Starting with polynomial:
P : 64*t^6 - 480*t^4 + 720*t^2 - 120
Extension levels are: 6 44
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P1 : 64*t^6 - 480*t^4 + 720*t^2 - 120
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 64*t^50 - 361666934392008231162093603961435390514828608/10283796262563126106561632595159527911147*t^48 + 1185334114974870045756556672883219397130434004024/133689351413320639385301223737073862844911*t^46 - 3460311038853437559096889970137899879569111129099180/2540097676853092148320723251004403394053309*t^44 + 363044732953483589671469108018977095872669922584069830/2540097676853092148320723251004403394053309*t^42 - 27620965516647967658771148153929696016983129359985783805/2540097676853092148320723251004403394053309*t^40 + 243033971583649335721651675243508877354044070047360875215/390784257977398792049342038616062060623586*t^38 - 1125320657397994934447253074161189753108226478183972502995/41135185050252504426246530380638111644588*t^36 + 77275683253277674347754373243734564608959365136122836486225/82270370100505008852493060761276223289176*t^34 - 4180573004581893996440079315963961989130139966859880756455825/164540740201010017704986121522552446578352*t^32 + 89553727629345549566981456876066296772859972679497520159822575/164540740201010017704986121522552446578352*t^30 - 3044371152392251160574408502621661566391562923499712243438093425/329081480402020035409972243045104893156704*t^28 + 6311674854109002093840310078435222026191601739555872891331526325/50627920061849236216918806622323829716416*t^26 - 134409007435010528837492151395489656906260411855779409313528111875/101255840123698472433837613244647659432832*t^24 + 2248012864469671204005828133917522838220235231095132053870871945625/202511680247396944867675226489295318865664*t^22 - 380524233050354946543944155782354295277567364989623923696327985801875/5265303686432320566559555888721678290507264*t^20 + 952828636054181356808150429538724115390613544487110921851082418926875/2632651843216160283279777944360839145253632*t^18 - 28897829495887660775820151991764808629334664045803356367822182967836875/21061214745729282266238223554886713162029056*t^16 + 324734879624759312968613877930689988086689246857847835099916874504959375/84244858982917129064952894219546852648116224*t^14 - 101056829246688293283558015039078676287157822026585893032890846113353125/12960747535833404471531214495314900407402496*t^12 + 282840025339085177346743262196640573889117645943509535340666997587128125/25921495071666808943062428990629800814804992*t^10 - 516906107792559986213377237959640538088629134834152397991756657023621875/51842990143333617886124857981259601629609984*t^8 + 564524036859985806619198623084241954382865335848226076810412839474103125/103685980286667235772249715962519203259219968*t^6 - 317497322877416021493557276788038777134390548449147437488603855263421875/207371960573334471544499431925038406518439936*t^4 + 68529262256641426691379188887060772100110756054251100895191535012703125/414743921146668943088998863850076813036879872*t^2 - 2351031588067984580369362913622700342502865269030033732515346147015625/829487842293337886177997727700153626073759744
