Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 6 48
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P2 : 3/2*t^8 - 161/52*t^6 + 105/52*t^4 - 245/572*t^2 + 25/1716
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^56 - 2976930421163427840748804646515588513877183024307742174159341992991906915211106709291035/137252649418551080131850141969220036795982588885563267817015507855081233962891238552892*t^54 + 48454852357605181053647321562055381495892047853077203490048301953090466936916869071461283965/326161498798457601686153393030138791968747530610755413051880229581583324036306845698511108*t^52 - 176943907845092678665877316330648752407427326176674125845698704677802097124005861115050793025/275982806675617970657514409487040516281247910516793041813129425030570504953798100206432476*t^50 + 5417373817841704531472290922647736800899639643284645558747552079097548881252336890733806911525/2769344715262235498666782522783751387511832481392647419573126299444690239363974040002477604*t^48 - 1141428392721102464348869890889849273033857941329912870371793954647307335807029866537943510189255/254318156351581959960899528342307835753169949541224788030798765165670720314924949340227526634*t^46 + 2044971592887214719614097876584509786597005927181820761794369791839383551542439194211598281365575/254318156351581959960899528342307835753169949541224788030798765165670720314924949340227526634*t^44 - 80600968936660940561953785341131136907844597751614138796375323056595087392112599754614075136925/6989716770762294882646287248308672018586066266460723561100177478126256583708296704911115954*t^42 + 129804254209849075135057430350488678552165164873580794720699195049346861078945158630199975850167650/9642314285266585790610553259041813049639478414582568152537694831075170957225595304424884458543*t^40 - 1113584047805748529185153426191147624671189378333238640819453775252615601675765093105186174418230025/86039112083917227054678782926834639519859961237813685053413276954209217772166850408714353630076*t^38 + 46770626990226236859503694011916688183577660935025103042930944058846982893317560321028467886751835/4528374320206169844983093838254454711571576907253351844916488260747853566956150021511281770004*t^36 - 29032014381968579342644057725928489078145759460182032095094427861403871912318533895454122560189075/4223090658169798844197716725563143157982481834854249473349084557776088157947870244780184122588*t^34 + 12942822483714228172880668014548908199212225389477832867884022367907371984997625321659862557848897125/3382695617194008874202371097176077669543967949718253828152616730778646614516244066068927482192988*t^32 - 11517652772850644220620530740760572150133315682831856207766492823667662759273076343483443096047584925/6465313397378871799886789919602664578080003258735694816711049719310800384196369706922063010320469*t^30 + 7362417651704236756120905603557099068478212755215124422854778449209186826366746575114180948540168725/10626894434772168590618516764404379708798166275852923664249196665074074194713573196435115062940541*t^28 - 264823263870618520166183519359529810225536475603754631444525912169710699071944830381318726640528715/1180766048308018732290946307156042189866462919539213740472132962786008243857063688492790562548949*t^26 + 2391297461198350444242348327828395890965970632186298374735098619677833692509304337902125496235284725/39782733012224015749494960194949729166270058366013509102061095207713200831491838119987866645879974*t^24 - 24921457325347090028020812134163788674961107599146449794302150146445169099411518348155918548786790325/1883049362578603412142761449227620513870116095991306097497558506498424839357280337679425687904985436*t^22 + 405605813137957392521542225224587886222457594060503106700159667510097843983994722920121769617817975/171186305688963946558432859020692773988192372362846008863414409681674985396116394334493244354998676*t^20 - 11708947010213614688643329894202925133458994160437529209321451084903272915065505367528870596697306925/34408447443481753258245004663159247571626666844932047781546296346016672064619395261233142115354733876*t^18 + 5744298244814147059876507302825863463189249553988834803467388426575243064373499830572768621107267465/149103272255087597452395020207023406143715556328038873720033950832738912280017379465343615833203846796*t^16 - 751540203254302357094533600242957314563546375785241009024884418902940322600134039419690522632288875/223654908382631396178592530310535109215573334492058310580050926249108368420026069198015423749805770194*t^14 + 11305040929092704877811991878352171928766247206804648144639713379667865285029476223719729903045925/51612671165222629887367506994738871357440000267398071672319444519025008096929092891849713173032100814*t^12 - 633865862843539802161170329494420292554352119858863116493663229184776352056515763138566649500283175/61918001174545414988211885891355066005142186987455219982892560274657001380282601772589039236580843609862*t^10 + 946664276797973189985237102395978637178260013220386450172123454964666670996158594728004117616925/2926472692329260907403049333173498144521645653635943233022285187110654294092958790246745635559791115889*t^8 - 163713850067109025900901499781756935441710454117012866457453896615892717361316709539146121195325683/25881724490959983465072568302586417590149434160756281952849090194806626576958127540942218400890792628922316*t^6 + 30220705817137423575602331507598863032405900095518422857613925036235312282858561557505711507175485/457243799340293041216282040012360044092640003506694314500333926774917069526260253223312525082404003110960916*t^4 - 1642560086120482054429993759895672270994246059295484033967180634285502649742353904356754760387955/5944169391423809535811666520160680573204320045587026088504341048073921903841383291903062826071252040442491908*t^2 + 118788953458557267363663266215721828819619550838057661107778703317855044984714623779758342275/614914074974876848532241364154553162745274487474519940190104246352474679707729306058937533731508831769912956
-------------------------------------------------
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:
| (-0.99018208009175982642 + 2.7750667843887144767e-822j)  +/-  (2.31e-234, 2.31e-234j)
| (0.99593968684358491332 + 2.5125169832472323573e-829j)  +/-  (1.36e-234, 1.36e-234j)
| (-0.94431043828562031503 + 1.0648129466720184547e-841j)  +/-  (6.26e-235, 6.26e-235j)
