Starting with polynomial:
P : t
Extension levels are: 1 10 46
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 46 Kronrod extension for:
P2 : t^11 - 55/21*t^9 + 330/133*t^7 - 330/323*t^5 + 55/323*t^3 - 33/4199*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^57 - 1145191119579130349824396454241293428457020448086072899933032683134603107639/81212624344938087535739736367040095472922541379395648922824896295953868684*t^55 + 6537234559341074415993010453035238191631478585082616075667196203206474069142122765/69417546422952314516311504276300293126721690237076363060220576832618416657941892*t^53 - 4877128938355358327348034715096048366616409281706566809401546132393296219927394885519865/12309605254542865076233970118803502079282177164670040232379734227997725970702861882684*t^51 + 2532909517017789925275881500947114624620480870992353929637040150881155121041972207101025/2149524315601340084591238201546526977207402026176264992653669349695121807466188454092*t^49 - 78335979671759599737322323196302179587626815346549034324606020763538894773513102220232756305/29726802654765557162301781948324397963392272292391877608455090604887264686929011058754006*t^47 + 12722315577127961583926959625391326241430237543465326927776947541031327694415627367674986502765/2764592646893196816094065721194169010595481323192444617586323426254515615884398028464122558*t^45 - 25690022384043038901319637743162648618920369894841486963683418318822075947785699417125019008775/3993300489956839845469206041724910793082361911277975558735800504589855889610797152225954806*t^43 + 2602529929748083768932370393852224045424659308762613761843188462255843120965654885058413275284925/355403743606158746246759337713517060584330210103739824727486244908497174175360946548109977734*t^41 - 2972475453195729133300849144281545542658962465428519145327046476574239429822553143752476243642783725/432881759712301352928552873335063779791714195906355106518078246298549558145589632895597952880012*t^39 + 1435206732570635694941684134585972690696005762229825728099165860578896211693341082663313094320245/268409742681880694451814525538756401373569002093884699668356500969301619012839616268197293612*t^37 - 1985162325173331691790088965606292683099922877691191577113975477277093188544264409654432466374515/571230990835797375371810400505558495230928901892113591601886912319282932770915080775907060764*t^35 + 9555160945475659005347427467492236668925090322316936407720687153713580704362436465926869348046325/5054674229832728035853078585986160466203093560440299260141066543463906959729189748378404495668*t^33 - 924454416337604988547021662739344379991750170731756564332227467327064878808876464404145215804575/1073438882141896545248368839497060959220549438910708713847161981004431854351091371295413857951*t^31 + 1056991089645531679261705688428119109857432276360515628340733169632766718830770458945588181961725/3220316646425689635745106518491182877661648316732126141541485943013295563053274113886241573853*t^29 - 34758798697673508170581049394618210798082697583149307725926576353048921727972363775646032493565/333136204802657548525355846740467194240860170696426842228429580311720230660683529022714645571*t^27 + 