Starting with polynomial:
P : t
Extension levels are: 1 2 4 44
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : t^3 - 3/5*t
Solvable: 1
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P3 : t^7 - 77/45*t^5 + 749/891*t^3 - 31/297*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^51 - 87157768709928771194357939184929783610143786534267915126581749199354139/6726819246303990742337927631392683227724879224498584138170345119954315*t^49 + 86534408076692623143295158039635061927040319787092768189906910573952394490338/1094164238146068222176460294739439675772045680019266200162373826176409014955*t^47 - 64509108261488051846878519642003429564909605350162066713289155779544636054718726/213362026438483303324409757474190736775548907603756909031662896104399757916225*t^45 + 31142883474897250869588692403531909926750526472126585829685860730620566855358332/38362061319242452516914077606470657723280510660069424048117167178366825160695*t^43 - 14718604435734436266243148852788775932179852418042330009434199260082725988171892/9044713644374236772280554882826415235570201700341571523539819903842584793985*t^41 + 7093107750982415701726056343754103533176495414898579405084730360297006257468906/2806980096529935550018103239497853004142476389761177369374426866709767694685*t^39 - 28385821024892698591938846909741346659177160470974174893604315231612358724651054/9117950192101963385821288120744038030999919932733001252475365004278557140495*t^37 + 1268471029082309045353506992530806553219635026721248771918608772315274175984500247/410307758644588352361957965433481711394996396972985056361391425192535071322275*t^35 - 3740702705370324148531084593005615739868063705028667947887807854242272629893809163/1496045212288729838612062120119002547701756093578422436271534888778935567744295*t^33 + 10746166402203951411123632483947631995165192426288823111856925982850493867091894396/6482862586584495967318935853849011040040943072173163890509984518042054126891945*t^31 - 2834556892186545746298240216293227621280949011545874575154796922037259658493443964/3136868993508627080960775413152747277439166002664434140569347347439703609786425*t^29 + 9599503065405430786196876212602208950080374615053064121509023105379854221656725776/23688769295806528645876200533808677715833701882190037130506450658251554846318175*t^27 - 39317137410676435781073764774918056154112213731720740465203928412872477310031960464/263545994587249271687027245255050958633420529487043005682699970998496642948354625*t^25 + 2050062959169007357087042978366644120610640279884586143227046246637912778437142172/45681305728456540425751389177542166163126225111087454318334661639739418111048135*t^23 - 27420718466730504732756079416834828137727175421907754804920396213689483330987321692/2504166123114481261520735243096175108760464885635066813995981906251169920087456855*t^21 + 23271377079655981912440393006389403331774951210116874615802286512670252757211776883/10851386533496085466589852720083425471295347837751956193982588260421736320378979705*t^19 - 721317851437026635219444189803616575559175275457004181351858953425295309705849351/2170277306699217093317970544016685094259069567550391238796517652084347264075795941*t^17 + 397087221875781433935863633249489727425003559027324537174576104555468119138566133738/9929018678148918201929715238876334306235243271543039917494068258285888733146766430075*t^15 - 