Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 43
-------------------------------------------------
Trying to find an order 43 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^47 - 4625517644991132802729138788794668/584052756600661157606210712525*t^45 + 13574873703035280166343963449844852992/7592685835808595048880739262825*t^43 - 618456921662192744869180450518646546901/2530895278602865016293579754275*t^41 + 11458738581924292860634415391381013722751/506179055720573003258715950855*t^39 - 234879704550295910624245805628832279042703/155747401760176308694989523340*t^37 + 5825506435342855949112254120604512322748737/77873700880088154347494761670*t^35 - 1758727453019977349469175844855605820910752943/622989607040705234779958093360*t^33 + 25579220822797304801370993876361082863891423251/311494803520352617389979046680*t^31 - 462142722687646787918109473789989541469056548653/249195842816282093911983237344*t^29 + 2031230883036297691859452502966566089265575901647/62298960704070523477995809336*t^27 - 444277583777458432644535452757080330712721458167165/996783371265128375647932949376*t^25 + 4699866352148790723808469230891958110460834063950635/996783371265128375647932949376*t^23 - 152604258010384370199036006747554672625681176242642635/3987133485060513502591731797504*t^21 + 469391728048716549662836935389184493984610477103841575/1993566742530256751295865898752*t^19 - 17208391421277724094713052736064704602099818179744674475/15948533940242054010366927190016*t^17 + 114815568885628042551534892106676954409667890475823285675/31897067880484108020733854380032*t^15 - 1081734201956281562154991754030473482718682296563542764725/127588271521936432082935417520128*t^13 + 215895820654988474055766121702084721469402721183347199175/15948533940242054010366927190016*t^11 - 7081871297037039805985077776124887570603989877070326445125/510353086087745728331741670080512*t^9 + 4334921788493153830146311367925789273886377251313406548875/510353086087745728331741670080512*t^7 - 5766319406827420812997055415222563751926923979828148252375/2041412344350982913326966680322048*t^5 + 458726798203410353282549776720199231767010251173931030125/1020706172175491456663483340161024*t^3 - 206399574846289241973958730964257727903619754592933648375/8165649377403931653307866721288192*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 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:
| (7.982903195537721898 + 4.9052988038860027908e-852j)  +/-  (4.21e-246, 4.21e-246j)
| (-8.6554180589708042199 - 7.351868090477731329e-856j)  +/-  (3.03e-247, 3.03e-247j)
| (8.6554180589708042199 - 5.2176868812749323407e-856j)  +/-  (3.55e-247, 3.55e-247j)
| (-4.8234782646736452601 - 1.3547065530737004845e-851j)  +/-  (2.03e-244, 2.03e-244j)
| (-7.4244695293212778683 - 3.6919180357622455972e-857j)  +/-  (2.45e-245, 2.45e-245j)
| (7.4244695293212778683 - 1.0340924878787558749e-855j)  +/-  (2.31e-245, 2.31e-245j)
| (-6.4623287168274653362 + 7.5123915787106631211e-862j)  +/-  (1.68e-244, 1.68e-244j)
| (1.3158315152144374736 - 3.0490405719962082284e-873j)  +/-  (2.71e-250, 2.71e-250j)
| (6.9246624499654483371 - 6.2845276173515601224e-866j)  +/-  (7.3e-245, 7.3e-245j)
| (-7.982903195537721898 + 1.7752985959331035073e-875j)  +/-  (3.98e-246, 3.98e-246j)
| (6.0265709238631223236 - 5.3318373688575923991e-872j)  +/-  (2.5e-244, 2.5e-244j)
| (5.6108458586168941359 - 1.0785800684444909951e-874j)  +/-  (3.15e-244, 3.15e-244j)
| (6.4623287168274653362 + 2.1105894656685293142e-876j)  +/-  (1.72e-244, 1.72e-244j)
| (-1.6506801238857845559 - 5.9101010041009159415e-882j)  +/-  (2.21e-249, 2.21e-249j)
