 - 2.0855596554361609544e-884j)  +/-  (3.39e-241, 3.39e-241j)
| (0.96747364105607170595 - 1.3329417842298501302e-904j)  +/-  (9.72e-241, 9.72e-241j)
| (0.94755615828187897822 + 2.230335024147022706e-921j)  +/-  (5.49e-241, 5.49e-241j)
| (-0.889429812900368172 - 2.9680891265394739028e-929j)  +/-  (8.58e-242, 8.58e-242j)
| (-0.92161768586040480965 - 1.1073260554594831773e-928j)  +/-  (2.45e-241, 2.45e-241j)
| (-0.98219129046748981137 - 8.1319147811573804463e-927j)  +/-  (1.17e-240, 1.17e-240j)
| (0.80686426297140222004 - 8.9976366737748428215e-931j)  +/-  (5.29e-243, 5.29e-243j)
| (0.85110112875893547946 + 2.258314817825486069e-931j)  +/-  (2.35e-242, 2.35e-242j)
| (-0.99255883638657954905 - 5.096547127972915884e-937j)  +/-  (9.25e-241, 9.25e-241j)
| (-0.85110112875893547946 + 2.9616940363478212057e-940j)  +/-  (2.38e-242, 2.38e-242j)
| (-0.80686426297140222004 - 6.0251429542025453016e-941j)  +/-  (5.13e-243, 5.13e-243j)
| (0.99255883638657954905 + 7.7133464711600955198e-937j)  +/-  (9.03e-241, 9.03e-241j)
| (0.92161768586040480965 + 1.1099203745970102507e-948j)  +/-  (2.51e-241, 2.51e-241j)
| (0.889429812900368172 - 2.0009515677083236488e-961j)  +/-  (8.41e-242, 8.41e-242j)
| (-0.96747364105607170595 + 7.6918627430144999663e-969j)  +/-  (1.02e-240, 1.02e-240j)
| (-0.75701250329774731927 - 7.8631785899089570881e-973j)  +/-  (9.91e-244, 9.91e-244j)
| (-0.2041968861768067152 - 7.3987878671082147773e-982j)  +/-  (2.19e-252, 2.19e-252j)
| (0.64185871675602425914 + 1.4297073178714510696e-971j)  +/-  (1.92e-245, 1.92e-245j)
| (0.75701250329774731927 + 2.203900430658754314e-974j)  +/-  (9.77e-244, 9.77e-244j)
| (0.12310074545548346218 + 2.8887260876621887422e-986j)  +/-  (1.04e-253, 1.04e-253j)
| (-0.70188445409563750148 + 7.0210398791173452164e-978j)  +/-  (1.52e-244, 1.52e-244j)
| (-0.64185871675602425914 + 2.1457550734776737619e-980j)  +/-  (2.02e-245, 2.02e-245j)
| (0.041163209615166211451 - 3.2723372428503844633e-989j)  +/-  (5.45e-255, 5.45e-255j)
| (0.70188445409563750148 - 4.3860245579528894928e-982j)  +/-  (1.42e-244, 1.42e-244j)
| (0.43670626833855805385 - 1.7005012550303285764e-987j)  +/-  (1.28e-248, 1.28e-248j)
| (-0.12310074545548346218 + 2.4415533572362266068e-993j)  +/-  (1.02e-253, 1.02e-253j)
| (-0.57735026918962576451 + 4.0744022550370534857e-987j)  +/-  (1.94e-246, 1.94e-246j)
| (-0.041163209615166211451 + 5.5765430555937517495e-994j)  +/-  (5.45e-255, 5.45e-255j)
| (0.36155112071223327151 + 1.8657747904475936841e-989j)  +/-  (8.2e-250, 8.2e-250j)
| (0.57735026918962576451 + 1.9665865332625003437e-988j)  +/-  (1.99e-246, 1.99e-246j)
| (-6.4020269760252710249e-999 + 6.9572028350597404637e-999j)  +/-  (3.88e-997, 3.88e-997j)
| (-0.43670626833855805385 + 5.0511972239061353256e-992j)  +/-  (1.32e-248, 1.32e-248j)
| (-0.36155112071223327151 - 1.2840286219038010008e-993j)  +/-  (8.59e-250, 8.59e-250j)
| (0.2041968861768067152 - 5.8553061646585529042e-997j)  +/-  (2.33e-252, 2.33e-252j)
| (0.50880701649762814941 - 6.9972560957254617835e-992j)  +/-  (1.71e-247, 1.71e-247j)
| (0.28386677098522270517 + 1.1543363170911096001e-998j)  +/-  (4.25e-251, 4.25e-251j)
| (-0.28386677098522270517 - 1.4223376526071310631e-1002j)  +/-  (4.81e-251, 4.81e-251j)
| (-0.50880701649762814941 + 7.5324741909734200197e-1001j)  +/-  (1.72e-247, 1.72e-247j)
-------------------------------------------------
The weights are:
| (0.012464055573647254803 - 2.0641280166473362847e-862j)  +/-  (9.26e-72, 8.67e-188j)
