Starting with polynomial:
P : 2*t
Extension levels are: 1 26 44
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P2 : 2*t^27 - 351*t^25 + 26325*t^23 - 2220075/2*t^21 + 233107875/8*t^19 - 7972289325/16*t^17 + 45176306175/8*t^15 - 677644592625/16*t^13 + 26428139112375/128*t^11 - 161505294575625/256*t^9 + 290709530236125/256*t^7 - 554990921359875/512*t^5 + 924984868933125/2048*t^3 - 213458046676875/4096*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^71 - 4123964009500291191467339877579250750572776110737902471/2240758616243123085684006629009389718779104141555315*t^69 + 34514262837776522421562868222626572476723230787851278255509/43321333247367046323224128160848201229729346736736090*t^67 - 18710719957878528493623522133643707173833469137439908003111421/86642666494734092646448256321696402459458693473472180*t^65 + 1604776162725951991809171989464706082297439513448600203940466626/38989199922630341690901715344763381106756412063062481*t^63 - 25440307745362798526124065073299705077609462454196060695522878363/4332133324736704632322412816084820122972934673673609*t^61 + 2824519802143489273197525920976158776655423458139647372374887431920/4332133324736704632322412816084820122972934673673609*t^59 - 500893199910638949177743550524168938436006773347516147579488883490015/8664266649473409264644825632169640245945869347347218*t^57 + 577979117687226536687081274952384996121225644214082097120812164857402365/138628266391574548234317210114714243935133909557555488*t^55 - 68707301768183431403680699234835454397785385421404446591423880968509163825/277256532783149096468634420229428487870267819115110976*t^53 + 6796987525074019540312476528198083516438700718845038971333813618331292069825/554513065566298192937268840458856975740535638230221952*t^51 - 563558276521932610236435584455734497843490016980841748092249521033665721339345/1109026131132596385874537680917713951481071276460443904*t^49 + 307525868694786003601517490163644971487858050856666187188546647300852017597545/17328533298946818529289651264339280491891738694694436*t^47 - 290544577554433180588818740111102158722543541131248707439721710647252233012061755/554513065566298192937268840458856975740535638230221952*t^45 + 29071029123908987590200267936944515118385024648191104235046817773865168179120555675/2218052262265192771749075361835427902962142552920887808*t^43 - 1233469948107467724849181396733641661765950546192541380421827634390267011018542267825/4436104524530385543498150723670855805924285105841775616*t^41 + 3989654462698425078282466746239909469711554429124836606660935337275898592155021452575/797501936994226614561465298637457223536950131387285504*t^39 - 10825042604105727008824270325885319525652905347375803327175476618338167707133615200405275/141955344784972337391940823157467385789577123386936819712*t^37 + 279042943281820009246091980990450506131352919536979245514672324498640384753009595401421975/283910689569944674783881646314934771579154246773873639424*t^35 - 6064056187559696868802523568787235093637627233443591362281820287665812199867998979611753375/567821379139889349567763292629869543158308493547747278848*t^33 + 13831899109920032922159933359377496451623231564190976216622713127346478016515331719810382625/141955344784972337391940823157467385789577123386936819712*t^31 - 7270885913149569081162090904398115877665930948770103755481651875473133994439043775014640875/9790023778273954302892470562583957640660491268064608256*t^29 + 46003187150649250561510561460230884721761128579795667262135472442981289569748743679713435375/9790023778273954302892470562583957640660491268064608256*t^27 - 29965874872426102330539193107631659382013013924203115343225164115190631240949046700304079625/1223752972284244287861558820322994705082561408508076032*t^25 + 32611993633028108156838032328227684133404267663574023147632815084917810968018045029382004278125/313280760904766537692559058002686644501135720578067464192*t^23 - 223583678069791163624276502575083134460743839507501883711593273277913487165970860587429519940625/626561521809533075385118116005373289002271441156134928384*t^21 + 1218496345179977012027202462252710842298574671931880634042465091581173227012977637789884206565625/1253123043619066150770236232010746578004542882312269856768*t^19 - 5186300219596615515059891018346556328725581644106809441769313774970391350186520749534127572165625/2506246087238132301540472464021493156009085764624539713536*t^17 + 2107762601528945576842201360736711278411160961358227397891018662915904212744769410218220985996875/626561521809533075385118116005373289002271441156134928384*t^15 - 1272055487211607687986414696477848962695911137871564515740465605692053135092196751641131634328125/313280760904766537692559058002686644501135720578067464192*t^13 + 17570592647617009520673113867023162715946769818393675889051192559407426193007119615106797452171875/5012492174476264603080944928042986312018171529249079427072*t^11 - 20611407803754581181689165976626587266370599852325481626243863844828232571235837407556253242828125/10024984348952529206161889856085972624036343058498158854144*t^9 + 243734256325537179260809527851432366121649351663547109413691906594921650236014583162728743806453125/320799499166480934597180475394751123969162977871941083332608*t^7 - 100273154854445507169319688790360148108481168327445002320009670519331115914909285988167113044640625/641598998332961869194360950789502247938325955743882166665216*t^5 + 201833253874725784362905665900184266125232413344988491373312343815555575094758059701198079453125/14417955018718244251558673051449488717715190016716453183488*t^3 - 698702956871074888834996210496515643563832302762889908059187431739722314206534208591870404453125/2566395993331847476777443803158008991753303822975528666660864*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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
Positive weights:   71 out of 71
Indefinite weights: 0 out of 71
Negative weights:   0 out of 71
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (7.5273715254517115826 + 1.7533939359088350607e-834j)  +/-  (5.21e-240, 5.21e-240j)
| (-7.1427239321314502757 + 4.2662632014427583165e-832j)  +/-  (1.64e-239, 1.64e-239j)