142251514313177866301968964992863619601382882495762868728510653794741541720184701266/39054140134052411594256879939580248271191956868069290342143335149257829017043947958295*t^13 + 585023109354283732442424041598322857235515969125280138209596530722123735730224828/2411794136122413283719005586734641550875342948515654983209285052554383807119723763405*t^11 - 1156311773100051641927966103966953883804753242226485190558865629603383057720257420/102742430198814805886429637994895730067289609606766902284715543238816750183300232321053*t^9 + 78875191096680075457068028378845809324927663617271680652141683793443768606621514/232707213698170286836785077509806568101126038852933582097859991096465288876705654402385*t^7 - 9959897953242369057127554134039525754728531395041647493140635853270469673856378/1680663210042340960487892226459714102952576947271186981817877713474471530776207504017225*t^5 + 4919343983943102954468925253149049590545009521558149302125725159088398397675803/99831394676515053052980798251707017715383070667908506719981936180383608928106725738623165*t^3 - 4099417174662853911847807282507809633367099946261884062700565068421535260777/33277131558838351017660266083902339238461023555969502239993978726794536309368908579541055*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:
| (0.99905441308740210245 + 3.3768141455858530782e-881j)  +/-  (1.27e-237, 1.27e-237j)
| (-0.9949208746921766185 - 3.5470699379660232294e-891j)  +/-  (3.55e-237, 3.55e-237j)
| (-0.91899265143257804311 + 3.1146054902705703603e-902j)  +/-  (1.28e-237, 1.28e-237j)
| (-0.49089683734372844131 + 4.5213448768374429015e-918j)  +/-  (1.91e-245, 1.91e-245j)
| (0.91899265143257804311 - 3.2847159137397537307e-907j)  +/-  (1.32e-237, 1.32e-237j)
| (0.94150076402621432443 + 1.4732406718331363425e-907j)  +/-  (2.25e-237, 2.25e-237j)
| (-0.99905441308740210245 + 8.3779702807530424779e-908j)  +/-  (1.21e-237, 1.21e-237j)
| (-0.89339912240291804607 + 2.4766185365280824004e-918j)  +/-  (6.85e-238, 6.85e-238j)
| (-0.77459666924148337704 + 7.4644448198104990099e-927j)  +/-  (9.12e-240, 9.12e-240j)
| (-0.97575567907989692765 - 9.8132989729511037912e-925j)  +/-  (4.41e-237, 4.41e-237j)
| (0.89339912240291804607 - 1.6366915912965182701e-933j)  +/-  (6.76e-238, 6.76e-238j)
| (0.96049126870802028342 + 4.1728744654372084762e-934j)  +/-  (3.56e-237, 3.56e-237j)
| (-0.064203956686681625733 - 2.328409758824793849e-955j)  +/-  (2.38e-254, 2.38e-254j)
| (-0.86562390118846295555 - 2.059486851452959046e-937j)  +/-  (3.27e-238, 3.27e-238j)
| (0.98721689144822372738 - 2.0182460521352942086e-938j)  +/-  (4.73e-237, 4.73e-237j)
| (0.80785683693812518704 - 6.0081596998211203407e-944j)  +/-  (4.28e-239, 4.28e-239j)
| (0.83713809943853406076 + 3.2327303653193856987e-943j)  +/-  (1.31e-238, 1.31e-238j)
| (0.9949208746921766185 - 2.2195860851460987445e-940j)  +/-  (3.42e-237, 3.42e-237j)
| (-0.80785683693812518704 + 1.4796875160580264978e-942j)  +/-  (4.45e-239, 4.45e-239j)
| (-0.98721689144822372738 + 3.0261606876038627808e-942j)  +/-  (4.6e-237, 4.6e-237j)
| (0.86562390118846295555 + 5.6849380867664757217e-960j)  +/-  (3.25e-238, 3.25e-238j)
| (0.77459666924148337704 - 3.2732831798810543937e-965j)  +/-  (9.66e-240, 9.66e-240j)
| (-0.94150076402621432443 + 3.5608910479373258504e-960j)  +/-  (2.11e-237, 2.11e-237j)
| (-0.73612040435187543268 + 4.1449526246827872859e-979j)  +/-  (1.52e-240, 1.52e-240j)
| (-0.96049126870802028342 + 1.3080048886193357667e-984j)  +/-  (3.41e-237, 3.41e-237j)
