Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 47
-------------------------------------------------
Trying to find an order 47 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^51 - 8183125494081144304867576559086425/149543807463080600475948040277192*t^49 + 63873244469804037196025700930821556594/198538097383172382206880516973007029*t^47 - 5244077418429883124339881691149951559/4437405204670759804191273270485377*t^45 + 973255163832957335752536297507948789683595/320043412981673880117491393360487330748*t^43 - 3858675518214375522124927863386830155191415/662415436171371519312947302536822614804*t^41 + 41381431037014059658032358574879054374876875/4802511912242443515018867943391963957329*t^39 - 195934041556609115268865680452356386195576/19443368065758880627606752807254914807*t^37 + 122171784410114829812583169432114392826103133/12910396395663896736730883864017263431848*t^35 - 837387486927118272709004941856379584721424495/116193567560975070630577954776155370886632*t^33 + 570834876368390859888581985929172381526553560/127490164407180980275217478157170476389499*t^31 - 28071655987179111568764177404474152859799950/12337757845856223897601691434564884811887*t^29 + 12066752959936231080258054967267811133043499/12763197771575404032001749759894708426090*t^27 - 2550662611571296176829182947084191528463457/7963362712179525592616476345917211240210*t^25 + 4973964328665696819277827790736865398308230/56539875256474631707576982056012199805491*t^23 - 14274106948222955667057973967916193067662860/735018378334170212198500766728158597471383*t^21 + 15068866999655565005157550432934780847849825/4426627536933879030768498999621269755557992*t^19 - 2387340853387332798258065089303186807198731591/5121608060232498038599153342561809107180596744*t^17 + 1185883378647370578778074075746732256347758/24311430665660591955375727891907321711300301*t^15 - 147908295371837118528020353816525900071736035/39052261459272797544318544237033794442252050173*t^13 + 148529782333241210911250831448893356078180655/708948746491413863112244341533844268336267987756*t^11 - 314841398985510308836013843652960914025382825/40410078550010590197397927467429123295167275302092*t^9 + 31625809641729941460025031460634084604697/177237186622853465778061085383461067084066996939*t^7 - 388367358516555757916141773456571330255388/178477846929213440038507512981145294553655465917573*t^5 + 15157210298384905489752427787258985642795/1427822775433707520308060103849162356429243727340584*t^3 - 12685541843957367794894258220149897265/1427822775433707520308060103849162356429243727340584*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:
| (0.99451353494093442613 + 9.5969278840552529654e-854j)  +/-  (1.04e-237, 1.04e-237j)
| (-0.98646273183988963758 + 4.8090874985416874119e-868j)  +/-  (1.32e-237, 1.32e-237j)
| (-0.9402412661265321465 - 3.1209253636620330969e-874j)  +/-  (5.63e-238, 5.63e-238j)