| (-0.98219129046748981137 - 1.4435150707900748555e-841j)  +/-  (2.39e-234, 2.39e-234j)
| (0.92578466680595349254 + 5.3297703696057265513e-842j)  +/-  (2.41e-235, 2.41e-235j)
| (0.94431043828562031503 - 2.8590696171726679041e-843j)  +/-  (6.21e-235, 6.21e-235j)
| (-0.99593968684358491332 + 1.1027015971925558176e-850j)  +/-  (1.39e-234, 1.39e-234j)
| (-0.87911721019119865021 + 9.4502889307477799123e-856j)  +/-  (2.37e-236, 2.37e-236j)
| (-0.90403717337664272286 - 3.9419709440039374473e-856j)  +/-  (8.23e-236, 8.23e-236j)
| (0.99922279410980347815 - 3.3573643538620327645e-851j)  +/-  (4.89e-235, 4.89e-235j)
| (0.90403717337664272286 + 6.9658812084776719903e-864j)  +/-  (7.79e-236, 7.79e-236j)
| (-0.95965708885402777501 - 5.1554024497535724687e-864j)  +/-  (1.28e-234, 1.28e-234j)
| (-0.82007894759491204921 + 9.1180912569936770459e-870j)  +/-  (1.52e-237, 1.52e-237j)
| (-0.85110112875893547946 + 5.0619320902633569288e-868j)  +/-  (5.88e-237, 5.88e-237j)
| (-0.97211099537097474203 + 4.074603170273225835e-866j)  +/-  (1.99e-234, 1.99e-234j)
| (0.87911721019119865021 + 2.4778343815757717325e-865j)  +/-  (2.48e-236, 2.48e-236j)
| (0.85110112875893547946 - 3.316724278269521927e-868j)  +/-  (6.03e-237, 6.03e-237j)
| (-0.99922279410980347815 + 2.8638244987007516365e-870j)  +/-  (4.54e-235, 4.54e-235j)
| (-0.78615285813171374537 - 3.7322996866198762793e-875j)  +/-  (2.9e-238, 2.9e-238j)
| (0.42615068161290895879 - 4.9092966904165197079e-882j)  +/-  (5.46e-246, 5.46e-246j)
| (0.82007894759491204921 + 2.879884603902635769e-871j)  +/-  (1.39e-237, 1.39e-237j)
| (0.78615285813171374537 - 1.9202457286818323595e-874j)  +/-  (3.01e-238, 3.01e-238j)
| (-0.92578466680595349254 + 2.1562726578260695461e-873j)  +/-  (2.38e-235, 2.38e-235j)
| (-0.71005729500031750961 + 1.9178246726817652747e-877j)  +/-  (6.83e-240, 6.83e-240j)
| (-0.7494370558439245515 - 3.6055516750436365136e-876j)  +/-  (4.67e-239, 4.67e-239j)
| (0.95965708885402777501 + 3.9006637859163936307e-870j)  +/-  (1.23e-234, 1.23e-234j)
| (0.7494370558439245515 - 4.151300831184755683e-887j)  +/-  (4.61e-239, 4.61e-239j)
| (0.97211099537097474203 + 5.0679330840899671977e-881j)  +/-  (2.07e-234, 2.07e-234j)
| (0.99018208009175982642 - 7.7926574740967974677e-901j)  +/-  (2.11e-234, 2.11e-234j)
| (-0.6681502035187630713 - 8.1169781443511076611e-938j)  +/-  (8.98e-241, 8.98e-241j)
| (0.98219129046748981137 - 1.5651520941422880321e-940j)  +/-  (2.38e-234, 2.38e-234j)
| (0.26128546511002611754 + 1.5991166746288284854e-964j)  +/-  (9.13e-250, 9.13e-250j)
| (0.6238625111029594555 - 9.5396228501207526264e-956j)  +/-  (1.23e-241, 1.23e-241j)
| (0.088036913256778013792 + 7.0290431047438495703e-968j)  +/-  (1.16e-253, 1.16e-253j)
| (-0.6238625111029594555 - 1.6397979257953022851e-955j)  +/-  (1.14e-241, 1.14e-241j)
| (-0.57735026918962576451 + 2.3983969607146271569e-956j)  +/-  (1.14e-242, 1.14e-242j)
| (0.029380644943578281183 - 3.9803869587187848454e-970j)  +/-  (5.07e-255, 5.07e-255j)
| (0.57735026918962576451 + 2.6430451827171197137e-956j)  +/-  (1.2e-242, 1.2e-242j)
| (0.71005729500031750961 - 3.4758567622686953184e-954j)  +/-  (7.25e-240, 7.25e-240j)
| (-0.37246081948834618654 - 3.2462714129435138424e-964j)  +/-  (3.39e-247, 3.39e-247j)
