Starting with polynomial:
P : t^5 - 10*t^3 + 15*t
Extension levels are: 5 14 34
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P1 : t^5 - 10*t^3 + 15*t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P2 : t^19 - 10067/33*t^17 + 4654486/165*t^15 - 13098722/11*t^13 + 26061308*t^11 - 305527040*t^9 + 1871898210*t^7 - 5508762714*t^5 + 6473363715*t^3 - 1927283085*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^53 - 418313987895796250264732305810739641229306913167703306430698070705020000777059650337582482009037701865687390802718891/365647758348046586595500362053237969559139497873017676422564541071752736738173161518266278197126512852408009787982*t^51 + 16462827807300024611693792015458431408196782819802555465548554989184822593357585388047232296287467361923027342877637513949/27423581876103493994662527153992847716935462340476325731692340580381455255362987113869970864784488463930600734098650*t^49 - 23710489848670123246244362811111077002587731742727486155419535769349673532697287270803940475807278854495788487699119647754247/123406118442465722975981372192967814726209580532143465792615532611716548649133442012414868891530198087687703303443925*t^47 + 54273887334014933163555752018813161981736077900906860808992473875832794843796756881526158763105992998400220411653169317035984853/1290154874625778012930714345653754426683100160108772596922798750031582099513667802857064538411452070916735079990550125*t^45 - 6337324987196839790549676660688430191049955204757099148246041376403938157939667642853526901805168010909079040241543818629576417928/946113574725570542815857186812753246234273450746433237743385750023160206310023055428513994835064852005605725326403425*t^43 + 25128289810794307376935429662546928856562270786960177357316736302975561765534252860474189530680779679315188643302724126790171709215176/31221747965943827912923287164820857125731023874632296845531729750764286808230760829140961829557140116184988935771313025*t^41 - 93336941376442000523112262838937597054902382383410385210592399869353138004978664663323931759466100129235184818887679756201971517158161/1248869918637753116516931486592834285029240954985291873821269190030571472329230433165638473182285604647399557430852521*t^39 + 3780429536935091471912084794679350662460681590702911031411675119279586733580363480135712689857274621134089399886544695281698073430361396/693816621465418398064961936996019047238467197214051041011816216683650817960683573980910262879047558137444198572695845*t^37 - 19675612583885186083146855202824090171091647337670888378128343488486281947418485898516603375736732432898573800221087929188251444272017010797/62443495931887655825846574329641714251462047749264593691063459501528573616461521658281923659114280232369977871542626050*t^35 + 1501065663988698894945515035526991613253772712131281254939770275011319649024028970165661388262454584910409935217283710902255988448727586133/103212389970062241034457147652300354134648012808701807753823900002526567961093424228565163072916165673338806399244010*t^33 - 101684363950728325139513121651230784204358988596737557177128569378769876730268106199691111228356293162253131924316406348842656960682688257222/189222714945114108563171437362550649246854690149286647548677150004632041262004611085702798967012970401121145065280685*t^31 + 