Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 49
-------------------------------------------------
Trying to find an order 49 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^53 - 35494244910246934992855244729935917895/635698590754030411481792344727264116*t^51 + 4694277545306993455175886096827148251121/13985368996588669052599431583999810552*t^49 - 642882789092401053619026609980860838518111/508717797250912836788304323867993108829*t^47 + 492790563903112965131299176121194815223637/147454433985771836750233137353041480820*t^45 - 5210695345185957251795920830480340487836653/789551469251087380417157435463103929118*t^43 + 15948855354170697294799674960184521430159087/1579102938502174760834314870926207858236*t^41 - 431156886926811102496589675299094866043078217/35135040381673388428563505878108124845751*t^39 + 177965571636644922582397153550058379290239157/14793701213336163548868844580256052566632*t^37 - 355728598388525847865785192754651681908624349/36984253033340408872172111450640131416580*t^35 + 224893038342092208902267295275499163244014663431/35608438820500145662127308904676318527883224*t^33 - 45654969092347335293152015504802981009298594422/13353164557687554623297740839253619447956209*t^31 + 935934231640864699738576317638016723734097800419/612522580678442021752560886239311188870765458*t^29 - 21809165971784872088187291864547301776787476793/38722691881970472639529711199036914238956437*t^27 + 36719358493050046628481168766478629018621893239/215126066010947070219609506661316190216424650*t^25 - 39861794171667863029427245815664916801322416554/942252169127948167561889639176564913147939967*t^23 + 137996075071909117204458919831302697937067251133/16218158547414380581065251971281480929334239432*t^21 - 11143305488069565074959560902518448958715891349/8109079273707190290532625985640740464667119716*t^19 + 7847427035009393074509667122875549869091156993/44655477644250554750604323920925721462961398984*t^17 - 11865103040043350227261199884109213536123489801/679135389172977186832107426297412013915871276215*t^15 + 715970870410778740120375272914933564477898251/543308311338381749465685941037929611132697020972*t^13 - 10882077543274746375306410575131181059030263429/149138131462385790228330790814911678255925332256814*t^11 + 16610870620696301874242919138253568259442015799/5866099837520507748981011105386526011399729735434684*t^9 - 35165050261558702369025861390044341763783351/488841653126708979081750925448877167616644144619557*t^7 + 302516863661721739980071454348927309819931661059/281983419189610807493517203835930305367985008382345259880*t^5 - 72515691891525767139035138370011594920593177/9399447306320360249783906794531010178932833612744841996*t^3 + 4487749874989087841218596920191693661423/264773163558320007036166388578338314899516439795629352*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:
| (0.99891192023712894231 + 5.469928015235505739e-897j)  +/-  (4.9e-238, 4.9e-238j)
| (-0.99427145552291961961 - 1.9294965842402478271e-913j)  +/-  (1.35e-237, 1.35e-237j)