| (-1.987029458146342359 - 8.312401610029635059e-881j)  +/-  (1.7e-248, 1.7e-248j)
| (2.3256949076116745138 - 1.10747602214613419e-880j)  +/-  (1.1e-247, 1.1e-247j)
| (4.0782319405633628314 - 1.4905326634472330249e-876j)  +/-  (5.58e-245, 5.58e-245j)
| (-6.9246624499654483371 - 2.4257495632378484485e-876j)  +/-  (7.6e-245, 7.6e-245j)
| (-2.6673465213743687334 - 2.8156497997763643761e-879j)  +/-  (5.19e-247, 5.19e-247j)
| (-5.6108458586168941359 + 1.5706302149698468274e-884j)  +/-  (2.88e-244, 2.88e-244j)
| (4.4465255103797399133 + 4.0251302301611731227e-895j)  +/-  (1.27e-244, 1.27e-244j)
| (3.3623359654257317755 + 1.9848826049752054947e-899j)  +/-  (8.26e-246, 8.26e-246j)
| (-5.2108315617300047796 + 6.4103350727462128433e-904j)  +/-  (2.76e-244, 2.76e-244j)
| (-4.0782319405633628314 + 7.3918231481359409171e-920j)  +/-  (5.42e-245, 5.42e-245j)
| (-6.0265709238631223236 - 3.5361830755586142695e-928j)  +/-  (2.77e-244, 2.77e-244j)
| (1.6506801238857845559 + 1.7035747771131762188e-941j)  +/-  (2.66e-249, 2.66e-249j)
| (-2.2453430003853762547e-957 - 1.5911540023223037711e-958j)  +/-  (1.06e-955, 1.06e-955j)
| (2.6673465213743687334 + 1.2127361878520085214e-938j)  +/-  (5.46e-247, 5.46e-247j)
| (-4.4465255103797399133 + 1.0283867767753559348e-935j)  +/-  (1.11e-244, 1.11e-244j)
| (-0.62940004351588261544 - 1.3723991603805548155e-946j)  +/-  (7.35e-252, 7.35e-252j)
| (-3.3623359654257317755 + 3.4091925219292608786e-939j)  +/-  (8.66e-246, 8.66e-246j)
| (3.7172127499033690995 + 1.7885437129522367879e-944j)  +/-  (2.25e-245, 2.25e-245j)
| (0.98083286496671762759 + 1.2742633770939901468e-964j)  +/-  (3.07e-251, 3.07e-251j)
| (4.8234782646736452601 - 3.1082854716842657913e-958j)  +/-  (2.11e-244, 2.11e-244j)
| (-0.34406588300538345532 + 1.7891138600726980629e-975j)  +/-  (2.82e-253, 2.82e-253j)
| (-1.3158315152144374736 + 1.6482437804679438025e-973j)  +/-  (2.79e-250, 2.79e-250j)
| (3.012652587482379936 - 6.971969296467378428e-968j)  +/-  (2.5e-246, 2.5e-246j)
| (0.34406588300538345532 - 4.2319788312769043802e-978j)  +/-  (2.82e-253, 2.82e-253j)
| (5.2108315617300047796 - 7.8707924513010088045e-972j)  +/-  (2.77e-244, 2.77e-244j)
| (-3.7172127499033690995 - 1.0700019785557108792e-978j)  +/-  (2.27e-245, 2.27e-245j)
| (-2.3256949076116745138 + 3.0293124631182808044e-982j)  +/-  (9.63e-248, 9.63e-248j)
| (-0.52464762327529031788 + 1.716026519707120597e-987j)  +/-  (3.88e-252, 3.88e-252j)
| (0.62940004351588261544 + 4.434346985587211569e-987j)  +/-  (6.71e-252, 6.71e-252j)
| (0.52464762327529031788 + 1.7182855738642908927e-987j)  +/-  (3.54e-252, 3.54e-252j)
| (-3.012652587482379936 - 3.8309468525217077377e-985j)  +/-  (2.27e-246, 2.27e-246j)
| (-0.98083286496671762759 + 1.3122752432970167182e-989j)  +/-  (3.42e-251, 3.42e-251j)
| (1.987029458146342359 + 2.1610033257476292445e-986j)  +/-  (1.62e-248, 1.62e-248j)
-------------------------------------------------
The weights are:
| (7.1404078724113570406e-29 + 1.3335124004332263089e-872j)  +/-  (3.37e-86, 3.84e-208j)
| (1.2748107701617869343e-33 + 1.600806520285286753e-874j)  +/-  (1.21e-88, 1.38e-210j)
| (1.2748107701617869343e-33 - 4.5509619717409064016e-875j)  +/-  (4.86e-88, 5.55e-210j)
| (1.6944174110676882168e-11 - 1.2034835238758819377e-861j)  +/-  (5.31e-78, 6.06e-200j)
| (3.3992802923936082045e-25 + 5.2407455027984575028e-870j)  +/-  (6.25e-86, 7.13e-208j)
| (3.3992802923936082045e-25 - 1.1129319663554232031e-870j)  +/-  (1.17e-85, 1.34e-207j)
| (1.843041947954596554e-19 + 8.0964924573471118945e-867j)  +/-  (6.37e-84, 7.26e-206j)
