Starting with polynomial:
P : 6435/128*t^8 - 3003/32*t^6 + 3465/64*t^4 - 315/32*t^2 + 35/128
Extension levels are: 8 43
-------------------------------------------------
Trying to find an order 43 Kronrod extension for:
P1 : 6435/128*t^8 - 3003/32*t^6 + 3465/64*t^4 - 315/32*t^2 + 35/128
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 6435/128*t^51 - 116708586018140419033359774673269474181701028856150787126411/182624663041891523938538958126450436698777855518633956160*t^49 + 258311498564574912417175911936724020807840928109237613333235029/67571125325499863857259414506786661578547806541894563779200*t^47 - 911914347933291720472631719259761808504636360560204514624467313961/63746599632076571562938531645702536533202000691623331469297280*t^45 + 31118538383122838760718651702569780388069846646639180702725561910031/828705795216995430318200911394132974931626008991103309100864640*t^43 - 60899915673974960372043780744500326741972180525967523681038402458821/828705795216995430318200911394132974931626008991103309100864640*t^41 + 221908296020816072119467489938782520853587054001828886625782867931949633/1994694849087308000775909593725678070660423803641585665005781188480*t^39 - 16160657677456790597470290166358200506617884684311001463857244550380221/121135314721901295593678720266741583238487275524792651720998857600*t^37 + 554965015294675433579287929300098126301661214164574374660391253505341/4310671109473064122477756261744407691820042687593972741422932320*t^35 - 1741647941698893181844934078840315211544439305039432234264223318819963/17242684437892256489911025046977630767280170750375890965691729280*t^33 + 11564748817833536261852537727505891124648306781262157150066794532885/178372597633368170585286466003216870006346593969405768610604096*t^31 - 3466648374397098240616329005389526574061738468473860838237672453442193/101509351932752800303508453905594116613826811675600003265765825600*t^29 + 55046517893684659826476350014605489468625614288118325923447041866000227/3727843441668335597352982876188197730818122566707379430277262216000*t^27 - 259914137720711548426786717162074546862598978765633028094777328366991/49704579222244474631373105015842636410908300889431725737030162880*t^25 + 5026552725702142010233509769050810880831907732559655437025907260217163/3330206807890379800301998036061456639530856159591925624381020912960*t^23 - 1173718537803956561084294413198351720971005591249287433639033160436983/3330206807890379800301998036061456639530856159591925624381020912960*t^21 + 438717673865888122665179578310528529801181803866480780552634233246407/6660413615780759600603996072122913279061712319183851248762041825920*t^19 - 16029850364415438867940136605611186403647679914682036323095748680849259/1650533749160669488524677776622959446967480584097748137583843489985800*t^17 + 5852988799384759042240786115381751807507657723153317375534545357961361/5281707997314142363278968885193470230295937869112794040268299167954560*t^15 - 503734868892524773650271058984707987869106607413716460372475998170317/5281707997314142363278968885193470230295937869112794040268299167954560*t^13 + 756687403772240007215908267991511834829981861091788898381447817621/126547858699834432411475925370335352302172534064493173726478794692480*t^11 - 