Starting with polynomial:
P : -t+1
Extension levels are: 1 5 15
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Trying to find an order 5 Kronrod extension for:
P1 : -t+1
Solvable: 1
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Trying to find an order 15 Kronrod extension for:
P2 : -t^6 + 1831/56*t^5 - 20575/56*t^4 + 12175/7*t^3 - 23925/7*t^2 + 16365/7*t - 2265/7
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^21 + 697026191409100249318812493140155286527947294343593310805825526866255557/1996999397132061986747965243088500322568312833822850400820269907538382*t^20 - 3513591961292729558176458440250420152686129677248834634866880288191027793925/63903980708225983575934887778832010322186010682331212826248637041228224*t^19 + 3645669426452611804376725511602258756538578953749275368535712518963774007859475/702943787790485819335283765567152113544046117505643341088735007453510464*t^18 - 115195287887531992506203862853282398078526063210914182092900725756129298643540175/351471893895242909667641882783576056772023058752821670544367503726755232*t^17 + 470044768568960717788611570268179199655168986991121025698422252749524566593923915/31951990354112991787967443889416005161093005341165606413124318520614112*t^16 - 85251755033704115283478747264448495109182383347534124352560081965779274180987735795/175735946947621454833820941391788028386011529376410835272183751863377616*t^15 + 2107476209778434536628104896923861655561290779040013242958100213740655868404134217875/175735946947621454833820941391788028386011529376410835272183751863377616*t^14 - 2821452390844557339165197542340360550215708380386467499243056345055311625701777581125/12552567639115818202415781527984859170429394955457916805155982275955544*t^13 + 40290969687792981376607479385830704051780962158663612903811064946889970213613428387375/12552567639115818202415781527984859170429394955457916805155982275955544*t^12 - 109546222965332825939965550862418739609826656191263575167886104903282940597653062029175/3138141909778954550603945381996214792607348738864479201288995568988886*t^11 + 82050989462102731274040280293883537601986923993920949181973512182870345217894119658425/285285628161723140963995034726928617509758976260407200117181415362626*t^10 - 253487392161764256879290532841500982917236983442404777487857404431903787943627177666875/142642814080861570481997517363464308754879488130203600058590707681313*t^9 + 1156488572425111611349053176193788833344538803735361196330287373825828761138306794568125/142642814080861570481997517363464308754879488130203600058590707681313*t^8 - 3811382783821634929462231296783824811910897328740287618954219520460729400118991777265000/142642814080861570481997517363464308754879488130203600058590707681313*t^7 + 8803770218010165990255524171449214930628054882988348920375499280602101869206525876569000/142642814080861570481997517363464308754879488130203600058590707681313*t^6 - 13671237906604273385162691309003684048638342279972952253995296369586691183362865703514000/142642814080861570481997517363464308754879488130203600058590707681313*t^5 + 13455883962716039218009336910258064472604469138095013340714341543021368573219117819550000/142642814080861570481997517363464308754879488130203600058590707681313*t^4 - 7692572055446178270739150402575459370578375132142950857197282098625381254271401066600000/142642814080861570481997517363464308754879488130203600058590707681313*t^3 + 2222602712839011382969119197114074155827380222718594237250588490943256057789064278600000/142642814080861570481997517363464308754879488130203600058590707681313*t^2 - 252951057118923929788156972950064394881455364778330110173984421716875859626420686320000/142642814080861570481997517363464308754879488130203600058590707681313*t + 6412174764914859865757574588281865585119927793995538558085117506800302565006991120000/142642814080861570481997517363464308754879488130203600058590707681313