| (0.25409192597105399968 - 1.0987546802840080863e-1006j)  +/-  (2.16e-250, 2.16e-250j)
| (0.73612040435187543268 + 1.2968925917039790757e-996j)  +/-  (1.54e-240, 1.54e-240j)
| (0.54541424387442191976 + 4.7807050164654134189e-1001j)  +/-  (2.46e-244, 2.46e-244j)
| (-0.83713809943853406076 - 3.0565379110582414161e-997j)  +/-  (1.37e-238, 1.37e-238j)
| (-0.5975258816308875806 - 2.314329061606908879e-1002j)  +/-  (2.85e-243, 2.85e-243j)
| (-0.37571742755949298204 - 4.429769882582515641e-1007j)  +/-  (8.49e-248, 8.49e-248j)
| (0.64693896816340327722 + 1.2412288884578479929e-1000j)  +/-  (2.68e-242, 2.68e-242j)
| (0.69330223855507760787 + 1.2578625512977237273e-1000j)  +/-  (2.09e-241, 2.09e-241j)
| (0.19152115560738434758 + 1.6814317274806493941e-1011j)  +/-  (1.05e-251, 1.05e-251j)
| (-0.64693896816340327722 - 1.2311669199573630657e-1000j)  +/-  (2.55e-242, 2.55e-242j)
| (-0.69330223855507760787 - 1.1832096121651605877e-1001j)  +/-  (2.2e-241, 2.2e-241j)
| (1.1163684775608522509e-1022 + 1.9928640398147845214e-1022j)  +/-  (1.16e-1020, 1.16e-1020j)
| (0.5975258816308875806 + 2.2668461885574467006e-1002j)  +/-  (2.84e-243, 2.84e-243j)
| (0.064203956686681625733 - 2.0457298350805898008e-1016j)  +/-  (2.38e-254, 2.38e-254j)
| (-0.31557918131088900878 + 9.744845356745371647e-1010j)  +/-  (4.39e-249, 4.39e-249j)
| (-0.54541424387442191976 + 3.8964758440640633622e-1004j)  +/-  (2.68e-244, 2.68e-244j)
| (-0.12813502444490821627 + 3.9520496608290616315e-1013j)  +/-  (4.89e-253, 4.89e-253j)
| (0.37571742755949298204 + 5.2414352984348758389e-1007j)  +/-  (8.07e-248, 8.07e-248j)
| (0.434243749346802558 - 1.93853665371897651e-1005j)  +/-  (1.37e-246, 1.37e-246j)
| (0.97575567907989692765 + 4.1701612498150511626e-1009j)  +/-  (4.62e-237, 4.62e-237j)
| (-0.434243749346802558 + 4.3488545380569956999e-1021j)  +/-  (1.36e-246, 1.36e-246j)
| (-0.25409192597105399968 - 9.0631108556790123532e-1025j)  +/-  (2.2e-250, 2.2e-250j)
| (0.12813502444490821627 - 2.3672535684480579105e-1027j)  +/-  (4.63e-253, 4.63e-253j)
| (0.49089683734372844131 + 2.1397321358629439726e-1019j)  +/-  (1.9e-245, 1.9e-245j)
| (0.31557918131088900878 - 2.0314314117586120381e-1023j)  +/-  (4.53e-249, 4.53e-249j)
| (-0.19152115560738434758 + 1.1806172664065407555e-1026j)  +/-  (1.02e-251, 1.02e-251j)
-------------------------------------------------
The weights are:
| (0.0024394398597399700267 - 4.1254356458342657823e-881j)  +/-  (5.13e-61, 2.47e-175j)
| (0.0058762760419998931994 + 1.3461684677691242764e-883j)  +/-  (2.09e-61, 1.01e-175j)
| (0.024150633192563131571 - 8.7610944348076310228e-883j)  +/-  (1.39e-61, 6.71e-176j)
| (0.055629315787025082165 + 7.5975936406467586341e-883j)  +/-  (1.23e-62, 5.93e-177j)
| (0.024150633192563131571 - 2.0989035399973586788e-881j)  +/-  (4.39e-62, 2.12e-176j)
| (0.020797609592264277592 + 2.1892224547226234276e-881j)  +/-  (4.38e-62, 2.11e-176j)
| (0.0024394398597399700267 - 4.1226660064614137267e-884j)  +/-  (3.97e-62, 1.91e-176j)
| (0.026892555756932373135 + 1.2119006283300256561e-882j)  +/-  (1.18e-62, 5.69e-177j)
| (0.035954788372977093332 + 1.9308778778274587935e-882j)  +/-  (1.19e-63, 5.73e-178j)
| (0.013366028153368181454 + 3.5569710019113199167e-883j)  +/-  (1.03e-62, 4.95e-177j)
| (0.026892555756932373135 + 2.1707059033180362641e-881j)  +/-  (4.82e-64, 2.33e-178j)
| (0.017149988721060519119 - 2.4675879418280243169e-881j)  +/-  (4.61e-64, 2.22e-178j)