601730183386478933035629519183261152951300531199524809439654084403969328081261112652223192780449659507264431082195666825050529052527588726594/37844542989022821712634287472510129849370938029857329509735430000926408252400922217140559793402594080224229013056137*t^29 - 14225346010251876965559858740649907233101297000491252616002929161428677630483452910616554677627444754804899444975819145177908601376909713917348/37844542989022821712634287472510129849370938029857329509735430000926408252400922217140559793402594080224229013056137*t^27 + 29717682302381490560743630364619496663146065275506930044067811115314968611736297301449882002093588257236575257955934222450578818000210360805844/4204949221002535745848254163612236649930104225539703278859492222325156472488991357460062199266954897802692112561793*t^25 - 19183232425702920412769802520718448978208371912172246223196396308909389932887797960228454694514990086240061205601351278645305249938973745830350/182823879174023293297750181026618984779569748936508838211282270535876368369086580759133139098563256426204004893991*t^23 + 20245279301030738131040344357715279603947975249740307275145339994889106990640528318965903289141957984874080192025417994395480201495617879226525/16620352652183935754340925547874453161779068085137167110116570048716033488098780069012103554414841493291273172181*t^21 - 3990700336751610178349853028161271515584063384962194934400052274915505837893705066779359633459358062918955239717274094346609972030875138749395025/365647758348046586595500362053237969559139497873017676422564541071752736738173161518266278197126512852408009787982*t^19 + 27135560299877185261490284835057347844610551043411824292449073654870838868656336850490179640345778403073825981635738038691349092062199720944271925/365647758348046586595500362053237969559139497873017676422564541071752736738173161518266278197126512852408009787982*t^17 - 68506612845678183544803107619820902745731888836270474373747324414924817225584755890940899333019988767707143286465920010328647769368226650610258865/182823879174023293297750181026618984779569748936508838211282270535876368369086580759133139098563256426204004893991*t^15 + 249676922209743617518631686833453433035074261154824953873003060030490099093112806822655335027954728651072866623311211147729787249383297616516681075/182823879174023293297750181026618984779569748936508838211282270535876368369086580759133139098563256426204004893991*t^13 - 57505511035068646366861992977632215176011798374521515540472931115934514329476426692148292911652071864043840225590259902079817176385051024392619300/16620352652183935754340925547874453161779068085137167110116570048716033488098780069012103554414841493291273172181*t^11 + 96195595793638055662088044207360958881829203396126558218658143487636891915698131594811228722679118464562188381033704780749953137515449816359260500/16620352652183935754340925547874453161779068085137167110116570048716033488098780069012103554414841493291273172181*t^9 - 98724767160899566735103082734342816657805176155820245672356273754525872350836173889783921616874767688785562093876933531237230665303793540356319625/16620352652183935754340925547874453161779068085137167110116570048716033488098780069012103554414841493291273172181*t^7 + 55623616037735957027352135700475755519563293971078623688630482045993697015772636420165581622219605435024247028913985729566308338824944094098261450/16620352652183935754340925547874453161779068085137167110116570048716033488098780069012103554414841493291273172181*t^5 - 28599230390192992312300186415823301038870396008838771089465037831926841345196879265270546102731887793373731462880112003127270458629143582999630875/33240705304367871508681851095748906323558136170274334220233140097432066976197560138024207108829682986582546344362*t^3 + 2261401261503784852686748288065936459450081809965977621022129425940392794138749914464118549708448634974341368003205127494969342536214366421290375/33240705304367871508681851095748906323558136170274334220233140097432066976197560138024207108829682986582546344362*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:
| (-11.761295484824087082 - 8.0344827469516025734e-773j)  +/-  (7.69e-246, 7.69e-246j)
| (6.6367905724765826016 + 2.503687708480283616e-765j)  +/-  (9.71e-242, 9.71e-242j)
| (-13.487781287282568426 + 7.6848395174270515576e-784j)  +/-  (1.55e-247, 1.55e-247j)
| (9.4027662330968962505 + 1.5288260596740093714e-777j)  +/-  (1.03e-243, 1.03e-243j)
| (13.487781287282568426 - 2.0332346364776647304e-782j)  +/-  (1.48e-247, 1.48e-247j)
| (-10.0928320945110984 + 4.9174816756618358811e-780j)  +/-  (3.31e-244, 3.31e-244j)
| (-10.857269988218551851 + 3.0785260960516069451e-780j)  +/-  (6.94e-245, 6.94e-245j)
| (8.1527603565456073362 + 8.4841177676826293681e-776j)  +/-  (4.92e-243, 4.92e-243j)
| (-8.1527603565456073362 + 3.8417013397745352405e-781j)  +/-  (4.92e-243, 4.92e-243j)
| (2.4609036013883145798 - 7.0065359465375401636e-785j)  +/-  (7.71e-248, 7.71e-248j)
| (6.0113763266093170797 - 1.0459441540398954064e-777j)  +/-  (3.45e-243, 3.45e-243j)
| (3.2609940129976570469 - 5.6456834881818111582e-787j)  +/-  (1.96e-246, 1.96e-246j)
| (11.761295484824087082 + 3.2515021122200529362e-786j)  +/-  (7.4e-246, 7.4e-246j)
| (-3.6693753049455151439 - 3.6435480134753054444e-786j)  +/-  (8.95e-246, 8.95e-246j)
| (-6.7179623569224259871 + 1.6385183397595544651e-780j)  +/-  (1.35e-241, 1.35e-241j)
| (10.857269988218551851 + 1.6347983160620620503e-783j)  +/-  (7.41e-245, 7.41e-245j)
| (-2.0872695419014224088 - 1.0797073218244703081e-790j)  +/-  (1.28e-248, 1.28e-248j)
| (-6.6367905724765826016 + 1.2362304504553837131e-782j)  +/-  (9.81e-242, 9.81e-242j)
| (-1.3556261799742658658 - 4.7155904574807082772e-792j)  +/-  (1.81e-250, 1.81e-250j)
| (5.0082624737480044992 - 1.5215780849120257392e-783j)  +/-  (3.24e-244, 3.24e-244j)
| (-4.5389269600723963503 - 2.3040793021800236703e-786j)  +/-  (1.07e-244, 1.07e-244j)
| (-6.0113763266093170797 + 1.0412942910235076774e-784j)  +/-  (3.77e-243, 3.77e-243j)
| (-8.7609232346863377922 - 4.5504937828440663926e-785j)  +/-  (2.56e-243, 2.56e-243j)
| (8.7609232346863377922 + 3.3074177889729547174e-782j)  +/-  (2.8e-243, 2.8e-243j)
| (7.5661396644993945836 - 1.6114028623437675783e-790j)  +/-  (9.53e-243, 9.53e-243j)
| (-6.9389405635821321151 - 2.8668756283725513382e-803j)  +/-  (4.75e-242, 4.75e-242j)
| (1.3556261799742658658 + 2.3920864164389556842e-811j)  +/-  (1.68e-250, 1.68e-250j)
| (2.8569700138728056542 + 1.3211790476453213981e-807j)  +/-  (4.06e-247, 4.06e-247j)
| (-3.2609940129976570469 + 6.1455262936661607159e-807j)  +/-  (2.01e-246, 2.01e-246j)
| (-2.4609036013883145798 - 3.2968525076164127192e-809j)  +/-  (6.87e-248, 6.87e-248j)
| (-1.7288283895133167871 + 4.0937821690642090393e-810j)  +/-  (1.7e-249, 1.7e-249j)