| (0.03340890462863506585 - 2.6091633977420984939e-857j)  +/-  (4.04e-58, 4.61e-180j)
| (4.0426221056936216576e-22 + 4.6031070400876463711e-869j)  +/-  (5.8e-85, 6.62e-207j)
| (7.1404078724113570406e-29 - 5.4052470136753979355e-872j)  +/-  (4.35e-88, 4.96e-210j)
| (4.0393131865254239186e-17 + 2.0837591866711694535e-866j)  +/-  (9.01e-84, 1.03e-205j)
| (4.8868964694899000476e-15 - 2.7526854820741823433e-865j)  +/-  (2.92e-83, 3.33e-205j)
| (1.843041947954596554e-19 - 1.1757192141627061666e-867j)  +/-  (1.19e-84, 1.36e-206j)
| (0.012407765696208062367 + 1.8324967467892681935e-857j)  +/-  (3.59e-68, 4.09e-190j)
| (0.0036714701840192188817 - 7.4432607511261985205e-858j)  +/-  (6.67e-71, 7.61e-193j)
| (0.00085887610668397894216 + 1.0225456878466608091e-858j)  +/-  (1.94e-73, 2.22e-195j)
| (1.2299487772504514618e-08 - 9.7638312694189142952e-862j)  +/-  (1e-80, 1.14e-202j)
| (4.0426221056936216576e-22 - 2.573689202960896472e-868j)  +/-  (1.53e-88, 1.75e-210j)
| (0.00015750305273598442249 - 1.0901923928358868875e-858j)  +/-  (4.72e-77, 5.38e-199j)
| (4.8868964694899000476e-15 + 3.6479038529402650774e-864j)  +/-  (1.99e-86, 2.27e-208j)
| (5.4413169743232090264e-10 + 1.6546249169946841683e-862j)  +/-  (4.11e-83, 4.69e-205j)
| (2.4451346374621333676e-06 - 2.2195108984039025958e-860j)  +/-  (1.74e-80, 1.99e-202j)
| (3.5793206511008841055e-13 - 7.3677216598580681053e-863j)  +/-  (9.23e-86, 1.05e-207j)
| (1.2299487772504514618e-08 - 1.1662559618541664658e-860j)  +/-  (3.15e-84, 3.59e-206j)
| (4.0393131865254239186e-17 - 1.8792309773864531375e-865j)  +/-  (7.99e-88, 9.12e-210j)
| (0.012407765696208062367 + 8.9805375677980453232e-858j)  +/-  (1.2e-76, 1.37e-198j)
| (0.1903325188960607081 + 4.4166914573031348262e-856j)  +/-  (6.28e-75, 7.16e-197j)
| (0.00015750305273598442249 - 3.1379700977322295923e-859j)  +/-  (8.65e-81, 9.87e-203j)
| (5.4413169743232090264e-10 + 4.0690455593803009539e-861j)  +/-  (5.81e-85, 6.62e-207j)
| (0.16223767106488753438 - 1.0324152604902039816e-855j)  +/-  (1.49e-76, 1.7e-198j)
| (2.4451346374621333676e-06 - 1.2434452118358549141e-859j)  +/-  (1.69e-83, 1.93e-205j)
| (2.0141822421730851743e-07 + 4.9735099233651717912e-861j)  +/-  (3.13e-84, 3.57e-206j)
| (0.072536708414656765118 + 8.5856146269962004223e-857j)  +/-  (5.93e-78, 6.77e-200j)
| (1.6944174110676882168e-11 - 2.3794430386821768063e-863j)  +/-  (2.65e-87, 3.02e-209j)
| (0.18551382751498953321 - 8.7778110647611311307e-856j)  +/-  (9.67e-79, 1.1e-200j)
| (0.03340890462863506585 - 4.5667262205526618769e-857j)  +/-  (2.4e-80, 2.74e-202j)
| (2.2414287873325494718e-05 + 8.7963943886031393739e-860j)  +/-  (1.35e-83, 1.54e-205j)
| (0.18551382751498953321 - 7.6089210720664898479e-856j)  +/-  (7.26e-80, 8.22e-202j)
| (3.5793206511008841055e-13 + 2.844153015423984372e-864j)  +/-  (2.82e-88, 3.21e-210j)
| (2.0141822421730851743e-07 + 3.8396940982839825953e-860j)  +/-  (2.31e-86, 2.64e-208j)
| (0.00085887610668397894216 + 2.9267374986105381357e-858j)  +/-  (5.65e-84, 6.36e-206j)
| (-0.065984059812508005744 + 1.5855708400675545126e-855j)  +/-  (3.08e-80, 3.43e-202j)
| (0.16223767106488753438 - 7.9408160464866754131e-856j)  +/-  (3.7e-81, 4.1e-203j)
| (-0.065984059812508005744 + 1.2744839316044373709e-855j)  +/-  (5.77e-81, 6.37e-203j)
| (2.2414287873325494718e-05 + 3.806534142238234069e-859j)  +/-  (7.96e-86, 9.37e-208j)
| (0.072536708414656765118 + 1.2968560299514772161e-856j)  +/-  (1.15e-82, 1.46e-204j)
| (0.0036714701840192188817 - 3.0999785766459924144e-858j)  +/-  (2.82e-84, 2.82e-206j)