| (-0.52877808774857929558 - 3.5003409733474358598e-960j)  +/-  (1.02e-243, 1.02e-243j)
| (-0.2041968861768067152 + 3.3420449774467781084e-968j)  +/-  (5.9e-251, 5.9e-251j)
| (0.6681502035187630713 + 3.695739172313754258e-961j)  +/-  (9.73e-241, 9.73e-241j)
| (0.52877808774857929558 - 7.421253291426835114e-967j)  +/-  (1.02e-243, 1.02e-243j)
| (-0.029380644943578281183 + 4.8455861473772176927e-978j)  +/-  (5.07e-255, 5.07e-255j)
| (-0.47831839037972760515 + 1.091465405838470692e-965j)  +/-  (7.37e-245, 7.37e-245j)
| (-0.31744028791076342062 + 1.2093489176482511784e-969j)  +/-  (1.86e-248, 1.86e-248j)
| (0.14637849892255915068 - 1.7166548349252994013e-974j)  +/-  (2.35e-252, 2.35e-252j)
| (0.47831839037972760515 - 1.0603542901437853597e-969j)  +/-  (7.56e-245, 7.56e-245j)
| (0.2041968861768067152 + 1.3291966419036054376e-974j)  +/-  (4.93e-251, 4.93e-251j)
| (-0.26128546511002611754 - 3.2700971195359779116e-971j)  +/-  (9.01e-250, 9.01e-250j)
| (-0.42615068161290895879 - 9.2791106415840157661e-968j)  +/-  (5.43e-246, 5.43e-246j)
| (-0.088036913256778013792 - 2.4492851805395313556e-975j)  +/-  (1.2e-253, 1.2e-253j)
| (0.37246081948834618654 + 2.0334148506965629062e-970j)  +/-  (3.33e-247, 3.33e-247j)
| (0.31744028791076342062 - 3.0637165670149437822e-971j)  +/-  (1.88e-248, 1.88e-248j)
| (-0.14637849892255915068 + 2.7477593906890360396e-974j)  +/-  (2.35e-252, 2.35e-252j)
-------------------------------------------------
The weights are:
| (0.0069181481230572646473 + 1.0292111175093955672e-822j)  +/-  (5.93e-42, 5.67e-153j)
| (0.0045538599782466378996 + 4.9014008841742815196e-825j)  +/-  (1.45e-43, 1.39e-154j)
| (0.016914849323472348382 + 7.2472974891261818892e-823j)  +/-  (1.5e-42, 1.44e-153j)
| (0.0090312958081915717443 - 3.6532571546204098782e-822j)  +/-  (3.73e-42, 3.57e-153j)
| (0.02014084107804970904 + 1.4647118921780529712e-824j)  +/-  (4.62e-44, 4.42e-155j)
| (0.016914849323472348382 - 1.7185074031017984505e-824j)  +/-  (4.85e-44, 4.64e-155j)
| (0.0045538599782466378996 + 1.6908196217118578733e-822j)  +/-  (3.46e-43, 3.3e-154j)
| (0.026481998970754530938 - 1.7293755992799480947e-823j)  +/-  (1.06e-44, 1.01e-155j)
| (0.023345061606546895878 + 2.6947747522717372387e-823j)  +/-  (1.71e-44, 1.64e-155j)
| (0.0019906969857880390572 - 1.3803263844780243519e-825j)  +/-  (1.15e-46, 1.1e-157j)
| (0.023345061606546895878 - 1.2255210589679092051e-824j)  +/-  (4e-47, 3.83e-158j)
| (0.013824525823054226286 - 1.2097336049433253833e-822j)  +/-  (4.76e-44, 4.55e-155j)
| (0.032492176622044320195 - 7.9533238218029631054e-824j)  +/-  (1.47e-46, 1.41e-157j)
| (0.029535152716499903221 + 1.1523590699580763909e-823j)  +/-  (6.38e-46, 6.11e-157j)
| (0.011180626572429115148 + 1.9926390287958202727e-822j)  +/-  (2.92e-44, 2.8e-155j)
| (0.026481998970754530938 + 1.0275107740214003487e-824j)  +/-  (1.92e-49, 1.84e-160j)
| (0.029535152716499903221 - 8.7043077843863931239e-825j)  +/-  (3.61e-50, 3.46e-161j)
| (0.0019906969857880390572 - 3.0371854275830119963e-823j)  +/-  (3.23e-45, 3.09e-156j)
| (0.035340961863522887767 + 5.6678904633064010409e-824j)  +/-  (1.15e-48, 1.1e-159j)