-------------------------------------------------
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:
| (-6.7151762477676059997 - 5.7195595944524830896e-951j)  +/-  (6.16e-244, 6.16e-244j)
| (-7.6660942987872169573 - 1.8176263311400135e-953j)  +/-  (6.96e-245, 6.96e-245j)
| (-8.88456845366957291 + 4.693095285588534327e-957j)  +/-  (8.61e-247, 8.61e-247j)
| (-5.4809874074574699278 + 2.7492188670438038448e-953j)  +/-  (1.45e-243, 1.45e-243j)
| (6.2850417248842027299 + 1.0913850872249730723e-955j)  +/-  (1.06e-243, 1.06e-243j)
| (-8.2186394033927601416 - 6.2085856836749548728e-967j)  +/-  (1.21e-245, 1.21e-245j)
| (3.3281058043010761753 - 2.2388688034230168024e-965j)  +/-  (3.97e-245, 3.97e-245j)
| (8.2186394033927601416 + 9.2533597462541753638e-966j)  +/-  (1.25e-245, 1.25e-245j)
| (-7.1719302144763079233 + 1.4104987023320645838e-969j)  +/-  (2.68e-244, 2.68e-244j)
| (4.3681482368439567949 - 3.5760106165433103151e-967j)  +/-  (5.26e-244, 5.26e-244j)
| (1.3358490740136969497 - 8.1930227230916200237e-978j)  +/-  (1.37e-249, 1.37e-249j)
| (-2.3506049736744922228 - 1.9062449667474633453e-974j)  +/-  (1.09e-246, 1.09e-246j)
| (8.88456845366957291 - 1.095885272286726129e-973j)  +/-  (8.47e-247, 8.47e-247j)
| (-4.0147256787568971698 - 2.7258286617686135161e-971j)  +/-  (2.47e-244, 2.47e-244j)
| (-5.0998384443369738593 - 8.2579770094319110622e-970j)  +/-  (1.31e-243, 1.31e-243j)
| (5.0998384443369738593 + 2.9663694548516384592e-976j)  +/-  (1.27e-243, 1.27e-243j)
| (6.7151762477676059997 + 3.5194981402359557735e-989j)  +/-  (5.89e-244, 5.89e-244j)
| (-4.3681482368439567949 - 1.224210488843509303e-995j)  +/-  (5.11e-244, 5.11e-244j)
| (-1.6268774144223775272 - 1.1193004904556725269e-1001j)  +/-  (2.07e-248, 2.07e-248j)
| (-2.9941243672520366602 + 7.7411218503371150509e-999j)  +/-  (1.24e-245, 1.24e-245j)
| (2.9941243672520366602 - 6.0718351665726299183e-998j)  +/-  (1.26e-245, 1.26e-245j)
| (4.0147256787568971698 + 2.7858034636322582109e-996j)  +/-  (2.66e-244, 2.66e-244j)
| (5.875062628151950898 - 1.7219350687558412674e-1005j)  +/-  (1.48e-243, 1.48e-243j)
| (-4.7294379396073098413 + 9.8895091935220326935e-1010j)  +/-  (8.88e-244, 8.88e-244j)
| (-6.2850417248842027299 + 1.1836042373875613693e-1011j)  +/-  (9.92e-244, 9.92e-244j)
| (7.6660942987872169573 + 6.4872351044503571366e-1016j)  +/-  (7.38e-245, 7.38e-245j)
| (1.8575156390822063419 + 5.5938739823293729312e-1027j)  +/-  (1.35e-247, 1.35e-247j)
| (2.6670312274025084987 + 4.7486881430631154118e-1025j)  +/-  (3.78e-246, 3.78e-246j)
| (-3.3281058043010761753 - 4.7680696427946515223e-1024j)  +/-  (3.57e-245, 3.57e-245j)
| (-1.0335501532241633918 + 3.7187097648191541336e-1029j)  +/-  (1.04e-250, 1.04e-250j)
| (-0.14462873763160085273 + 1.4236255972128005257e-1032j)  +/-  (2.91e-254, 2.91e-254j)
| (3.6682472498177987429 - 9.906697321929349345e-1022j)  +/-  (1.07e-244, 1.07e-244j)