| (0.99896141967383319859 + 4.8444737774820165743e-879j)  +/-  (3.78e-238, 3.78e-238j)
| (0.82777911719968129412 - 1.1101272643575348344e-892j)  +/-  (1.41e-239, 1.41e-239j)
| (0.9402412661265321465 - 5.8498303577421488858e-898j)  +/-  (6.18e-238, 6.18e-238j)
| (-0.99451353494093442613 + 7.6560289508138864925e-905j)  +/-  (9.58e-238, 9.58e-238j)
| (-0.89106529492522053478 + 2.3226814418719871679e-907j)  +/-  (1.24e-238, 1.24e-238j)
| (-0.75129109507987767796 - 6.5369759167829196747e-910j)  +/-  (7.87e-241, 7.87e-241j)
| (-0.99896141967383319859 + 5.7246623464724612506e-906j)  +/-  (3.73e-238, 3.73e-238j)
| (0.86113631159405257522 - 1.6065147759312374576e-906j)  +/-  (4.88e-239, 4.88e-239j)
| (0.66277991661249811343 + 2.4369599547716055217e-910j)  +/-  (2.1e-242, 2.1e-242j)
| (-0.91746129271838911689 + 4.3388754196396518099e-907j)  +/-  (3.04e-238, 3.04e-238j)
| (-0.86113631159405257522 + 3.3538211371575237399e-908j)  +/-  (4.43e-239, 4.43e-239j)
| (0.98646273183988963758 - 2.7498522547512557878e-904j)  +/-  (1.4e-237, 1.4e-237j)
| (0.91746129271838911689 - 7.8024000143248320629e-916j)  +/-  (2.98e-238, 2.98e-238j)
| (0.89106529492522053478 + 2.4516652359642580563e-917j)  +/-  (1.26e-238, 1.26e-238j)
| (-0.82777911719968129412 - 2.522393230291402661e-922j)  +/-  (1.43e-239, 1.43e-239j)
| (-0.79111730264262335159 - 8.2021873965242915152e-923j)  +/-  (3.55e-240, 3.55e-240j)
| (-0.97475302777792357991 - 6.7880768688483320266e-920j)  +/-  (1.32e-237, 1.32e-237j)
| (0.95934771382046572549 + 2.0415122614320624279e-922j)  +/-  (1.02e-237, 1.02e-237j)
| (0.79111730264262335159 + 2.1137895887737618847e-938j)  +/-  (3.55e-240, 3.55e-240j)
| (-0.95934771382046572549 + 5.024608355434715202e-935j)  +/-  (1.13e-237, 1.13e-237j)
| (-0.66277991661249811343 + 5.3947659813952306523e-942j)  +/-  (2.46e-242, 2.46e-242j)
| (-0.70845569107894240504 - 3.1539344625585606893e-941j)  +/-  (1.44e-241, 1.44e-241j)
| (0.15717412747849810755 + 4.234944138231272753e-942j)  +/-  (2.13e-252, 2.13e-252j)
| (0.75129109507987767796 - 1.9208925010282209388e-940j)  +/-  (7.4e-241, 7.4e-241j)
| (0.70845569107894240504 - 1.7840165841693771228e-943j)  +/-  (1.42e-241, 1.42e-241j)
| (0.97475302777792357991 + 5.9663036467276728894e-958j)  +/-  (1.37e-237, 1.37e-237j)
| (-0.61444508487038480709 + 1.2362889072854363339e-969j)  +/-  (2.88e-243, 2.88e-243j)
| (-0.28007735272877389374 - 3.1199614674255440646e-971j)  +/-  (7.96e-250, 7.96e-250j)
| (0.39852280016012275714 + 1.002375255604368022e-973j)  +/-  (2.2e-247, 2.2e-247j)
| (0.61444508487038480709 - 2.5899099364081455476e-970j)  +/-  (2.87e-243, 2.87e-243j)
| (-0.094716935269349539396 + 6.5540340563849620757e-974j)  +/-  (1.09e-253, 1.09e-253j)
| (-0.45546559241603880948 + 1.2063396854326976057e-971j)  +/-  (2.89e-246, 2.89e-246j)
| (-0.39852280016012275714 - 1.5066547339064156389e-974j)  +/-  (2.18e-247, 2.18e-247j)