-------------------------------------------------
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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (59.505959071402544218 + 7.8120966486034821444e-272j)  +/-  (1.11e-119, 1.11e-119j)
| (41.448095439754859588 + 3.1854684522691140284e-268j)  +/-  (4.45e-118, 4.45e-118j)
| (35.026012709865604338 + 5.7443035796501844766e-270j)  +/-  (1.15e-117, 1.15e-117j)
| (49.245525333747172939 + 4.0676325854235371243e-275j)  +/-  (9.82e-119, 9.82e-119j)
| (15.751176541741921472 + 3.683531986361110452e-281j)  +/-  (7.38e-116, 7.38e-116j)
| (5.1384848875831238418 - 3.380285770270299129e-301j)  +/-  (3.8e-120, 3.8e-120j)
| (2.5922508199253002476 - 2.0776884197527139911e-304j)  +/-  (9.01e-122, 9.01e-122j)
| (6.874546730052592601 - 2.1652726768560453467e-300j)  +/-  (2.15e-119, 2.15e-119j)
| (8.9529512477548957267 + 3.306725540772164936e-297j)  +/-  (1.12e-118, 1.12e-118j)
| (3.7210971507514272678 - 4.4539116203111011115e-307j)  +/-  (6.2e-121, 6.2e-121j)
| (20.596097276307811007 - 5.7922254697253974361e-301j)  +/-  (4.9e-117, 4.9e-117j)
| (0.49182826766644119027 + 1.2435817271650337334e-317j)  +/-  (7.87e-125, 7.87e-125j)
| (14.829781217182764814 + 3.835959710212980634e-323j)  +/-  (1.84e-116, 1.84e-116j)
| (29.55236664638205411 + 5.8074068263488242145e-347j)  +/-  (2.28e-117, 2.28e-117j)
| (0.18296039898248679851 - 5.5398015249612653217e-354j)  +/-  (5.31e-126, 5.31e-126j)
| (1 - 2.6794295478797247168e-354j)  +/-  (1.26e-123, 1.26e-123j)
| (0.034767713968554585827 - 5.4402161036356864052e-356j)  +/-  (1.99e-127, 1.99e-127j)
| (16.174388394601862068 - 2.5379757692245660501e-361j)  +/-  (5.54e-116, 5.54e-116j)
| (24.797444792962782897 + 7.296698727431398182e-376j)  +/-  (2.9e-117, 2.9e-117j)
| (11.421117035640697237 + 9.9480770615047308919e-380j)  +/-  (6.13e-118, 6.13e-118j)
| (1.6999043738851732137 + 1.817959548952086891e-393j)  +/-  (1.16e-122, 1.16e-122j)
-------------------------------------------------
The weights are:
| (1.7771580681414551437e-25 + 5.4947241485370029199e-291j)  +/-  (4.97e-48, 7.58e-106j)
| (6.999862599568101889e-18 - 1.3663104636345861745e-285j)  +/-  (2.96e-45, 4.51e-103j)
| (3.624075148864889805e-15 + 1.2189375965839036204e-285j)  +/-  (2.71e-44, 4.13e-102j)
| (3.5833542993250644807e-21 - 3.3194323154188348908e-288j)  +/-  (9.49e-47, 1.45e-104j)
| (-2.9948971976790039129e-06 - 1.3283580916507930037e-278j)  +/-  (8.6e-40, 1.31e-97j)
| (0.0092284204238989032453 + 1.0347307658330273433e-277j)  +/-  (4.47e-33, 6.81e-91j)
| (0.074896388678643138533 + 5.3366510315409631623e-277j)  +/-  (1.97e-29, 3e-87j)
| (0.0019668811913583415837 - 3.8065395740324440038e-278j)  +/-  (4.09e-35, 6.23e-93j)
| (0.00029244382204133541119 + 1.3384794224296196682e-278j)  +/-  (4.9e-37, 7.47e-95j)
| (0.030654674287163894562 - 2.5461338153921076411e-277j)  +/-  (1.39e-32, 2.11e-90j)
| (4.5309583727025440335e-09 - 2.7285222197051054095e-281j)  +/-  (7.25e-43, 1.1e-100j)
| (0.24904352986221186505 - 1.594385860015076961e-276j)  +/-  (5.66e-33, 8.62e-91j)
| (3.1429193940548472903e-06 + 7.3053055811222025235e-279j)  +/-  (1.95e-40, 2.98e-98j)
| (7.4442596802614070785e-13 - 9.1979660558489629952e-284j)  +/-  (8.02e-46, 1.22e-103j)
| (0.18110137302756193733 + 1.4221368069197650834e-276j)  +/-  (6.51e-34, 9.92e-92j)
| (0.22319350114904240277 + 1.3149704588813824033e-276j)  +/-  (8.23e-35, 1.25e-92j)
| (0.08482305750504719265 - 5.7967816405666371618e-277j)  +/-  (3.4e-34, 5.18e-92j)
| (1.6916526146637541965e-06 + 7.4632884501776964641e-279j)  +/-  (7.07e-41, 1.08e-98j)
| (7.569315990976527084e-11 + 1.6746255818845257988e-282j)  +/-  (8.31e-45, 1.27e-102j)
| (2.9617612758624827267e-05 - 4.9417080149093413889e-279j)  +/-  (6.84e-41, 1.04e-98j)
| (0.14476826815806173478 - 9.1740504078448695055e-277j)  +/-  (6.92e-38, 1.05e-95j)