1255884120611918647251658016575658381075995913721325931118240884992177/4827724880683463695838359667323071489116500871039975881760930130241296512*t^9 + 882847552278799841373418891371784416546637063112188245496451315121003/120693122017086592395958991683076787227912521775999397044023253256032412800*t^7 - 2869147727646359174310550111493052870492795049964220661771706274459/24138624403417318479191798336615357445582504355199879408804650651206482560*t^5 + 151117748058554155592875447596289004286773401819150531023684663/165333043859022729309532865319283270175222632569862187731538703090455360*t^3 - 50739790649386497387455745440598025210527384685096486555011733/24138624403417318479191798336615357445582504355199879408804650651206482560*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: 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:
| (0.99464265057494703957 + 1.2738846706809097035e-902j)  +/-  (1.62e-237, 1.62e-237j)
| (-0.99464265057494703957 + 7.4251640469797610867e-907j)  +/-  (1.74e-237, 1.74e-237j)
| (-0.89371618187146213137 - 1.0401223702428884496e-915j)  +/-  (2.35e-238, 2.35e-238j)
| (-0.99898606550421288641 - 3.7155165604783963281e-913j)  +/-  (5.75e-238, 5.75e-238j)
| (0.94163887649927103449 - 2.2661224158156879988e-921j)  +/-  (1.06e-237, 1.06e-237j)
| (0.83221629395934612287 - 3.2942274515272862987e-923j)  +/-  (2.82e-239, 2.82e-239j)
| (0.96028985649753623168 - 3.034236394772492704e-921j)  +/-  (1.83e-237, 1.83e-237j)
| (-0.91942429841746662581 + 3.5446150709605366986e-920j)  +/-  (6.21e-238, 6.21e-238j)
| (-0.94163887649927103449 + 9.3924874702279191184e-924j)  +/-  (1.08e-237, 1.08e-237j)
| (-0.96028985649753623168 - 9.9110359057701368314e-934j)  +/-  (1.95e-237, 1.95e-237j)
| (0.89371618187146213137 + 4.7452923836370235065e-949j)  +/-  (2.87e-238, 2.87e-238j)
| (0.79666647741362673959 - 5.1168955866875674119e-951j)  +/-  (7.52e-240, 7.52e-240j)
| (-0.86460899575729718655 - 1.9705877214810136853e-948j)  +/-  (9.28e-239, 9.28e-239j)
| (-0.83221629395934612287 - 3.9107006009571517627e-953j)  +/-  (2.86e-239, 2.86e-239j)
| (-0.97533763698718994306 + 1.0063423225225541957e-967j)  +/-  (2.23e-237, 2.23e-237j)
| (0.86460899575729718655 + 2.2493772272833657525e-982j)  +/-  (9.64e-239, 9.64e-239j)
| (0.91942429841746662581 + 2.4254520663357536505e-980j)  +/-  (5.55e-238, 5.55e-238j)
| (-0.36063452713093315945 + 1.6098281151173654153e-991j)  +/-  (5.57e-248, 5.57e-248j)
| (-0.79666647741362673959 + 7.7202607157116569668e-984j)  +/-  (7.61e-240, 7.61e-240j)
| (0.98677816264908579017 - 1.7510898037369254237e-978j)  +/-  (2.39e-237, 2.39e-237j)
| (0.97533763698718994306 - 1.1006066201633211782e-990j)  +/-  (2.39e-237, 2.39e-237j)
| (0.75809962498199005967 + 1.7590083587375326706e-1003j)  +/-  (1.82e-240, 1.82e-240j)
| (-0.98677816264908579017 - 3.8063590716198293196e-1007j)  +/-  (2.38e-237, 2.38e-237j)
| (-0.71666533623020203887 + 3.1183094877866829752e-1023j)  +/-  (3.53e-241, 3.53e-241j)
| (-0.75809962498199005967 + 5.6226618594182934027e-1023j)  +/-  (1.69e-240, 1.69e-240j)
| (0.24349951170277980423 + 3.757845404473490423e-1032j)  +/-  (1.76e-250, 1.76e-250j)
| (0.71666533623020203887 - 1.7249744990341028137e-1021j)  +/-  (3.64e-241, 3.64e-241j)
| (0.67252152377328090973 - 3.0561339668362681802e-1022j)  +/-  (5.39e-242, 5.39e-242j)