| (0.0036756543256161923904 - 9.7361417932769531989e-865j)  +/-  (2.26e-72, 2.12e-188j)
| (0.0228438768424225509 - 8.1076319710364530411e-864j)  +/-  (2.09e-72, 1.96e-188j)
| (0.0036756543256161923904 + 1.1780642119300997384e-862j)  +/-  (1.69e-72, 1.58e-188j)
| (0.017136873549948841737 + 1.0220945113606279314e-861j)  +/-  (2.35e-72, 2.2e-188j)
| (0.0228438768424225509 - 4.5172866751772960456e-862j)  +/-  (6.72e-73, 6.29e-189j)
| (0.03529035283406984969 - 7.0800384987184934448e-864j)  +/-  (5.68e-74, 5.32e-190j)
| (0.029064020665903213731 + 7.6845364470397577588e-864j)  +/-  (9.31e-74, 8.72e-190j)
| (0.012464055573647254803 - 5.9675030060307044088e-864j)  +/-  (2.3e-74, 2.15e-190j)
| (0.047097208839913833914 - 6.3536513337100450995e-863j)  +/-  (3.53e-76, 3.31e-192j)
| (0.041327452128831425364 + 9.1885093263248357039e-863j)  +/-  (6.66e-76, 6.23e-192j)
| (0.00825312454095661327 + 3.3355985315905305044e-864j)  +/-  (1.6e-74, 1.5e-190j)
| (0.041327452128831425364 + 6.570273028002494236e-864j)  +/-  (3.69e-76, 3.46e-192j)
| (0.047097208839913833914 - 6.2265635068999769791e-864j)  +/-  (4.03e-77, 3.78e-193j)
| (0.00825312454095661327 - 6.3534549784477623639e-862j)  +/-  (2.16e-75, 2.02e-191j)
| (0.029064020665903213731 + 2.41522517302560696e-862j)  +/-  (1.89e-76, 1.77e-192j)
| (0.03529035283406984969 - 1.4285185849125752167e-862j)  +/-  (6e-77, 5.61e-193j)
| (0.017136873549948841737 + 7.7155968906848189687e-864j)  +/-  (2.25e-76, 2.11e-192j)
| (0.05254980067320109297 + 6.0581946389477068047e-864j)  +/-  (2.27e-79, 2.12e-195j)
| (0.0804774676609453376 + 1.9514960650638280168e-863j)  +/-  (4.51e-83, 4.22e-199j)
| (0.06233911514355524101 + 2.9896681978463329697e-863j)  +/-  (1.59e-81, 1.49e-197j)
| (0.05254980067320109297 + 4.6791419528712447173e-863j)  +/-  (4.3e-80, 4.03e-196j)
| (0.081618805559217325222 - 4.3878042081084455692e-863j)  +/-  (1.51e-83, 1.41e-199j)
| (0.057643139388610071844 - 6.0667983437691953839e-864j)  +/-  (2.88e-81, 2.7e-197j)
| (0.06233911514355524101 + 6.2650870834689019644e-864j)  +/-  (3.17e-82, 2.97e-198j)
| (0.082127022172580114656 + 1.1859427268390045874e-862j)  +/-  (3.66e-84, 3.43e-200j)
| (0.057643139388610071844 - 3.6449157181253160869e-863j)  +/-  (1.99e-82, 1.87e-198j)
| (0.073713762403210812448 - 2.2239438346707981895e-863j)  +/-  (7.16e-85, 6.7e-201j)
| (0.081618805559217325222 - 3.4104299913842441643e-863j)  +/-  (4.15e-85, 3.89e-201j)
| (0.066603070443535583829 - 6.6873922239244529296e-864j)  +/-  (7.02e-85, 6.57e-201j)
| (0.082127022172580114656 + 1.090536474064403413e-862j)  +/-  (3.57e-85, 3.34e-201j)
| (0.076508938528671613997 + 2.250444818507648945e-863j)  +/-  (2.2e-86, 2.06e-202j)
| (0.066603070443535583829 - 2.5761386694506545207e-863j)  +/-  (1.11e-85, 1.04e-201j)
| (0.00018668099465842688239 - 1.7814516485374656397e-862j)  +/-  (2.66e-85, 2.49e-201j)
| (0.073713762403210812448 - 8.5497930723744853677e-864j)  +/-  (1.14e-87, 1.07e-203j)
| (0.076508938528671613997 + 1.0394227662705039618e-863j)  +/-  (9.65e-88, 9.04e-204j)
| (0.0804774676609453376 + 2.9758978285588686395e-863j)  +/-  (1.24e-87, 1.16e-203j)
| (0.07040382296912131527 + 2.3319758331261840336e-863j)  +/-  (7.62e-88, 7.14e-204j)
| (0.078769095258712501915 - 2.4528619593948638309e-863j)  +/-  (5.66e-88, 5.3e-204j)
| (0.078769095258712501915 - 1.3529345148557606837e-863j)  +/-  (1e-88, 9.44e-205j)
| (0.07040382296912131527 + 7.4039030193582119657e-864j)  +/-  (5.55e-89, 5.12e-205j)