| (-2.8569700138728056542 + 8.7411758901766633654e-808j)  +/-  (4.19e-247, 4.19e-247j)
| (0.66248171638301031012 - 5.3607484110719784993e-813j)  +/-  (1.93e-252, 1.93e-252j)
| (-7.5661396644993945836 + 1.3479760203013158096e-804j)  +/-  (9.23e-243, 9.23e-243j)
| (5.4983291699947363701 + 2.8769429386833606601e-801j)  +/-  (9.72e-244, 9.72e-244j)
| (4.0925598234978037931 - 4.1152360617896521271e-809j)  +/-  (3.55e-245, 3.55e-245j)
| (10.0928320945110984 - 1.0300242094514537921e-812j)  +/-  (3.31e-244, 3.31e-244j)
| (2.0872695419014224088 + 6.007120023423336362e-830j)  +/-  (1.26e-248, 1.26e-248j)
| (3.6693753049455151439 - 4.5497980692624744484e-823j)  +/-  (8.29e-246, 8.29e-246j)
| (6.9389405635821321151 - 3.0436074327238601264e-831j)  +/-  (4.44e-242, 4.44e-242j)
| (-0.66248171638301031012 + 2.0536264057839379873e-869j)  +/-  (1.93e-252, 1.93e-252j)
| (-4.0925598234978037931 - 4.2339411453846781674e-860j)  +/-  (3.31e-245, 3.31e-245j)
| (1.7288283895133167871 - 2.8729570777573740531e-865j)  +/-  (1.66e-249, 1.66e-249j)
| (0.3676366580839030176 - 2.8580237502429572857e-869j)  +/-  (1.49e-253, 1.49e-253j)
| (-0.97927684786915201525 + 4.7205095610682419701e-868j)  +/-  (1.56e-251, 1.56e-251j)
| (-7.2540701746319059767e-886 - 1.0713932784735295623e-886j)  +/-  (3.89e-884, 3.89e-884j)
| (-5.0082624737480044992 + 2.6062739687457728678e-859j)  +/-  (3.57e-244, 3.57e-244j)
| (6.7179623569224259871 - 3.1398810928886568252e-873j)  +/-  (1.25e-241, 1.25e-241j)
| (0.97927684786915201525 - 1.385909065167192587e-897j)  +/-  (1.52e-251, 1.52e-251j)
| (4.5389269600723963503 - 2.1377786557611103332e-890j)  +/-  (1.07e-244, 1.07e-244j)
| (-5.4983291699947363701 - 4.5729951875392905999e-892j)  +/-  (9.91e-244, 9.91e-244j)
| (-0.3676366580839030176 + 7.0386852798350940113e-903j)  +/-  (1.49e-253, 1.49e-253j)
| (-9.4027662330968962505 - 5.8865324214282210016e-900j)  +/-  (1.02e-243, 1.02e-243j)
-------------------------------------------------
The weights are:
| (3.7546383737659892368e-31 + 6.6367003218250831439e-790j)  +/-  (2.6e-81, 2.1e-200j)
| (2.0241316990158214336e-10 + 5.2578904645183075016e-774j)  +/-  (2.33e-69, 1.88e-188j)
| (1.5440111084716206997e-39 - 3.0500886265770598763e-794j)  +/-  (1.23e-84, 9.87e-204j)
| (1.6748016754317815248e-20 + 5.8409586891183760276e-783j)  +/-  (1.6e-77, 1.29e-196j)
| (1.5440111084716206997e-39 + 8.9595403496277670867e-794j)  +/-  (7.96e-86, 6.41e-205j)
| (2.1838622048811742759e-23 + 1.8215994421968744232e-785j)  +/-  (4.37e-79, 3.52e-198j)
| (8.2352151912197738969e-27 - 1.8430479153125378167e-787j)  +/-  (2.58e-80, 2.07e-199j)
| (8.7551948258744416149e-16 + 1.1307751648366210067e-779j)  +/-  (7.84e-76, 6.31e-195j)
| (8.7551948258744416149e-16 - 1.1590757493370367185e-780j)  +/-  (5.13e-76, 4.13e-195j)
| (0.00747346416696310876 + 6.1043736012495629172e-771j)  +/-  (1.9e-54, 1.53e-173j)
| (3.0018569961484434466e-09 + 7.5525273014515874703e-775j)  +/-  (2.64e-70, 2.13e-189j)
| (0.00079337230202003917395 + 9.0522241154017948499e-772j)  +/-  (5.75e-60, 4.63e-179j)
| (3.7546383737659892368e-31 - 2.3827196138192403862e-789j)  +/-  (2.94e-84, 2.37e-203j)
| (0.00019669023039080363819 - 8.9811116909531247116e-773j)  +/-  (2.04e-64, 1.64e-183j)
| (-1.1444195078768980587e-10 + 3.4645097937115508333e-776j)  +/-  (1.74e-74, 1.4e-193j)