| (10.005657618840929504 + 5.188444986000904048e-852j)  +/-  (2.06e-244, 2.06e-244j)
| (-6.7788505681606735609 - 3.5707621533704785583e-845j)  +/-  (5.02e-239, 5.02e-239j)
| (-8.3676684081034303566 - 2.7177731326616149405e-855j)  +/-  (3.27e-241, 3.27e-241j)
| (9.3670099949817366354 + 1.0443274382723440856e-862j)  +/-  (4.97e-243, 4.97e-243j)
| (-6.4519401407534719686 + 1.3947811364493511374e-854j)  +/-  (1.53e-238, 1.53e-238j)
| (7.9339088431372477753 + 1.9927677523248291566e-864j)  +/-  (1.48e-240, 1.48e-240j)
| (-4.0183186704087389185 + 3.2959191268629541633e-862j)  +/-  (3.85e-240, 3.85e-240j)
| (6.7788505681606735609 - 6.9562515289877864537e-863j)  +/-  (4.62e-239, 4.62e-239j)
| (8.8386831757822520151 + 1.9236589552919163754e-866j)  +/-  (5.21e-242, 5.21e-242j)
| (4.2770968639109494276 - 5.3626179552967408512e-865j)  +/-  (9.34e-240, 9.34e-240j)
| (3.5262753401343531784 + 1.2258835445818014318e-864j)  +/-  (6.35e-241, 6.35e-241j)
| (-7.9339088431372477753 - 1.4340080186669225655e-861j)  +/-  (1.55e-240, 1.55e-240j)
| (-10.005657618840929504 + 4.618064269201589973e-870j)  +/-  (2.06e-244, 2.06e-244j)
| (-7.5273715254517115826 - 1.076988268462359468e-863j)  +/-  (5.45e-240, 5.45e-240j)
| (2.1482966453616273647 + 3.7280587071888352459e-876j)  +/-  (1.37e-244, 1.37e-244j)
| (5.0939100031131838921 + 4.5272152957221632703e-870j)  +/-  (3.75e-239, 3.75e-239j)
| (-1.5235490768483334651 - 1.2660176452066626231e-878j)  +/-  (5.91e-247, 5.91e-247j)
| (2.5954163389108182612 - 2.9255534170729609374e-875j)  +/-  (4.45e-243, 4.45e-243j)
| (3.2951132713116664583 - 2.1799276578709107926e-873j)  +/-  (2.21e-241, 2.21e-241j)
| (-9.3670099949817366354 + 1.3788633496702938278e-874j)  +/-  (5.3e-243, 5.3e-243j)
| (5.3974326166016869756 + 2.9032984052108969561e-870j)  +/-  (5.48e-239, 5.48e-239j)
| (4.0183186704087389185 + 3.3398178130551839211e-872j)  +/-  (3.82e-240, 3.82e-240j)
| (6.0267072225663441108 - 2.8753316398069629617e-869j)  +/-  (1.54e-238, 1.54e-238j)
| (1.2770668173398579882 - 1.0936790158865439166e-880j)  +/-  (3.48e-248, 3.48e-248j)
| (1.7095607392603373503 - 1.2232901318675663525e-878j)  +/-  (4.42e-246, 4.42e-246j)
| (-5.0939100031131838921 - 1.3382100058833092404e-869j)  +/-  (3.63e-239, 3.63e-239j)
| (-8.8386831757822520151 - 1.6691151517047630398e-878j)  +/-  (5.1e-242, 5.1e-242j)
| (-1.0224372639513100212 + 3.8639389911813154716e-896j)  +/-  (2.94e-249, 2.94e-249j)
| (8.3676684081034303566 - 2.2015700537484713782e-888j)  +/-  (3.44e-241, 3.44e-241j)
| (4.8066266773040317457 - 7.7292570400172139948e-886j)  +/-  (2.51e-239, 2.51e-239j)
| (5.7122555528165366544 - 3.6450216190770381447e-885j)  +/-  (8.43e-239, 8.43e-239j)
| (-1.9040500766284958362 + 1.0834890116523386104e-891j)  +/-  (2.07e-245, 2.07e-245j)
| (-0.84901134206010306228 - 1.1522806744533356548e-896j)  +/-  (5.25e-250, 5.25e-250j)
| (-0.16187578618389736225 - 4.1940241143356403904e-900j)  +/-  (5.23e-254, 5.23e-254j)
| (-2.5954163389108182612 + 2.0765328899420833212e-889j)  +/-  (4.47e-243, 4.47e-243j)
| (-5.7122555528165366544 + 6.7041427918482497927e-884j)  +/-  (8.7e-239, 8.7e-239j)