| (1.6268774144223775272 + 6.2988040281318662346e-1030j)  +/-  (1.83e-248, 1.83e-248j)
| (4.7294379396073098413 + 6.5503927069972608046e-1024j)  +/-  (9.11e-244, 9.11e-244j)
| (-2.0644603800567334888 + 2.5012027506972419663e-1035j)  +/-  (4.21e-247, 4.21e-247j)
| (-1.8575156390822063419 - 1.1630419044114915314e-1036j)  +/-  (1.33e-247, 1.33e-247j)
| (1.0335501532241633918 + 1.9001323515646270168e-1039j)  +/-  (1.12e-250, 1.12e-250j)
| (0.73248269202500827087 - 4.8201962912871542628e-1041j)  +/-  (6.76e-252, 6.76e-252j)
| (-1.3358490740136969497 + 5.0417417610872310506e-1038j)  +/-  (1.44e-249, 1.44e-249j)
| (-2.6670312274025084987 + 1.0694192726319247901e-1034j)  +/-  (4.34e-246, 4.34e-246j)
| (-0.43607741192761650868 - 2.8516436471153990993e-1041j)  +/-  (4.16e-253, 4.16e-253j)
| (-3.6682472498177987429 - 2.1585409148001454056e-1032j)  +/-  (1.05e-244, 1.05e-244j)
| (2.3506049736744922228 - 4.2674360813712798047e-1036j)  +/-  (1.15e-246, 1.15e-246j)
| (0.14462873763160085273 + 2.8256008438573296511e-1043j)  +/-  (2.91e-254, 2.91e-254j)
| (-5.875062628151950898 - 2.0004840967193256869e-1033j)  +/-  (1.31e-243, 1.31e-243j)
| (-0.73248269202500827087 + 4.382173043965146201e-1052j)  +/-  (7.04e-252, 7.04e-252j)
| (5.4809874074574699278 - 5.2123850367078770205e-1046j)  +/-  (1.46e-243, 1.46e-243j)
| (7.1719302144763079233 - 6.4500324954311214392e-1078j)  +/-  (2.63e-244, 2.63e-244j)
| (0.43607741192761650868 - 6.1331385413739267517e-1088j)  +/-  (4.11e-253, 4.11e-253j)
| (2.0644603800567334888 + 1.4501702970210813921e-1084j)  +/-  (4.2e-247, 4.2e-247j)
-------------------------------------------------
The weights are:
| (6.5021331183287754157e-21 - 1.3543078022078186124e-970j)  +/-  (4.13e-81, 3.61e-202j)
| (8.7714201647827364852e-27 + 8.7126950986691650619e-974j)  +/-  (3.79e-84, 3.31e-205j)
| (2.2687044447003512647e-35 + 1.6052230385480819221e-978j)  +/-  (5.53e-88, 4.83e-209j)
| (1.9616248423856651879e-14 + 3.3737823530431145641e-966j)  +/-  (9.92e-79, 8.67e-200j)
| (1.6537185828575344832e-18 - 3.2905996971377726495e-970j)  +/-  (1.94e-84, 1.7e-205j)
| (1.5508870538932460682e-30 - 6.9184723674285746573e-976j)  +/-  (4.48e-86, 3.91e-207j)
| (2.9429854381374346202e-06 - 5.0481344410833784851e-963j)  +/-  (1.64e-72, 1.43e-193j)
| (1.5508870538932460682e-30 - 1.1804380795452199964e-976j)  +/-  (2.39e-90, 2.08e-211j)
| (1.2239705811867524647e-23 - 6.2672286230456081695e-972j)  +/-  (7.97e-84, 6.97e-205j)
| (1.0414958309917377063e-09 + 3.2156905543674486092e-965j)  +/-  (1.95e-78, 1.7e-199j)
| (0.028453302069352038501 + 5.3494786424906627366e-960j)  +/-  (1.7e-58, 1.48e-179j)
| (0.00069134551778413865217 - 1.0292864991729453879e-960j)  +/-  (3.4e-68, 2.97e-189j)
| (2.2687044447003512647e-35 + 3.3874834027481832088e-979j)  +/-  (3.27e-92, 2.85e-213j)
| (1.9738030479770587481e-08 + 1.1744460556875309641e-963j)  +/-  (7.86e-77, 6.87e-198j)
| (1.07326880311692897e-12 - 1.3944488020527711657e-965j)  +/-  (6.4e-80, 5.6e-201j)
| (1.07326880311692897e-12 + 5.7446288619706604576e-967j)  +/-  (1.82e-82, 1.59e-203j)