173571934319288051707384259416715357578410036481828973949095701833726536044756279924556079993470/6304911135339185455424327321643656898410353600958300606619537612566260661763306790022488292103*t^25 - 824674715732590717909690019341050610470149219135386147888725736373276016927299834740973996894375/137738058648948359180039150718984504549887724820935182483072975536062925226213779105106667304404*t^23 + 5712132470805432766726060516764280970501775794390433171575807631261226670648200380613758978954625/5371784287308986008021526878040395677445621268016472116839846045906454083822337385099160024871756*t^21 - 38973393414219001577105839235417918076722428465599056826303232695032006806842795460596760925975/255799251776618381334358422763828365592648631810308196039992668852688289705825589766626667851036*t^19 + 5731389213074759946074649745288321645633401678598747978217962367200795763327921481678989228285/330594354635278726753761470355591045590499108947825212425955437523064982602265820692540898216836*t^17 - 134330633266623545698217911458549459035894273537365109040359841392092689565424613152335204835/87510270344632604140701565682362335597485058250894909171576439344340730688835070183319649527986*t^15 + 25916582788501904996182649552997769389713867607460497003754959150555344993245933561011799912525/251682778632287244790292543701203053561166934383583051181497231274299657784448507590567434992470254*t^13 - 105497217747232658503694478528200466866232220229903561128012136331048754125473258618476212558325/20892168718575447146326690978750237594991854729364773724999074138509048267650510978727673456087115154*t^11 + 489211294914634053749848085299631614483334160992119709211394391121254243102087337949746216906025/2839727855824831931350712535342436140796200562060581167082566461749652945302957915339369153608148652086*t^9 - 31214879900965323170887080888281438080792455956051061962210853505842687213976374507137449127743/8203658250160625579457613990989259962300134957063901149349636445054552953097433977647066443756873883804*t^7 + 56956682688471396172707983912612622890259451992335339357914802015329799646818995928517135929/1171951178594375082779659141569894280328590708151985878478519492150650421871061996806723777679553411972*t^5 - 17551636388803838277460724728779531244705769656474385295728387098203848079618743747861190905/59769510108313129221762616220064608296758126115751279802404494099683171515424161837142912661657224010572*t^3 + 127168850759172387695100234492750332650299970807995947919874340412460674578865440552885/240038193206076824183785607309496418862482434199804336555841341765795869539856071635112099042800096428*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:
| (0.99517773150949149605 - 9.0468924113062594089e-870j)  +/-  (1.26e-235, 1.26e-235j)
| (-0.93147640686806033658 - 1.2946934682562118665e-885j)  +/-  (9.26e-236, 9.26e-236j)
| (-0.91058449598720274479 + 5.3493247141951385619e-886j)  +/-  (4.67e-236, 4.67e-236j)
| (-0.99517773150949149605 + 1.56722321017152409e-884j)  +/-  (1.27e-235, 1.27e-235j)
| (0.96537282366713347561 - 9.4974572756728219072e-884j)  +/-  (1.87e-235, 1.87e-235j)
| (0.91058449598720274479 - 1.4529516373029674185e-890j)  +/-  (4.51e-236, 4.51e-236j)