| (6.2590056198986720212 - 1.3128258393339433117e-901j)  +/-  (2.21e-238, 2.21e-238j)
| (-3.2951132713116664583 - 1.4841033222319467281e-901j)  +/-  (2.23e-241, 2.23e-241j)
| (7.1427239321314502757 + 5.478432722018503551e-906j)  +/-  (1.57e-239, 1.57e-239j)
| (-1.2770668173398579882 + 1.0709105720786376666e-914j)  +/-  (3.48e-248, 3.48e-248j)
| (2.3870322637646171986 + 9.6864378672558196798e-912j)  +/-  (9.54e-244, 9.54e-244j)
| (0.84901134206010306228 + 2.0976126244113410932e-917j)  +/-  (4.9e-250, 4.9e-250j)
| (6.4519401407534719686 + 7.6735490883893979244e-906j)  +/-  (1.47e-238, 1.47e-238j)
| (-4.2770968639109494276 - 2.790919906731366468e-905j)  +/-  (8.17e-240, 8.17e-240j)
| (-2.3870322637646171986 - 4.4888596655566953512e-923j)  +/-  (9.87e-244, 9.87e-244j)
| (-3.0535824198222552775 + 9.7538666330208222264e-917j)  +/-  (6.28e-242, 6.28e-242j)
| (1.9040500766284958362 - 6.2536804356427241368e-923j)  +/-  (2.33e-245, 2.33e-245j)
| (-0.68153750954038311637 - 8.0493049042127702865e-929j)  +/-  (5.48e-251, 5.48e-251j)
| (3.764668571820993057 - 6.4786841284865841483e-918j)  +/-  (1.5e-240, 1.5e-240j)
| (2.8116312701837529322 + 1.4194537886288730962e-920j)  +/-  (1.62e-242, 1.62e-242j)
| (0.68153750954038311637 - 1.6687778001199418567e-928j)  +/-  (5.33e-251, 5.33e-251j)
| (-2.1482966453616273647 + 1.1539728426224712401e-921j)  +/-  (1.31e-244, 1.31e-244j)
| (-6.0267072225663441108 + 4.1537990323652083196e-915j)  +/-  (1.64e-238, 1.64e-238j)
| (-4.5369066633724417512 - 1.4156503267025108121e-931j)  +/-  (1.53e-239, 1.53e-239j)
| (-3.764668571820993057 + 5.10102412991336153e-931j)  +/-  (1.54e-240, 1.54e-240j)
| (4.5369066633724417512 - 2.3766303421950010492e-931j)  +/-  (1.56e-239, 1.56e-239j)
| (0.16187578618389736225 - 8.9367473539230152645e-946j)  +/-  (5.23e-254, 5.23e-254j)
| (0.42380790054385304107 + 1.0252414563961097146e-943j)  +/-  (1.24e-252, 1.24e-252j)
| (-2.8116312701837529322 - 6.151013032268047257e-933j)  +/-  (1.63e-242, 1.63e-242j)
| (-4.8066266773040317457 - 8.3141131649383763734e-930j)  +/-  (2.59e-239, 2.59e-239j)
| (-3.5262753401343531784 - 2.5640835595272831121e-936j)  +/-  (6.46e-241, 6.46e-241j)
| (-6.2590056198986720212 - 1.6623347696808630091e-935j)  +/-  (2.27e-238, 2.27e-238j)
| (9.8040419441981882251e-980 - 6.0581778256293530829e-980j)  +/-  (8.18e-978, 8.18e-978j)
| (1.0224372639513100212 + 6.1387601955176241606e-953j)  +/-  (3.29e-249, 3.29e-249j)
| (-5.3974326166016869756 + 5.8390323116276748721e-953j)  +/-  (5.77e-239, 5.77e-239j)
| (-0.42380790054385304107 + 7.823329967658388014e-969j)  +/-  (1.22e-252, 1.22e-252j)
| (1.5235490768483334651 - 4.2599924469745099537e-963j)  +/-  (6.12e-247, 6.12e-247j)
| (-1.7095607392603373503 + 7.6604877413852490273e-964j)  +/-  (4.48e-246, 4.48e-246j)
| (3.0535824198222552775 - 3.2871978395181446376e-965j)  +/-  (6.21e-242, 6.21e-242j)
-------------------------------------------------
The weights are:
| (5.4995138193328032404e-26 - 9.908176210340973392e-858j)  +/-  (9.92e-56, 8.49e-173j)