| (6.5021331183287754157e-21 + 1.6078217146482815118e-971j)  +/-  (3.82e-87, 3.34e-208j)
| (1.0414958309917377063e-09 - 2.6211568875051721666e-964j)  +/-  (1.6e-78, 1.39e-199j)
| (0.010937144823513650447 + 8.4543875848369773171e-960j)  +/-  (4.41e-67, 3.86e-188j)
| (2.3857022099754340344e-05 - 7.4409342979939058555e-962j)  +/-  (1.88e-74, 1.65e-195j)
| (2.3857022099754340344e-05 + 2.2722684579138624489e-962j)  +/-  (4.34e-76, 3.79e-197j)
| (1.9738030479770587481e-08 - 1.9400650740791706926e-964j)  +/-  (9.3e-80, 8.12e-201j)
| (2.316257000470181315e-16 + 4.9864407942269022759e-969j)  +/-  (1.62e-85, 1.42e-206j)
| (3.9840371523075322625e-11 + 5.6968185256220490583e-965j)  +/-  (8.41e-81, 7.35e-202j)
| (1.6537185828575344832e-18 - 2.275012927020259864e-969j)  +/-  (2.51e-85, 2.19e-206j)
| (8.7714201647827364852e-27 + 1.1471765515573160512e-974j)  +/-  (2.79e-91, 2.43e-212j)
| (0.0033659108289750805932 + 3.6716040706111483482e-960j)  +/-  (3e-74, 2.62e-195j)
| (0.00014836577910296507644 - 9.7947237002884115452e-962j)  +/-  (2.47e-77, 2.16e-198j)
| (2.9429854381374346202e-06 + 1.970288751339674346e-962j)  +/-  (1.98e-79, 1.73e-200j)
| (0.058661696802104975079 + 9.8856996827172484581e-960j)  +/-  (2.91e-71, 2.54e-192j)
| (0.16003853890054324364 - 1.3831874342765803353e-959j)  +/-  (2.82e-71, 2.46e-192j)
| (2.7741957673009694755e-07 + 1.0398147182938095321e-963j)  +/-  (3.67e-80, 3.21e-201j)
| (0.010937144823513650447 - 4.6690207454112201576e-960j)  +/-  (1.44e-74, 1.26e-195j)
| (3.9840371523075322625e-11 - 4.6480766922946755067e-966j)  +/-  (2.6e-83, 2.27e-204j)
| (0.0020035791532031195833 + 3.7647306944906852909e-960j)  +/-  (5.11e-77, 4.46e-198j)
| (0.0033659108289750805932 - 7.2789577072720131525e-960j)  +/-  (1.78e-76, 1.56e-197j)
| (0.058661696802104975079 - 6.8249863157522764911e-960j)  +/-  (3.96e-75, 3.46e-196j)
| (0.098655360293697799866 + 8.9279240593161949129e-960j)  +/-  (6.82e-75, 5.96e-196j)
| (0.028453302069352038501 - 8.6687270186035587162e-960j)  +/-  (4.45e-76, 3.89e-197j)
| (0.00014836577910296507644 + 2.7420728090573338611e-961j)  +/-  (3.33e-79, 2.91e-200j)
| (0.13701765758414856607 + 1.3150476989848357853e-959j)  +/-  (2.19e-76, 1.91e-197j)
| (2.7741957673009694755e-07 - 4.9614228650459555824e-963j)  +/-  (6.4e-82, 5.59e-203j)
| (0.00069134551778413865217 + 4.2330564741983654602e-961j)  +/-  (1.64e-80, 1.44e-201j)
| (0.16003853890054324364 + 1.3140768596159210294e-959j)  +/-  (3.44e-77, 3e-198j)
| (2.316257000470181315e-16 + 1.061985614205513514e-967j)  +/-  (6.46e-88, 5.65e-209j)
| (0.098655360293697799866 - 1.159098725834922587e-959j)  +/-  (2.1e-77, 1.84e-198j)
| (1.9616248423856651879e-14 - 5.9349339035556389455e-968j)  +/-  (2.37e-88, 2.07e-209j)
| (1.2239705811867524647e-23 - 5.4766696370665672051e-973j)  +/-  (2.01e-93, 1.76e-214j)
| (0.13701765758414856607 - 1.1264215536170674545e-959j)  +/-  (9.73e-80, 7.59e-201j)
| (0.0020035791532031195833 - 1.7464199285565901632e-960j)  +/-  (7.99e-81, 7.11e-202j)