| (-0.93918092363945194315 - 2.1261153361943454225e-916j)  +/-  (1.12e-237, 1.12e-237j)
| (-0.89048504867904741649 + 3.8069927843162823625e-919j)  +/-  (2.79e-238, 2.79e-238j)
| (0.9165327408833869705 + 1.4295030968308144828e-917j)  +/-  (5.74e-238, 5.74e-238j)
| (0.828597894698212756 - 6.8666797885843651267e-932j)  +/-  (3.45e-239, 3.45e-239j)
| (-0.95834421043633015845 + 1.1773185859380825784e-934j)  +/-  (1.79e-237, 1.79e-237j)
| (-0.9165327408833869705 - 3.9186359852126525144e-936j)  +/-  (6.4e-238, 6.4e-238j)
| (0.93918092363945194315 + 5.9903502215247809479e-933j)  +/-  (1.06e-237, 1.06e-237j)
| (-0.99891192023712894231 + 7.9216696464634216226e-945j)  +/-  (4.93e-238, 4.93e-238j)
| (0.89048504867904741649 + 1.6337051447582983529e-944j)  +/-  (2.72e-238, 2.72e-238j)
| (0.95834421043633015845 + 2.1056639442930526716e-948j)  +/-  (1.77e-237, 1.77e-237j)
| (-0.37182864042743481677 - 1.1441063406156010624e-963j)  +/-  (1.04e-246, 1.04e-246j)
| (-0.828597894698212756 + 1.2678988238798273703e-956j)  +/-  (3.45e-239, 3.45e-239j)
| (0.99427145552291961961 - 3.0600335395434825984e-952j)  +/-  (1.41e-237, 1.41e-237j)
| (0.86113631159405257522 - 6.9503317873365512625e-962j)  +/-  (1.07e-238, 1.07e-238j)
| (0.66922770057154316459 + 2.1782994228127186689e-969j)  +/-  (9.92e-242, 9.92e-242j)
| (-0.86113631159405257522 - 6.3257963700446806137e-968j)  +/-  (1.06e-238, 1.06e-238j)
| (-0.79299396318808796834 - 8.1593618832240032652e-970j)  +/-  (1.02e-239, 1.02e-239j)
| (-0.98594117928805506484 - 1.2305242001670397242e-965j)  +/-  (2.08e-237, 2.08e-237j)
| (0.97395049728239641652 + 9.8643673285106095139e-966j)  +/-  (2.25e-237, 2.25e-237j)
| (0.75446156256348163454 - 8.7363194745225202903e-985j)  +/-  (2.46e-240, 2.46e-240j)
| (0.98594117928805506484 - 2.7165089763345403171e-988j)  +/-  (2.09e-237, 2.09e-237j)
| (-0.71315109700312325592 + 7.2377485010151872553e-1007j)  +/-  (5.49e-241, 5.49e-241j)
| (-0.75446156256348163454 - 1.7387178123937096503e-1006j)  +/-  (2.36e-240, 2.36e-240j)
| (0.79299396318808796834 + 3.2358241292614561945e-1006j)  +/-  (1.05e-239, 1.05e-239j)
| (0.71315109700312325592 - 4.4203187733460278497e-1012j)  +/-  (5.3e-241, 5.3e-241j)
| (0.37182864042743481677 - 3.8093578397113919062e-1020j)  +/-  (9.9e-247, 9.9e-247j)
| (-0.97395049728239641652 - 1.3496952503971136031e-1020j)  +/-  (2.24e-237, 2.24e-237j)
| (-0.66922770057154316459 + 1.744156241252796431e-1026j)  +/-  (1.01e-241, 1.01e-241j)
| (-0.3399810435848562648 - 2.2160118700456324923e-1033j)  +/-  (2.11e-247, 2.11e-247j)
| (0.5743030365761770878 - 2.953851746073765244e-1027j)  +/-  (2.41e-243, 2.41e-243j)
| (0.62287474439793953329 - 1.4777535091565062601e-1028j)  +/-  (1.68e-242, 1.68e-242j)
| (-0.060572461564290051541 - 2.9595159259810550896e-1039j)  +/-  (2.78e-254, 2.78e-254j)
| (-0.62287474439793953329 + 2.491819580925745957e-1028j)  +/-  (1.55e-242, 1.55e-242j)
| (-0.5743030365761770878 - 3.0738468477962098474e-1031j)  +/-  (2.56e-243, 2.56e-243j)
| (0.23898943561928946733 - 4.2068402551510118826e-1039j)  +/-  (4.57e-250, 4.57e-250j)