| (-0.9782286581460569928 + 1.0476301432628944102e-893j)  +/-  (2.13e-235, 2.13e-235j)
| (-0.86087034530358105589 - 4.6961083873854635265e-898j)  +/-  (7.15e-237, 7.15e-237j)
| (0.99908256323684178661 + 7.8354023193933297041e-894j)  +/-  (4.93e-236, 4.93e-236j)
| (0.93147640686806033658 - 1.8735649045424600575e-907j)  +/-  (9.2e-236, 9.2e-236j)
| (0.86087034530358105589 - 8.4253320625856953563e-920j)  +/-  (7.93e-237, 7.93e-237j)
| (0.9782286581460569928 - 2.9554787910235508344e-934j)  +/-  (2.21e-235, 2.21e-235j)
| (-0.99908256323684178661 + 5.8732582581161159653e-948j)  +/-  (4.3e-236, 4.3e-236j)
| (-0.88706259976809529908 - 3.8205097346901272382e-955j)  +/-  (1.89e-236, 1.89e-236j)
| (0.98820015390876626721 + 1.0673614796959010025e-955j)  +/-  (1.91e-235, 1.91e-235j)
| (0.83199954223615288791 - 4.3663929511611301413e-967j)  +/-  (2.55e-237, 2.55e-237j)
| (0.80050514731905676044 + 7.3885848258186191365e-968j)  +/-  (6.63e-238, 6.63e-238j)
| (-0.98820015390876626721 + 8.8346883622339557936e-964j)  +/-  (1.92e-235, 1.92e-235j)
| (-0.73015200557404932409 - 2.755533483130456447e-970j)  +/-  (3.2e-239, 3.2e-239j)
| (-0.94975469992948673877 - 9.046020336767078898e-966j)  +/-  (1.47e-235, 1.47e-235j)
| (0.88706259976809529908 - 1.2699669288093588365e-967j)  +/-  (2.08e-236, 2.08e-236j)
| (0.73015200557404932409 + 3.049678515772406003e-977j)  +/-  (3.2e-239, 3.2e-239j)
| (-0.69163223854401875069 + 3.529502886638250053e-978j)  +/-  (6.09e-240, 6.09e-240j)
| (-0.80050514731905676044 + 1.1620819898308882266e-975j)  +/-  (6.6e-238, 6.6e-238j)
| (-0.37312588626162280713 - 1.0668991932607604163e-985j)  +/-  (9.97e-247, 9.97e-247j)
| (0.26954315595234497233 - 8.5689428668875435393e-988j)  +/-  (3.04e-249, 3.04e-249j)
| (0.76650308196363655889 + 1.3977493778655364708e-975j)  +/-  (1.67e-238, 1.67e-238j)
| (0.94975469992948673877 - 5.6998092175265683819e-974j)  +/-  (1.44e-235, 1.44e-235j)
| (-0.96537282366713347561 + 7.5570250812017751977e-986j)  +/-  (1.95e-235, 1.95e-235j)
| (-0.65112471728962944325 - 3.5608740200446479734e-992j)  +/-  (9.05e-241, 9.05e-241j)
| (-0.83199954223615288791 - 3.8052682938266749422e-990j)  +/-  (2.34e-237, 2.34e-237j)
| (0.69163223854401875069 - 9.8639897620070811672e-996j)  +/-  (5.75e-240, 5.75e-240j)
| (0.65112471728962944325 - 1.0534360506431490437e-996j)  +/-  (9.75e-241, 9.75e-241j)
| (0.10868212659497518436 + 2.4509195893056934769e-1010j)  +/-  (4.12e-253, 4.12e-253j)
| (-0.60879008506346990507 + 2.2852733769891403881e-995j)  +/-  (1.25e-241, 1.25e-241j)
| (-0.76650308196363655889 - 8.2129452729135865179e-999j)  +/-  (1.62e-238, 1.62e-238j)
| (0.054389768728458715745 - 1.1293489532307655446e-1015j)  +/-  (2.22e-254, 2.22e-254j)
| (0.60879008506346990507 + 1.3561244593699960009e-1001j)  +/-  (1.27e-241, 1.27e-241j)
| (0.56475229853097072992 - 2.2696569392993393693e-1004j)  +/-  (1.63e-242, 1.63e-242j)
| (-0.21643987019364440628 + 1.0535518952985809642e-1012j)  +/-  (1.72e-250, 1.72e-250j)
| (-0.56475229853097072992 - 2.4623028361212218532e-1005j)  +/-  (1.52e-242, 1.52e-242j)
| (-0.16275325376456354625 + 1.9194295756488475526e-1016j)  +/-  (9.86e-252, 9.86e-252j)