| (0.064112951116559575978 - 7.5332808247213488227e-883j)  +/-  (7.13e-67, 3.44e-181j)
| (0.02838316796991635877 - 1.693553027667751234e-882j)  +/-  (9.22e-64, 4.45e-178j)
| (0.0095635049906522821344 - 4.0536934132010776312e-881j)  +/-  (9.51e-65, 4.59e-179j)
| (0.030734357311530544346 - 2.1451119878088366804e-881j)  +/-  (2.28e-66, 1.1e-180j)
| (0.028523171469449218301 + 2.4673450258207292896e-881j)  +/-  (4.8e-66, 2.32e-180j)
| (0.0058762760419998931994 + 6.4937746639222209147e-881j)  +/-  (5.16e-65, 2.49e-179j)
| (0.030734357311530544346 - 2.2698414896014300076e-882j)  +/-  (4.76e-67, 2.29e-181j)
| (0.0095635049906522821344 - 2.4158674813007872635e-883j)  +/-  (4.01e-66, 1.94e-180j)
| (0.02838316796991635877 - 2.3667237450748997115e-881j)  +/-  (2.9e-66, 1.4e-180j)
| (0.035954788372977093332 + 1.5257676484138550033e-881j)  +/-  (4.88e-68, 2.35e-182j)
| (0.020797609592264277592 + 6.4928708035121206335e-883j)  +/-  (2.37e-67, 1.14e-181j)
| (0.040812962435280026809 - 1.5223946976657458114e-882j)  +/-  (8.54e-70, 4.12e-184j)
| (0.017149988721060519119 - 4.856123056133098785e-883j)  +/-  (2.42e-67, 1.17e-181j)
| (0.062073490711514640576 + 1.1590279207257137256e-882j)  +/-  (1.48e-73, 7.14e-188j)
| (0.040812962435280026809 - 1.0046706987964899469e-881j)  +/-  (1.35e-70, 6.5e-185j)
| (0.053360708661568265813 - 2.7851835751577248281e-882j)  +/-  (3.79e-73, 1.83e-187j)
| (0.028523171469449218301 + 2.1757163695919486293e-882j)  +/-  (1.28e-68, 6.16e-183j)
| (0.050814301913615499622 + 9.0456775110206060169e-883j)  +/-  (1.32e-72, 6.36e-187j)
| (0.059375916195586446405 + 6.9872880874927466813e-883j)  +/-  (4.08e-74, 1.97e-188j)
| (0.047954623233322139204 - 4.8293254273319025049e-882j)  +/-  (5.65e-73, 2.73e-187j)
| (0.044692305821131317985 + 6.7929597610156550356e-882j)  +/-  (3.01e-72, 1.45e-186j)
| (0.063023350667564370777 - 1.0319078032222473941e-882j)  +/-  (1.27e-75, 6.1e-190j)
| (0.047954623233322139204 - 1.0331026177269746976e-882j)  +/-  (3.38e-73, 1.63e-187j)
| (0.044692305821131317985 + 1.227260350558875841e-882j)  +/-  (1.11e-72, 5.36e-187j)
| (0.064249466613503203872 + 7.9784605147202016321e-883j)  +/-  (7.04e-77, 3.4e-191j)
| (0.050814301913615499622 + 3.5967930892250427267e-882j)  +/-  (3.02e-75, 1.46e-189j)
| (0.064112951116559575978 - 8.5680269331459343961e-883j)  +/-  (3.85e-77, 1.86e-191j)
| (0.060856771403426132977 - 6.8839284813622289207e-883j)  +/-  (2.1e-77, 1.01e-191j)
| (0.053360708661568265813 - 8.180620191418920837e-883j)  +/-  (1.07e-75, 5.17e-190j)
| (0.063703829912370769888 + 7.2112923642225155024e-883j)  +/-  (7.61e-78, 3.67e-192j)
| (0.059375916195586446405 + 1.5410487632711336425e-882j)  +/-  (5.19e-79, 2.51e-193j)
| (0.057633217401830286884 - 1.8311199858535305304e-882j)  +/-  (5.71e-79, 2.75e-193j)
| (0.013366028153368181454 + 3.0149029926072983432e-881j)  +/-  (3.5e-77, 1.68e-191j)
| (0.057633217401830286884 - 7.2157777183539915895e-883j)  +/-  (3.44e-78, 1.65e-192j)
| (0.062073490711514640576 + 6.8901156670690837177e-883j)  +/-  (2.95e-79, 1.42e-193j)
| (0.063703829912370769888 + 9.3332318584734641764e-883j)  +/-  (1.13e-79, 5.58e-194j)
| (0.055629315787025082165 + 2.2276641513964550755e-882j)  +/-  (8.4e-80, 4.12e-194j)
| (0.060856771403426132977 - 1.3240924064658096273e-882j)  +/-  (4.57e-80, 2.28e-194j)
| (0.063023350667564370777 - 6.9991346338208325341e-883j)  +/-  (3.63e-80, 1.58e-194j)