| (0.52377782042158493088 - 3.4360729179573078415e-1032j)  +/-  (3.01e-244, 3.01e-244j)
| (0.29483659338740393697 + 5.01159131462117719e-1038j)  +/-  (1.39e-248, 1.39e-248j)
| (-0.18050018945355375286 - 3.4171147975809056075e-1041j)  +/-  (1.56e-251, 1.56e-251j)
| (-0.52377782042158493088 - 7.4726085311233541219e-1034j)  +/-  (3.13e-244, 3.13e-244j)
| (-0.1208523861502706071 + 1.7212016654628685662e-1043j)  +/-  (5.87e-253, 5.87e-253j)
| (0.3399810435848562648 + 3.6533127978803098195e-1036j)  +/-  (2.36e-247, 2.36e-247j)
| (0.41918825415757078745 + 1.38262093723538853e-1033j)  +/-  (5.6e-246, 5.6e-246j)
| (0.060572461564290051541 + 7.4712680360696138667e-1043j)  +/-  (2.78e-254, 2.78e-254j)
| (-0.47171628825664342898 + 3.8791140219344651767e-1035j)  +/-  (4.21e-245, 4.21e-245j)
| (-0.23898943561928946733 - 2.525838372362927246e-1042j)  +/-  (4.35e-250, 4.35e-250j)
| (0.1208523861502706071 - 1.3619249054884641953e-1042j)  +/-  (6.27e-253, 6.27e-253j)
| (0.47171628825664342898 + 3.4550616888568547976e-1036j)  +/-  (3.87e-245, 3.87e-245j)
| (0.18050018945355375286 + 8.8087140845078417035e-1045j)  +/-  (1.66e-251, 1.66e-251j)
| (-0.29483659338740393697 + 7.2504259763747159499e-1040j)  +/-  (1.37e-248, 1.37e-248j)
| (-0.41918825415757078745 - 9.2770967936304740655e-1038j)  +/-  (5.45e-246, 5.45e-246j)
| (-7.0955183905663336657e-1150 + 7.5182963764670548468e-1150j)  +/-  (5.48e-1148, 5.48e-1148j)
-------------------------------------------------
The weights are:
| (0.0027918524225296769494 - 7.0485618513122123826e-897j)  +/-  (2.15e-57, 3.34e-171j)
| (0.0064887374044078259414 + 2.7055953967638698432e-899j)  +/-  (1.05e-57, 1.62e-171j)
| (0.020918865974766619127 + 1.8304244889510566667e-898j)  +/-  (5.6e-58, 8.7e-172j)
| (0.027715705574112351833 + 3.2441059777340926784e-898j)  +/-  (1.67e-58, 2.6e-172j)
| (0.024363265001536922786 - 5.7295909889816100893e-897j)  +/-  (1.23e-59, 1.91e-173j)
| (0.034092934611022055492 + 5.8376284579846826177e-897j)  +/-  (3.93e-60, 6.09e-174j)
| (0.017395686753834046119 - 1.3118012810187124444e-898j)  +/-  (1.22e-58, 1.89e-172j)
| (0.024363265001536922786 - 2.4641745767209215368e-898j)  +/-  (2.24e-58, 3.47e-172j)
| (0.020918865974766619127 + 5.9391820082748473106e-897j)  +/-  (4.27e-60, 6.62e-174j)
| (0.0027918524225296769494 - 7.6439330991130586795e-900j)  +/-  (5.76e-60, 8.94e-174j)
| (0.027715705574112351833 + 5.653030390985946411e-897j)  +/-  (2.74e-60, 4.25e-174j)
| (0.017395686753834046119 - 6.3290018394102698036e-897j)  +/-  (1.03e-60, 1.6e-174j)
| (0.038984111636461280811 + 3.0401587569815980022e-896j)  +/-  (8.97e-64, 1.39e-177j)
| (0.034092934611022055492 + 5.440353830959224161e-898j)  +/-  (9.77e-62, 1.52e-175j)
| (0.0064887374044078259414 + 1.1621137318100558604e-896j)  +/-  (2.13e-61, 3.3e-175j)
| (0.030963205852743545675 - 5.6901052670217646123e-897j)  +/-  (3.95e-61, 6.14e-175j)
| (0.045170562301981620777 + 7.9859851538608182181e-897j)  +/-  (4.91e-64, 7.62e-178j)
| (0.030963205852743545675 - 4.2147171400781727371e-898j)  +/-  (1.31e-61, 2.03e-175j)