| (8.2352151912197738969e-27 + 7.6395093236410498265e-787j)  +/-  (1.34e-83, 1.08e-202j)
| (0.016310724138184862519 - 7.1216171360133456909e-771j)  +/-  (1.28e-57, 1.03e-176j)
| (2.0241316990158214336e-10 - 3.8179550792536394717e-776j)  +/-  (2.28e-74, 1.84e-193j)
| (0.060749995158456637497 - 2.8712943026999113163e-770j)  +/-  (2.47e-52, 1.99e-171j)
| (6.8459409303688327738e-07 + 6.9272074413921454773e-774j)  +/-  (1.45e-71, 1.17e-190j)
| (6.1436542154789987687e-06 - 4.8916785723499253107e-774j)  +/-  (2.22e-70, 1.79e-189j)
| (3.0018569961484434466e-09 + 3.7345001882924952417e-776j)  +/-  (3.9e-74, 3.14e-193j)
| (5.352544459061152108e-18 + 3.8308140507924145873e-782j)  +/-  (1.57e-80, 1.26e-199j)
| (5.352544459061152108e-18 - 2.7769347674241320106e-781j)  +/-  (2.06e-81, 1.65e-200j)
| (8.6083015792596419291e-14 - 5.1572101012489247324e-778j)  +/-  (4.9e-79, 3.95e-198j)
| (1.3196266713027581056e-11 - 3.7958805670501040099e-777j)  +/-  (3.2e-76, 2.57e-195j)
| (0.060749995158456637497 - 4.3453638214134850684e-770j)  +/-  (8.82e-60, 7.1e-179j)
| (0.0027094503498386385668 - 2.4157516705859350273e-771j)  +/-  (3.22e-67, 2.59e-186j)
| (0.00079337230202003917395 + 3.0874047379494710622e-772j)  +/-  (7.38e-69, 5.94e-188j)
| (0.00747346416696310876 + 2.8019379087657615777e-771j)  +/-  (2.04e-66, 1.64e-185j)
| (0.032461097542052436777 + 1.487825796908755762e-770j)  +/-  (1.31e-63, 1.06e-182j)
| (0.0027094503498386385668 - 9.618009371428020288e-772j)  +/-  (6.38e-68, 5.13e-187j)
| (0.088888303936965807354 - 1.2363505813971092074e-769j)  +/-  (1.62e-62, 1.31e-181j)
| (8.6083015792596419291e-14 + 3.3745490860433772165e-779j)  +/-  (2.34e-79, 1.89e-198j)
| (5.4390458483482717595e-08 - 1.9702834947304852323e-774j)  +/-  (1.28e-77, 1.03e-196j)
| (3.9960104294883245134e-05 + 9.4932356231367246242e-773j)  +/-  (3.06e-75, 2.46e-194j)
| (2.1838622048811742759e-23 - 8.8177966393427904825e-785j)  +/-  (1.39e-87, 1.12e-206j)
| (0.016310724138184862519 - 1.3656254271302277699e-770j)  +/-  (1.58e-70, 1.27e-189j)
| (0.00019669023039080363819 - 3.1192407703580502075e-772j)  +/-  (2.41e-74, 1.94e-193j)
| (1.3196266713027581056e-11 + 1.7055057262720824647e-775j)  +/-  (9.14e-81, 7.36e-200j)
| (0.088888303936965807354 - 1.0119283039968668567e-769j)  +/-  (1.37e-69, 1.11e-188j)
| (3.9960104294883245134e-05 + 2.2511131697899352751e-773j)  +/-  (1.84e-76, 1.48e-195j)
| (0.032461097542052436777 + 2.5359982890584838575e-770j)  +/-  (9.82e-72, 7.9e-191j)
| (0.12527950938315767265 + 1.275590115122204063e-769j)  +/-  (1.01e-69, 8.14e-189j)
| (0.088695626110698927293 + 5.9348813789955337261e-770j)  +/-  (2.59e-70, 2.08e-189j)
| (0.15278984167019547457 - 1.098708216508996169e-769j)  +/-  (4.53e-70, 3.64e-189j)
| (6.8459409303688327738e-07 + 9.6875058612649324717e-775j)  +/-  (6.7e-79, 5.39e-198j)
| (-1.1444195078768980587e-10 - 5.6999698395068068978e-774j)  +/-  (4.45e-80, 3.59e-199j)
| (0.088695626110698927293 + 7.9894559544038030149e-770j)  +/-  (2.36e-72, 1.9e-191j)
| (6.1436542154789987687e-06 - 2.6058899950133930224e-773j)  +/-  (8.71e-78, 7.01e-197j)
| (5.4390458483482717595e-08 - 1.848429812220365033e-775j)  +/-  (3e-80, 2.41e-199j)
| (0.12527950938315767265 + 1.1416880353169113409e-769j)  +/-  (3.89e-74, 3.12e-193j)
| (1.6748016754317815248e-20 - 1.0072566071844108954e-783j)  +/-  (1.24e-88, 1e-207j)