| (0.99898606550421288641 + 1.2046492908935984298e-1026j)  +/-  (5.53e-238, 5.53e-238j)
| (-0.67252152377328090973 + 4.8696787351417483665e-1034j)  +/-  (5.61e-242, 5.61e-242j)
| (-0.24349951170277980423 + 1.0339629179160600164e-1045j)  +/-  (1.73e-250, 1.73e-250j)
| (0.52553240991632898582 + 5.4566411213167012951e-1037j)  +/-  (1.04e-244, 1.04e-244j)
| (0.57677681047426009782 + 4.2563328873593232061e-1035j)  +/-  (9.72e-244, 9.72e-244j)
| (0.061453831857281410877 + 2.5001544772378057128e-1049j)  +/-  (2.12e-254, 2.12e-254j)
| (-0.62583402722801477973 + 4.3261653861918265501e-1037j)  +/-  (8.24e-243, 8.24e-243j)
| (-0.57677681047426009782 + 8.5096248517984960685e-1041j)  +/-  (9.85e-244, 9.85e-244j)
| (-4.7823840096330817124e-1064 - 1.4414246365922733378e-1063j)  +/-  (7.75e-1062, 7.75e-1062j)
| (0.62583402722801477973 - 1.881786620221179098e-1039j)  +/-  (8.09e-243, 8.09e-243j)
| (0.30264151014192989531 - 2.8973423867607770057e-1046j)  +/-  (3.38e-249, 3.38e-249j)
| (-0.30264151014192989531 + 6.7613103784657573067e-1047j)  +/-  (3.45e-249, 3.45e-249j)
| (-0.52553240991632898582 - 2.3921804507046496903e-1042j)  +/-  (1.04e-244, 1.04e-244j)
| (-0.12267587005166801065 - 4.9387124441082821812e-1053j)  +/-  (4.75e-253, 4.75e-253j)
| (0.36063452713093315945 + 7.7768614590621888788e-1046j)  +/-  (5.27e-248, 5.27e-248j)
| (0.41725676400229209896 - 2.1187453794060932095e-1043j)  +/-  (8.07e-247, 8.07e-247j)
| (-0.061453831857281410877 + 4.149042984884354898e-1054j)  +/-  (2.12e-254, 2.12e-254j)
| (-0.47229228112487224457 + 1.0174655104600260608e-1044j)  +/-  (9.78e-246, 9.78e-246j)
| (-0.41725676400229209896 - 1.3888193242392484849e-1046j)  +/-  (7.83e-247, 7.83e-247j)
| (0.12267587005166801065 - 2.7973598433776014434e-1052j)  +/-  (3.99e-253, 3.99e-253j)
| (0.47229228112487224457 + 1.8915782668224047946e-1044j)  +/-  (1.03e-245, 1.03e-245j)
| (0.18343464249564980494 + 1.5402920275037634012e-1051j)  +/-  (9.92e-252, 9.92e-252j)
| (-0.18343464249564980494 - 1.6103798471948728214e-1053j)  +/-  (8.6e-252, 8.6e-252j)
-------------------------------------------------
The weights are:
| (0.0060937847333506209052 - 6.6156551600251314368e-903j)  +/-  (5.99e-55, 2.51e-169j)
| (0.0060937847333506209052 - 3.8637343050257828763e-905j)  +/-  (2.9e-55, 1.22e-169j)
| (0.027425146253347327255 - 2.5470560647089758886e-904j)  +/-  (5.09e-56, 2.14e-170j)
| (0.0026039090267911831319 + 1.1796917459487321333e-905j)  +/-  (2.34e-55, 9.84e-170j)
| (0.020442122634014861212 - 6.6684360485036692833e-903j)  +/-  (7.89e-57, 3.31e-171j)
| (0.033993720909323551155 - 3.6994823702871995593e-903j)  +/-  (1.91e-57, 8.03e-172j)
| (0.016853142103927757616 + 8.3132051395612313789e-903j)  +/-  (6.72e-57, 2.82e-171j)
| (0.023975252783316662862 + 2.1841763201181867044e-904j)  +/-  (3.9e-57, 1.64e-171j)
| (0.020442122634014861212 - 1.8215338408136326183e-904j)  +/-  (1.88e-57, 7.9e-172j)
| (0.016853142103927757616 + 1.4559829502751917637e-904j)  +/-  (9.84e-58, 4.13e-172j)
| (0.027425146253347327255 - 4.7707920492267014854e-903j)  +/-  (1.57e-59, 6.59e-174j)
| (0.037082529868645063297 + 3.3215504202333760837e-903j)  +/-  (6.88e-60, 2.89e-174j)
| (0.030770229846291293472 + 2.9137178951952306914e-904j)  +/-  (2.84e-59, 1.19e-173j)