| (0.037092094435876500633 - 7.0160611555730088231e-898j)  +/-  (6.8e-63, 1.06e-176j)
| (0.010166770226267040959 - 5.4198962391344557882e-899j)  +/-  (9.79e-62, 1.52e-175j)
| (0.013807115245550765689 + 7.0098183869434563795e-897j)  +/-  (4.4e-62, 6.82e-176j)
| (0.039947659805024849482 + 6.5175534903674876706e-897j)  +/-  (4.79e-65, 7.44e-179j)
| (0.010166770226267040959 - 8.2938190590562069925e-897j)  +/-  (3.55e-62, 5.52e-176j)
| (0.042645800628532433055 - 1.1881363817301335536e-897j)  +/-  (1.93e-66, 3e-180j)
| (0.039947659805024849482 + 9.0865882112729400566e-898j)  +/-  (1.26e-65, 1.96e-179j)
| (0.037092094435876500633 - 6.1054030660124770149e-897j)  +/-  (5.61e-65, 8.71e-179j)
| (0.042645800628532433055 - 7.1184157981377979655e-897j)  +/-  (2.26e-66, 3.51e-180j)
| (0.038984111636461280811 + 6.6454792421174310278e-896j)  +/-  (1.05e-70, 1.64e-184j)
| (0.013807115245550765689 + 8.8690949778622564247e-899j)  +/-  (4.01e-65, 6.23e-179j)
| (0.045170562301981620777 + 1.5783170970036761758e-897j)  +/-  (3.53e-68, 5.48e-182j)
| (0.033839508929411787255 - 3.5040519835336167752e-896j)  +/-  (1.23e-70, 1.9e-184j)
| (0.04959983439397671399 + 1.1221373834561346018e-896j)  +/-  (1.05e-69, 1.63e-183j)
| (0.047500583196302674636 - 9.2616626049634213282e-897j)  +/-  (7.19e-69, 1.12e-182j)
| (0.06047677226150204054 + 1.0385442930888012989e-896j)  +/-  (5.18e-73, 8.04e-187j)
| (0.047500583196302674636 - 2.1474645990689239622e-897j)  +/-  (6.41e-70, 9.96e-184j)
| (0.04959983439397671399 + 3.0286357222833951327e-897j)  +/-  (1.03e-70, 1.6e-184j)
| (0.057598836140492792611 - 2.4230168381891115044e-896j)  +/-  (8.77e-74, 1.36e-187j)
| (0.051386251301951380436 - 1.4470017408116342536e-896j)  +/-  (5.26e-72, 8.17e-186j)
| (0.053110659666458435151 + 4.1655815030676209753e-896j)  +/-  (1.49e-73, 2.31e-187j)
| (0.059187253806752972887 + 1.1893802028472175045e-896j)  +/-  (5.02e-75, 7.79e-189j)
| (0.051386251301951380436 - 4.5151671492489376284e-897j)  +/-  (1.29e-73, 2e-187j)
| (0.060028174575283194091 - 1.0690111999987356288e-896j)  +/-  (4.44e-75, 6.9e-189j)
| (0.033839508929411787255 - 7.1199433990030327465e-896j)  +/-  (3.99e-74, 6.2e-188j)
| (0.051825444799497447941 - 3.4713441035305973668e-896j)  +/-  (2.24e-74, 3.47e-188j)
| (0.06047677226150204054 + 1.1726262262197139978e-896j)  +/-  (8.76e-77, 1.36e-190j)
| (0.052592295050136471942 + 7.3788777591628733615e-897j)  +/-  (4.97e-76, 7.73e-190j)
| (0.057598836140492792611 - 1.4874407942413629591e-896j)  +/-  (1.41e-76, 2.19e-190j)
| (0.060028174575283194091 - 1.3632795253818560362e-896j)  +/-  (4.08e-77, 6.34e-191j)
| (0.052592295050136471942 + 2.0583603355905492541e-896j)  +/-  (2.68e-76, 4.16e-190j)
| (0.059187253806752972887 + 1.7140143053928489836e-896j)  +/-  (5.27e-77, 8.2e-191j)
| (0.053110659666458435151 + 2.2669654321571455718e-896j)  +/-  (1.3e-77, 2.05e-191j)
| (0.051825444799497447941 - 1.4190960316194829436e-896j)  +/-  (8.69e-78, 1.39e-191j)
| (0.060620036007173106388 - 1.0726833669928750031e-896j)  +/-  (4.62e-78, 6.86e-192j)