| (0.032263065402726217572 - 2.2207303760483750668e-979j)  +/-  (6.63e-255, 6.63e-255j)
| (0.56364397004520172671 + 1.1939252860492053947e-975j)  +/-  (3.16e-244, 3.16e-244j)
| (0.3399810435848562648 - 1.6171068843739019436e-981j)  +/-  (1.37e-248, 1.37e-248j)
| (-0.032263065402726217572 + 2.6876603982596968762e-981j)  +/-  (6.63e-255, 6.63e-255j)
| (-0.56364397004520172671 + 1.00348533708350863e-976j)  +/-  (3.2e-244, 3.2e-244j)
| (-0.15717412747849810755 + 3.9597865815653306298e-983j)  +/-  (2.13e-252, 2.13e-252j)
| (0.28007735272877389374 + 2.2299141018921596251e-983j)  +/-  (8.29e-250, 8.29e-250j)
| (0.45546559241603880948 - 1.7289031231596258268e-979j)  +/-  (2.73e-246, 2.73e-246j)
| (-2.5256666517674654955e-984 + 3.4415818295776837874e-985j)  +/-  (1.3e-982, 1.3e-982j)
| (-0.51057984945848640482 + 3.8272616625980797889e-980j)  +/-  (3.28e-245, 3.28e-245j)
| (-0.3399810435848562648 - 2.6960161197703550323e-982j)  +/-  (1.26e-248, 1.26e-248j)
| (0.094716935269349539396 + 1.4770652046507107039e-985j)  +/-  (1.09e-253, 1.09e-253j)
| (0.51057984945848640482 + 4.6642585235318365167e-985j)  +/-  (3.54e-245, 3.54e-245j)
| (0.21905647956906808202 - 6.3910733003916692432e-992j)  +/-  (4.54e-251, 4.54e-251j)
| (-0.21905647956906808202 - 6.0665182718417234061e-1001j)  +/-  (4.46e-251, 4.46e-251j)
-------------------------------------------------
The weights are:
| (0.0062393168898905190684 - 5.0066718265447545729e-854j)  +/-  (9.33e-59, 6.58e-173j)
| (0.0098719466333502897323 + 5.6459765115976880488e-856j)  +/-  (2.52e-59, 1.78e-173j)
| (0.020950448686718870351 - 1.4264890514808548603e-855j)  +/-  (2.19e-59, 1.55e-173j)
| (0.0026670577408130742643 - 3.9657293702149169501e-854j)  +/-  (3.51e-59, 2.48e-173j)
| (0.035031551887770772709 - 2.9193420477360252889e-854j)  +/-  (2.93e-60, 2.07e-174j)
| (0.020950448686718870351 - 5.0852978902733315726e-854j)  +/-  (4.64e-60, 3.27e-174j)
| (0.0062393168898905190684 - 3.0104303327325094097e-856j)  +/-  (2.04e-60, 1.44e-174j)
| (0.028178253417995083453 - 2.0178995779154212346e-855j)  +/-  (3.64e-61, 2.57e-175j)
| (0.041357848299784907463 - 3.4638970503207289207e-855j)  +/-  (3.21e-62, 2.26e-176j)
| (0.0026670577408130742643 + 8.84842173699842137e-857j)  +/-  (5.55e-61, 3.92e-175j)
| (0.031662202655266231602 + 3.2452389781466689469e-854j)  +/-  (4.59e-62, 3.24e-176j)
| (0.047036509881502944001 - 2.2547069514150679466e-854j)  +/-  (3.4e-63, 2.4e-177j)
| (0.02459983855594791251 + 1.7183197721122031989e-855j)  +/-  (3.09e-61, 2.18e-175j)
| (0.031662202655266231602 + 2.332557323842836568e-855j)  +/-  (5.8e-62, 4.1e-176j)
| (0.0098719466333502897323 + 1.3892459338401502043e-853j)  +/-  (2.02e-62, 1.42e-176j)
| (0.02459983855594791251 + 4.2638397733559479718e-854j)  +/-  (9.19e-63, 6.49e-177j)
| (0.028178253417995083453 - 3.6780797085913498153e-854j)  +/-  (8.3e-63, 5.86e-177j)
| (0.035031551887770772709 - 2.671112106746766845e-855j)  +/-  (9.18e-64, 6.48e-178j)