| (1.4719744950923565439e-23 + 6.402881497325203004e-854j)  +/-  (1.38e-54, 1.18e-171j)
| (1.3832863553192683137e-44 + 3.2311420902232312345e-869j)  +/-  (4.52e-65, 3.87e-182j)
| (2.1907361259294111108e-21 - 7.3662216303853390795e-853j)  +/-  (3.32e-53, 2.84e-170j)
| (9.9180320924307222936e-32 + 2.1273460673427014003e-860j)  +/-  (3.7e-60, 3.17e-177j)
| (2.5190487503878494076e-39 - 3.9688772305168918118e-866j)  +/-  (1.76e-63, 1.51e-180j)
| (1.3282549926230348833e-19 + 1.4819288135877037816e-851j)  +/-  (1.66e-52, 1.42e-169j)
| (1.086651747580477608e-28 + 1.4100869972097614783e-859j)  +/-  (5.12e-59, 4.38e-176j)
| (1.4144519366029079262e-08 - 1.1040996791502765956e-844j)  +/-  (3.07e-42, 2.63e-159j)
| (2.1907361259294111108e-21 - 1.9516470730133655128e-854j)  +/-  (1.09e-55, 9.32e-173j)
| (3.2952723011274121237e-35 + 1.1844966601895991331e-863j)  +/-  (3.64e-62, 3.12e-179j)
| (1.657410114767693126e-09 + 5.5801797231328089254e-846j)  +/-  (1.83e-45, 1.57e-162j)
| (5.1862346028768780271e-07 - 7.0767049206261642354e-844j)  +/-  (7.02e-41, 6.01e-158j)
| (1.086651747580477608e-28 - 2.7622998131858621195e-858j)  +/-  (2.12e-61, 1.81e-178j)
| (1.3832863553192683137e-44 - 1.945057306805893216e-868j)  +/-  (2.16e-70, 1.85e-187j)
| (5.4995138193328032404e-26 + 3.407174714392239081e-856j)  +/-  (1.02e-59, 8.72e-177j)
| (0.0013885460717841200731 - 4.7528608804033082212e-841j)  +/-  (7.37e-33, 6.31e-150j)
| (8.9911284752761203736e-13 - 1.4898286610410756076e-848j)  +/-  (2.49e-52, 2.13e-169j)
| (0.012364282699326593069 + 6.5404640821003095337e-840j)  +/-  (2.53e-27, 2.17e-144j)
| (0.00013552770907513562153 - 9.4935187049118299545e-842j)  +/-  (1.21e-37, 1.04e-154j)
| (2.5555616445254239506e-06 + 2.5431078579156347634e-843j)  +/-  (1.85e-42, 1.59e-159j)
| (2.5190487503878494076e-39 + 2.9651878545023087544e-865j)  +/-  (2.2e-69, 1.89e-186j)
| (3.8993256749580877621e-14 + 1.5755994625487212792e-849j)  +/-  (3.86e-54, 3.31e-171j)
| (1.4144519366029079262e-08 - 3.0974161955069409721e-845j)  +/-  (1.53e-47, 1.31e-164j)
| (2.8584979679956462728e-17 + 2.3344917679933946497e-851j)  +/-  (2.54e-57, 2.18e-174j)
| (0.028596352631651867875 - 6.0858687322318385597e-840j)  +/-  (5.98e-29, 5.12e-146j)
| (0.0049871314254789840684 - 2.9971751771572294353e-840j)  +/-  (8.07e-34, 6.9e-151j)
| (8.9911284752761203736e-13 - 8.8663284242223599459e-848j)  +/-  (5.74e-58, 4.91e-175j)
| (3.2952723011274121237e-35 - 1.1261914223030839713e-862j)  +/-  (6.84e-69, 5.85e-186j)
| (0.047171510003564886746 + 1.9340448097778840523e-839j)  +/-  (8.49e-29, 7.27e-146j)
| (9.9180320924307222936e-32 - 1.6573638720578564848e-861j)  +/-  (4.16e-66, 3.56e-183j)
| (1.4515458673450920112e-11 + 1.2828344828593971293e-847j)  +/-  (1.01e-52, 8.61e-170j)
| (1.2107695452685224286e-15 - 1.7000937997872423347e-850j)  +/-  (2.43e-56, 2.08e-173j)
| (0.0034555781177128993524 + 2.3411542658554119363e-840j)  +/-  (4.8e-43, 4.11e-160j)
| (0.032040300554836178222 - 3.2464424725372419782e-839j)  +/-  (5.15e-33, 4.41e-150j)
| (0.13446799548390881431 + 4.2340286976581576405e-839j)  +/-  (1.65e-33, 1.41e-150j)