| (0.052960254907709909063 - 3.5425535414792701852e-825j)  +/-  (1.56e-53, 1.49e-164j)
| (0.032492176622044320195 + 7.4734176635385184488e-825j)  +/-  (3.26e-51, 3.12e-162j)
| (0.035340961863522887767 - 6.5101131618439807654e-825j)  +/-  (5.75e-52, 5.5e-163j)
| (0.02014084107804970904 - 4.3578586977105776478e-823j)  +/-  (1.77e-46, 1.69e-157j)
| (0.040667065473975035755 + 3.1319919183357514045e-824j)  +/-  (1.17e-51, 1.12e-162j)
| (0.038069671858624852522 - 4.1581652112852328238e-824j)  +/-  (1.38e-50, 1.32e-161j)
| (0.013824525823054226286 + 1.8938420722592224955e-824j)  +/-  (3.41e-53, 3.26e-164j)
| (0.038069671858624852522 + 5.7544594092764094024e-825j)  +/-  (1.56e-55, 1.5e-166j)
| (0.011180626572429115148 - 1.8350368086124905928e-824j)  +/-  (7.94e-54, 7.6e-165j)
| (0.0069181481230572646473 - 9.6939478885758824296e-825j)  +/-  (1.8e-54, 1.73e-165j)
| (0.043122649490217993934 - 2.416337685076635913e-824j)  +/-  (3.11e-58, 2.98e-169j)
| (0.0090312958081915717443 + 1.4800401180999277019e-824j)  +/-  (2.3e-54, 2.2e-165j)
| (0.056655432692352090402 + 3.4531103457929928689e-825j)  +/-  (8.08e-63, 7.73e-174j)
| (0.045426714051025039237 - 4.3248868093555750287e-825j)  +/-  (3.57e-61, 3.41e-172j)
| (0.058533800467910497393 - 3.7257297275121394235e-825j)  +/-  (1.65e-63, 1.58e-174j)
| (0.045426714051025039237 + 1.9055939476160331028e-824j)  +/-  (3.19e-60, 3.05e-171j)
| (0.047570322382439184232 - 1.5334817531383817486e-824j)  +/-  (2.29e-61, 2.19e-172j)
| (0.058743779921392988214 + 3.9084957816933709165e-825j)  +/-  (1.18e-64, 1.13e-175j)
| (0.047570322382439184232 + 4.0386393959688593239e-825j)  +/-  (8.09e-63, 7.74e-174j)
| (0.040667065473975035755 - 5.1601437983193526822e-825j)  +/-  (2.29e-61, 2.19e-172j)
| (0.054387543169658482607 - 7.6601935058403819271e-825j)  +/-  (3.06e-65, 2.93e-176j)
| (0.049545291038529497115 + 1.2573266637771415018e-824j)  +/-  (2.36e-63, 2.25e-174j)
| (0.057487721359663110683 + 5.3218640487874664113e-825j)  +/-  (2.88e-66, 2.76e-177j)
| (0.043122649490217993934 + 4.692288281823998145e-825j)  +/-  (8.87e-63, 8.49e-174j)
| (0.049545291038529497115 - 3.8192926553722455684e-825j)  +/-  (1.7e-64, 1.63e-175j)
| (0.058743779921392988214 - 4.147534047461636703e-825j)  +/-  (8.45e-67, 8.08e-178j)
| (0.05134417416707975062 - 1.0490014555579274276e-824j)  +/-  (2.16e-65, 2.07e-176j)
| (0.055620777991108612365 + 6.6927278970315804477e-825j)  +/-  (1.17e-66, 1.12e-177j)
| (0.058114605556655505654 + 3.5919673561231544093e-825j)  +/-  (1.53e-67, 1.47e-178j)
| (0.05134417416707975062 + 3.6564210174009236937e-825j)  +/-  (6.72e-67, 6.43e-178j)
| (0.057487721359663110683 - 3.5021597372759579462e-825j)  +/-  (8.4e-68, 8.03e-179j)
| (0.056655432692352090402 - 5.928764120552111095e-825j)  +/-  (3.61e-68, 3.44e-179j)
| (0.052960254907709909063 + 8.8956676638218699977e-825j)  +/-  (1.43e-67, 1.37e-178j)
| (0.058533800467910497393 + 4.4528894813551674714e-825j)  +/-  (6.24e-69, 6.03e-180j)
| (0.054387543169658482607 + 3.4725630801280127112e-825j)  +/-  (2.62e-69, 2.56e-180j)
| (0.055620777991108612365 - 3.4432548122576747652e-825j)  +/-  (2.09e-69, 2.06e-180j)
| (0.058114605556655505654 - 4.8381979842961225808e-825j)  +/-  (1.71e-69, 1.55e-180j)