| (0.42319154672295271095 + 5.336839750751224844e-1009j)  +/-  (1.31e-245, 1.31e-245j)
| (0.47188488502503861943 - 8.5966190602152019335e-1007j)  +/-  (1.71e-244, 1.71e-244j)
| (-0.10868212659497518436 + 3.7425532019558838659e-1018j)  +/-  (4.51e-253, 4.51e-253j)
| (-0.51909612920681181593 + 1.6499862260267382176e-1007j)  +/-  (1.74e-243, 1.74e-243j)
| (-0.32184444394277959768 + 6.123394592683921475e-1013j)  +/-  (5.82e-248, 5.82e-248j)
| (0.16275325376456354625 - 9.0686227760417651067e-1018j)  +/-  (9.33e-252, 9.33e-252j)
| (0.51909612920681181593 + 2.3393344513437841467e-1009j)  +/-  (1.58e-243, 1.58e-243j)
| (0.21643987019364440628 + 4.2566517802579095708e-1018j)  +/-  (1.83e-250, 1.83e-250j)
| (-0.26954315595234497233 - 3.3227376560762725778e-1015j)  +/-  (3.17e-249, 3.17e-249j)
| (-0.47188488502503861943 - 8.1899903048928923663e-1011j)  +/-  (1.46e-244, 1.46e-244j)
| (-0.054389768728458715745 - 4.5581410217263719732e-1021j)  +/-  (2.08e-254, 2.08e-254j)
| (0.32184444394277959768 + 1.2285242234159641891e-1014j)  +/-  (5.75e-248, 5.75e-248j)
| (0.37312588626162280713 - 3.7484092063418941196e-1013j)  +/-  (9.8e-247, 9.8e-247j)
| (9.430087298539252984e-1028 + 6.3780978949170220112e-1028j)  +/-  (6.49e-1026, 6.49e-1026j)
| (-0.42319154672295271095 + 2.7883462790301159645e-1012j)  +/-  (1.3e-245, 1.3e-245j)
-------------------------------------------------
The weights are:
| (0.0054511657837997395443 + 5.4338869494270526898e-870j)  +/-  (1.08e-54, 3.46e-166j)
| (0.019587062344163492076 - 2.4188288363268824995e-871j)  +/-  (5.11e-55, 1.63e-166j)
| (0.02220022477259497779 + 3.053162659331945224e-871j)  +/-  (4.47e-55, 1.43e-166j)
| (0.0054511657837997395443 + 2.4777539127330347379e-872j)  +/-  (4.99e-56, 1.59e-167j)
| (0.014256965507394366722 - 8.4811682626491290213e-870j)  +/-  (2.5e-56, 7.98e-168j)
| (0.02220022477259497779 + 6.8783302052855175385e-870j)  +/-  (7.68e-57, 2.45e-168j)
| (0.01143379956651599523 + 8.5195597671169314785e-872j)  +/-  (1.22e-56, 3.89e-168j)
| (0.027535037024308313048 + 4.2856575969989327916e-871j)  +/-  (3.13e-57, 1e-168j)
| (0.0023531104514441655084 + 3.5273622060918166026e-870j)  +/-  (1.23e-56, 3.94e-168j)
| (0.019587062344163492076 - 7.3157765772815246621e-870j)  +/-  (5.11e-57, 1.63e-168j)
| (0.027535037024308313048 + 5.9225235227151920043e-870j)  +/-  (2.77e-58, 8.85e-170j)
| (0.01143379956651599523 + 9.9194530113656419171e-870j)  +/-  (4.73e-57, 1.51e-168j)
| (0.0023531104514441655084 - 6.9066991367560465386e-873j)  +/-  (2.43e-59, 7.76e-171j)
| (0.024851361769850741242 - 3.6817540361733735167e-871j)  +/-  (2.96e-59, 9.46e-171j)
| (0.0084906522200366127226 - 1.4420645126972992634e-869j)  +/-  (5.74e-57, 1.83e-168j)
| (0.030197317679816748372 - 5.4584520777203582495e-870j)  +/-  (1.12e-59, 3.59e-171j)
| (0.032771815960905934281 + 5.0531845340332962821e-870j)  +/-  (1.42e-60, 4.52e-172j)
| (0.0084906522200366127226 - 5.0732223630094383899e-872j)  +/-  (2.8e-59, 8.95e-171j)
| (0.037466234043698443236 + 6.855535327828655348e-871j)  +/-  (8.66e-63, 2.77e-174j)
| (0.016961577189564722908 + 1.8182332713611193319e-871j)  +/-  (7.67e-60, 2.45e-171j)