| (0.00013552770907513562153 - 2.030775672412966436e-841j)  +/-  (5.51e-49, 4.72e-166j)
| (1.2107695452685224286e-15 - 1.51999927915668861e-849j)  +/-  (4.53e-62, 3.88e-179j)
| (8.2279095412414385696e-19 - 5.0550840064407363823e-852j)  +/-  (2.76e-59, 2.37e-176j)
| (2.5555616445254239506e-06 + 6.8882740620275884817e-843j)  +/-  (1.56e-54, 1.33e-171j)
| (1.4719744950923565439e-23 + 4.5160855745003571127e-856j)  +/-  (1.84e-63, 1.57e-180j)
| (0.028596352631651867875 - 8.7315189215868220031e-840j)  +/-  (5.5e-41, 4.71e-158j)
| (0.00042261810704884475037 + 2.1079927038300682322e-841j)  +/-  (3.84e-47, 3.29e-164j)
| (0.032040300554836178222 - 2.5575004335532557396e-839j)  +/-  (8.14e-41, 6.97e-158j)
| (1.3282549926230348833e-19 + 7.5998647269081742965e-853j)  +/-  (2.53e-60, 2.16e-177j)
| (1.657410114767693126e-09 + 2.2184217876348321633e-845j)  +/-  (1.11e-59, 9.48e-177j)
| (0.00042261810704884475037 + 4.2198640351853469584e-841j)  +/-  (3.6e-51, 3.08e-168j)
| (1.2372154338403625237e-05 - 2.1963499401970177359e-842j)  +/-  (1.25e-54, 1.07e-171j)
| (0.0034555781177128993524 + 1.3567316858023969978e-840j)  +/-  (3.1e-47, 2.65e-164j)
| (0.083413215790777066472 + 3.0030298506473532727e-839j)  +/-  (4.64e-44, 3.97e-161j)
| (9.752625198450785774e-08 + 1.6138818646701483161e-844j)  +/-  (4.17e-54, 3.57e-171j)
| (4.843212401428029878e-05 + 3.1973884702212951616e-842j)  +/-  (3.18e-51, 2.73e-168j)
| (0.083413215790777066472 + 2.480516883767152098e-839j)  +/-  (5.3e-45, 4.53e-162j)
| (0.0013885460717841200731 - 8.8337716030212297705e-841j)  +/-  (1.49e-51, 1.28e-168j)
| (2.8584979679956462728e-17 + 2.7372836858726165265e-850j)  +/-  (6.88e-67, 5.89e-184j)
| (1.7047480523948158652e-10 - 4.1250518353310960455e-846j)  +/-  (1.72e-62, 1.47e-179j)
| (9.752625198450785774e-08 + 5.2011119840565130014e-844j)  +/-  (5.76e-60, 4.93e-177j)
| (1.7047480523948158652e-10 - 9.2282946695563744834e-847j)  +/-  (1.21e-59, 1.04e-176j)
| (0.13446799548390881431 + 4.0466192578410849855e-839j)  +/-  (3.7e-50, 3.16e-167j)
| (0.12593573166226323326 - 2.1952958482809747992e-839j)  +/-  (2.69e-50, 2.3e-167j)
| (4.843212401428029878e-05 + 7.3395750658209884221e-842j)  +/-  (1.19e-56, 1.02e-173j)
| (1.4515458673450920112e-11 + 6.5415911647953978773e-847j)  +/-  (6.93e-64, 5.93e-181j)
| (5.1862346028768780271e-07 - 2.084134719917791133e-843j)  +/-  (1.36e-59, 1.16e-176j)
| (8.2279095412414385696e-19 - 7.6073365162012758785e-851j)  +/-  (8.9e-69, 7.61e-186j)
| (0.051114435530005607035 - 5.7619296191211344692e-839j)  +/-  (5.69e-54, 4.79e-171j)
| (0.047171510003564886746 + 1.4502596477844234818e-839j)  +/-  (1.03e-55, 8.62e-173j)
| (3.8993256749580877621e-14 + 1.1273188339807323178e-848j)  +/-  (2.78e-66, 2.38e-183j)
| (0.12593573166226323326 - 2.4718402979901420447e-839j)  +/-  (1.11e-55, 9.73e-173j)
| (0.012364282699326593069 + 4.2433749069651541708e-840j)  +/-  (7.46e-57, 6.25e-174j)
| (0.0049871314254789840684 - 4.8799652394840288041e-840j)  +/-  (3.56e-57, 3.26e-174j)
| (1.2372154338403625237e-05 - 8.820536173412688103e-843j)  +/-  (5.89e-60, 4.72e-177j)