| (0.038268678699354775173 + 3.044006128233238864e-855j)  +/-  (2.43e-64, 1.71e-178j)
| (0.013553783628636129705 - 8.4827358107583517372e-856j)  +/-  (1.68e-63, 1.19e-177j)
| (0.017257781696568902795 + 6.3177759349099900006e-854j)  +/-  (2.12e-65, 1.5e-179j)
| (0.038268678699354775173 + 2.6723558990977075913e-854j)  +/-  (8.68e-67, 6.13e-181j)
| (0.017257781696568902795 + 1.1370806322462935595e-855j)  +/-  (1.01e-63, 7.12e-178j)
| (0.047036509881502944001 - 4.5131542308462384877e-855j)  +/-  (1.94e-68, 1.37e-182j)
| (0.04428480319285176536 + 3.9466910331828393722e-855j)  +/-  (1.94e-67, 1.37e-181j)
| (0.062222792178244062758 + 4.4886482360131921943e-854j)  +/-  (5.97e-73, 4.21e-187j)
| (0.041357848299784907463 - 2.4863197293061236627e-854j)  +/-  (3.96e-69, 2.8e-183j)
| (0.04428480319285176536 + 2.3495574473257145839e-854j)  +/-  (8.2e-70, 5.79e-184j)
| (0.013553783628636129705 - 8.4536129840642651159e-854j)  +/-  (1.16e-67, 8.19e-182j)
| (0.049601008657082613744 + 5.1914342589997838502e-855j)  +/-  (4.47e-71, 3.15e-185j)
| (0.060503785472710488048 + 1.6275878530990036082e-854j)  +/-  (2.08e-74, 1.47e-188j)
| (0.057781167989297403293 + 2.378753004787803065e-854j)  +/-  (1.99e-74, 1.41e-188j)
| (0.049601008657082613744 + 2.1977101489615541477e-854j)  +/-  (3.79e-72, 2.67e-186j)
| (0.062623485875139246029 - 5.7439091168475711934e-854j)  +/-  (1.66e-75, 1.17e-189j)
| (0.05606614526247653293 - 8.3977650242584841309e-855j)  +/-  (1.31e-74, 9.24e-189j)
| (0.057781167989297403293 + 1.017715558067414349e-854j)  +/-  (5.32e-75, 3.75e-189j)
| (0.061645222535904417695 + 1.8748418649271062108e-853j)  +/-  (2.94e-76, 2.07e-190j)
| (0.0519673262484136349 - 2.1774320753416549965e-854j)  +/-  (5.47e-75, 3.86e-189j)
| (0.059262841058710794432 - 2.5784877166082725356e-854j)  +/-  (1.99e-76, 1.4e-190j)
| (0.061645222535904417695 + 1.7570204309605225891e-853j)  +/-  (1.55e-76, 1.09e-190j)
| (0.0519673262484136349 - 6.0211448963937207484e-855j)  +/-  (6.87e-76, 4.85e-190j)
| (0.062222792178244062758 + 3.2634907682824448243e-854j)  +/-  (4.41e-77, 3.12e-191j)
| (0.060503785472710488048 + 2.9037004257237244522e-854j)  +/-  (1.09e-77, 7.7e-192j)
| (0.05606614526247653293 - 2.2589055705487156569e-854j)  +/-  (1.55e-77, 1.09e-191j)
| (0.0034904724960576824445 - 2.818840067557173098e-853j)  +/-  (6.5e-77, 4.58e-191j)
| (0.054125422281326589313 + 7.0603005449723702507e-855j)  +/-  (1.31e-77, 9.21e-192j)
| (0.059262841058710794432 - 1.2646765421460662983e-854j)  +/-  (3.91e-78, 2.76e-192j)
| (0.062623485875139246029 - 6.9531723396960306596e-854j)  +/-  (2.65e-78, 1.88e-192j)
| (0.054125422281326589313 + 2.195840455188735856e-854j)  +/-  (4.86e-79, 3.45e-193j)
| (0.061495544326213197449 - 3.4538510701965624641e-854j)  +/-  (6.21e-79, 4.44e-193j)
| (0.061495544326213197449 - 2.2069704661160536572e-854j)  +/-  (5.34e-79, 3.58e-193j)