| (0.033993720909323551155 - 3.287077109667648925e-904j)  +/-  (4.1e-60, 1.72e-174j)
| (0.013241729189341886789 - 1.0869256926752730211e-904j)  +/-  (9.65e-59, 4.05e-173j)
| (0.030770229846291293472 + 4.1695600457743738948e-903j)  +/-  (3.87e-61, 1.63e-175j)
| (0.023975252783316662862 + 5.5662748526381815234e-903j)  +/-  (3.37e-61, 1.41e-175j)
| (0.057344156133322998211 - 7.5990051039362849486e-904j)  +/-  (1.29e-65, 5.42e-180j)
| (0.037082529868645063297 + 3.6690778717011466531e-904j)  +/-  (3.46e-62, 1.45e-176j)
| (0.0096447180242930122026 + 1.8391266039119378012e-902j)  +/-  (8.07e-63, 3.39e-177j)
| (0.013241729189341886789 - 1.1157894586106367987e-902j)  +/-  (1.59e-62, 6.68e-177j)
| (0.040026221889817209696 - 3.0102107913913604975e-903j)  +/-  (9.87e-65, 4.14e-179j)
| (0.0096447180242930122026 + 7.1925091792400442384e-905j)  +/-  (1.27e-61, 5.33e-176j)
| (0.042816030984753296771 + 4.4624005733199698755e-904j)  +/-  (8.06e-66, 3.38e-180j)
| (0.040026221889817209696 - 4.0607363917847628057e-904j)  +/-  (6.22e-65, 2.61e-179j)
| (0.05964140202157536396 - 1.4264255332504265336e-903j)  +/-  (1.86e-69, 7.81e-184j)
| (0.042816030984753296771 + 2.7481417592348764151e-903j)  +/-  (2.01e-66, 8.42e-181j)
| (0.045443958104283740077 - 2.5233729972032171113e-903j)  +/-  (2.03e-67, 8.52e-182j)
| (0.0026039090267911831319 - 5.2736969030999014762e-903j)  +/-  (3.11e-65, 1.31e-179j)
| (0.045443958104283740077 - 4.874119228193379081e-904j)  +/-  (5.69e-68, 2.39e-182j)
| (0.05964140202157536396 - 8.6531638115156611554e-904j)  +/-  (5.34e-71, 2.24e-185j)
| (0.052274923723386083753 + 2.0008127502300162871e-903j)  +/-  (4.54e-70, 1.9e-184j)
| (0.050181967888469478438 - 2.154759087666059238e-903j)  +/-  (1.81e-69, 7.59e-184j)
| (0.061376553177189975038 + 1.1823253366593682017e-903j)  +/-  (1.3e-72, 5.46e-187j)
| (0.047902049357459092922 + 5.2960304426654224427e-904j)  +/-  (3.39e-70, 1.42e-184j)
| (0.050181967888469478438 - 5.728685612551077317e-904j)  +/-  (4.7e-71, 1.97e-185j)
| (0.061492473382052277494 - 1.1114407055572265227e-903j)  +/-  (1.4e-73, 5.88e-188j)
| (0.047902049357459092922 + 2.3275427622374281623e-903j)  +/-  (8.79e-71, 3.69e-185j)
| (0.058604885052691458477 + 1.5212032376623256394e-903j)  +/-  (1.44e-73, 6.05e-188j)
| (0.058604885052691458477 + 8.1138127452636428793e-904j)  +/-  (1.22e-73, 5.12e-188j)
| (0.052274923723386083753 + 6.1732452274886687599e-904j)  +/-  (5.68e-73, 2.39e-187j)
| (0.061028936308638103692 - 9.8168346387952415779e-904j)  +/-  (1.13e-74, 4.73e-189j)
| (0.057344156133322998211 - 1.6245471177774913348e-903j)  +/-  (1.39e-74, 5.82e-189j)
| (0.055864303588578875522 + 1.7378253624505562984e-903j)  +/-  (1.22e-74, 5.11e-189j)
| (0.061376553177189975038 + 1.0447121519643706237e-903j)  +/-  (3.16e-75, 1.33e-189j)
| (0.054171934556736007466 - 6.6315189020526531824e-904j)  +/-  (4.32e-75, 1.81e-189j)
| (0.055864303588578875522 + 7.1058655109896154535e-904j)  +/-  (2.84e-75, 1.19e-189j)
| (0.061028936308638103692 - 1.2579437322465725974e-903j)  +/-  (1.12e-76, 4.69e-191j)
| (0.054171934556736007466 - 1.8626190400195025331e-903j)  +/-  (1.53e-76, 6.45e-191j)
| (0.060450155149428957335 + 1.3390178440388088856e-903j)  +/-  (7.65e-77, 3.22e-191j)
| (0.060450155149428957335 + 9.2198844032265778565e-904j)  +/-  (6.85e-77, 2.83e-191j)