| (0.024851361769850741242 - 6.4097835567598971961e-870j)  +/-  (3.66e-59, 1.17e-170j)
| (0.037466234043698443236 + 4.4629852151072312263e-870j)  +/-  (1.17e-62, 3.73e-174j)
| (0.039542785656619103025 - 7.6681394954440582123e-871j)  +/-  (1.68e-63, 5.37e-175j)
| (0.032771815960905934281 + 5.4782306120397234131e-871j)  +/-  (1.7e-62, 5.43e-174j)
| (0.050703396613933934773 + 1.3987378532775629874e-870j)  +/-  (1.46e-66, 4.67e-178j)
| (0.052739383812689072261 + 2.7642115587103148255e-870j)  +/-  (3.56e-67, 1.14e-178j)
| (0.035205517392641906382 - 4.7222270764352434403e-870j)  +/-  (2.49e-62, 7.96e-174j)
| (0.016961577189564722908 + 7.7853475084830192389e-870j)  +/-  (2.55e-60, 8.14e-172j)
| (0.014256965507394366722 - 1.2893339465099553517e-871j)  +/-  (8.92e-61, 2.85e-172j)
| (0.04144518382641411604 + 8.5610593335806453174e-871j)  +/-  (5.89e-65, 1.88e-176j)
| (0.030197317679816748372 - 4.8747340451089259377e-871j)  +/-  (3.16e-62, 1.01e-173j)
| (0.039542785656619103025 - 4.2612044825014991554e-870j)  +/-  (7.36e-65, 2.35e-176j)
| (0.04144518382641411604 + 4.0964887278045001993e-870j)  +/-  (6.59e-66, 2.1e-177j)
| (0.054205531633892955872 - 2.4160569740407341688e-870j)  +/-  (3.94e-70, 1.26e-181j)
| (0.043203358927053177787 - 9.5078480095418405128e-871j)  +/-  (2.42e-67, 7.73e-179j)
| (0.035205517392641906382 - 6.1296780524667040552e-871j)  +/-  (7.44e-65, 2.38e-176j)
| (0.05435877263072972341 + 2.3071682164283840455e-870j)  +/-  (1.27e-70, 4.05e-182j)
| (0.043203358927053177787 - 3.9468865923752444596e-870j)  +/-  (3.5e-68, 1.12e-179j)
| (0.04485839794789849918 + 3.7937681940065088452e-870j)  +/-  (3.65e-69, 1.17e-180j)
| (0.053430388995563865161 - 1.6947818481659137943e-870j)  +/-  (2.08e-72, 6.66e-184j)
| (0.04485839794789849918 + 1.0467997192688488331e-870j)  +/-  (2.72e-70, 8.69e-182j)
| (0.053909427860666874885 + 1.8140252465270521593e-870j)  +/-  (1.3e-72, 4.15e-184j)
| (0.049401690164968320395 - 3.258161819432381649e-870j)  +/-  (1.81e-72, 5.78e-184j)
| (0.047966854391364858384 + 3.4452909850226303696e-870j)  +/-  (4.93e-72, 1.58e-183j)
| (0.054205531633892955872 - 1.9403041726583748413e-870j)  +/-  (1.42e-73, 4.53e-185j)
| (0.046443957824078193404 - 1.1401894110867255084e-870j)  +/-  (1.08e-72, 3.45e-184j)
| (0.051826524705096843472 - 1.488041911904646839e-870j)  +/-  (1.04e-73, 3.31e-185j)
| (0.053909427860666874885 + 2.5233713053626937064e-870j)  +/-  (1.92e-74, 6.13e-186j)
| (0.046443957824078193404 - 3.626603114094788245e-870j)  +/-  (2.38e-73, 7.6e-185j)
| (0.053430388995563865161 - 2.6368661654835639419e-870j)  +/-  (1.21e-74, 3.87e-186j)
| (0.052739383812689072261 + 1.5859684939499730747e-870j)  +/-  (7.18e-75, 2.29e-186j)
| (0.047966854391364858384 + 1.2289155937859660964e-870j)  +/-  (5.18e-75, 1.66e-186j)
| (0.05435877263072972341 + 2.0680481108977905382e-870j)  +/-  (1.15e-75, 3.68e-187j)
| (0.051826524705096843472 - 2.9105707859224762067e-870j)  +/-  (5.17e-76, 1.65e-187j)
| (0.050703396613933934773 + 3.076750080518538029e-870j)  +/-  (5.3e-76, 1.69e-187j)
| (0.054405006604588605775 - 2.1914678851264042792e-870j)  +/-  (2.65e-76, 8.58e-188j)
| (0.049401690164968320395 - 1.3139198494462102836e-870j)  +/-  (1.66e-76, 5.02e-188j)
