Starting with polynomial:
P : t
Extension levels are: 1 2 4 48
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : t^3 - 3/5*t
Solvable: 1
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P3 : t^7 - 77/45*t^5 + 749/891*t^3 - 31/297*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^55 - 474839113644184188621825289487691535573429410480327645265728043132751947353964525513/35296696756878098795825420638227434423521047925229355488666552898639306090889305105*t^53 + 30183139239392438277411077357007827756978203148660806287821806690016729049692496653758621/352931670872024109859458380961636116800786958204368325531176862433494421602802161744895*t^51 - 785640628973824815213272155236095584714712005587063612427527772269844467929205320481090563/2299403310226823746054047027477326215520278667089066363309182588581857595290983781065225*t^49 + 77920515124109603428071050082306280398132737383731875805869539982788570270893453382085578191194/80964289956396690922309049884504133374684532146873115718479628126555787787790829915087637475*t^47 - 46899378883769158498295422361636520440102497366170915949060252844877340501332715084805317118814946/23074822637573056912858079217083678011785091661858837979766694016068399519520386525799976680375*t^45 + 254121630764699922354949911607400877199372287323902350634914473431341783628830492742739057227402/76057363292372649048229713527867519230764257471305048099177832482522103679439870526294447325*t^43 - 147245235493931456503763973436962472579156247488026983608361545284538231258744308622464677743082/33606741919885589114334059465801927101965602138483625904287879469021394649054826511618476725*t^41 + 41812423358109263472591337855285985772159720051320597895493571531046778247772546797487649216040669/8973000092609452293527193877369114536224815770975128116444863818228712371297638678602133285575*t^39 - 18556954954629221293936783967473103929768174660977154176026329139814423247793830095860780648141129/4565210573432879237057695130591303886851222058917170445208790363660222083642658275078278338275*t^37 + 22293395585031116478830334587560846636639453726402469735700053569003046513268760622491957298572477/7608684289054798728429491884318839811418703431528617408681317272767036806071097125130463897125*t^35 - 1992560228187609819174418801553014695637095769419996758747521890284360473544816779039534368715607099/1136737432784786930027366087517234667825954292670375440856988800551395298827021910494491306230475*t^33 + 270354652116792123031213932990553480494408148813857071553114392038642328445988587103859432979648764/310019299850396435462008932959245818497987534364647847506451491059471445134642339225770356244675*t^31 - 324270664987336632508719089511904467373661363378625936181912205682998748063300135949100627980900492/899021484660715803392054825611517073219414351600263557785671898990035659027822667810437506929775*t^29 + 333735270145677557600671125381742154242851728534958515192653048399375774415417998960395816454780348/2697064453982147410176164476834551219658243054800790673357015696970106977083468003431312520789325*t^27 - 962916420418087628622089111818845432023287758249301619053876986899197533939972893000176058375332924/27470100920188538436979453004796355015037660743341386487895530246917756248072359294207812711743125*t^25 + 653296398193156247338795172166394661502435716070202813789063669378191595527243110972820340324581251/80212694686950532235980002774005356643909969370556848544654948320999848244371289139086813118289925*t^23 - 2388441899390520165580053514675002667707330065768360692335760458415409174326092467684429237753178421/1553209451665496669660340053714830996832074861448055340001045817488451606913734962420499199472341275*t^21 + 120645978546809248588458663014778862811270058034722215798124780572004985839718561841692921939856717/517736483888498889886780017904943665610691620482685113333681939162817202304578320806833066490780425*t^19 - 35826517675922202968761448446332952430946062360086946442346902564610371290451134140648288045863901/1284753497056645393422750414801156503552456984160737133087284811996620464978027684965104276106751425*t^17 + 1342434663622077048243162175836500681184704013657576966523045194626757986886777650015993478604039046/520325166307941384336213917994468383938745078585098538900350348858631288316101212410867231823234327125*t^15 - 2074935849144459860389404974476300542331603112919250321846315198642893240296127287349984317002286/11562781473509808540804753733210408531972112857446634197785563307969584184802249164685938484960762825*t^13 + 940308487406916776714837785796576086963966720075845197768946004771087640811295935243838906101058/104065033261588276867242783598893676787749015717019707780070069771726257663220242482173446364646865425*t^11 - 523312349806566287946233946585109459466220737595981068018782239622932776364345039845318174018806/1674500989754647727772906608818561890130143252901135297915672940872322509671816629031336364231135925475*t^9 + 16310562012328497610288323206446139576819423207065928987669965787140916835859780104411788045830483/2372023679820222653486309595091982837474355147915174879236323813686804408422887800391167478620305768208975*t^7 - 53247726615340387266997725770438813149535908913467009630186914986355026618282873959224810480541/624216757847427014075344630287363904598514512609256547167453635180738002216549421155570389110606781107625*t^5 + 37679601440216012641908220469817910998283880247038840872741718742364017354487271405562729030641/78276781434067347565048216638035433636653719881200771014798685851664545477955297412908526794470090350896175*t^3 - 250529212125800956619989303817271189760375193968256532155817725397359473132090875909223501/330281778202815812510751968936858369774910210469201565463285594310820866995591972206365091959789410763275*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:
| (-0.98665391451426154956 - 2.810577750352300957e-912j)  +/-  (1.63e-236, 1.63e-236j)
| (0.98665391451426154956 + 4.5234064828879436945e-912j)  +/-  (1.67e-236, 1.67e-236j)
| (-0.89649714092533581661 - 6.5752373309035054516e-928j)  +/-  (3.64e-237, 3.64e-237j)
| (0.99896672095990331616 - 1.2647122741621226158e-924j)  +/-  (3.76e-237, 3.76e-237j)
| (0.92098382515801065045 + 3.2859379897283916361e-931j)  +/-  (6.7e-237, 6.7e-237j)
| (0.94235998510772295663 - 1.9268050162191465876e-943j)  +/-  (1.1e-236, 1.1e-236j)
| (0.97528003238311993722 + 1.1396374019714538784e-966j)  +/-  (1.81e-236, 1.81e-236j)
| (-0.92098382515801065045 - 2.0717264482476855804e-983j)  +/-  (6.8e-237, 6.8e-237j)
| (6.0614148984032207078e-1002 + 1.5297233279474602117e-1001j)  +/-  (9.05e-1000, 9.05e-1000j)
| (0.9945606278002295985 - 8.9081371510423642394e-991j)  +/-  (1.2e-236, 1.2e-236j)
| (0.83911234808857255807 + 1.3605168834332690994e-1003j)  +/-  (6.86e-238, 6.86e-238j)
| (-0.99896672095990331616 + 2.4337386134239546204e-1001j)  +/-  (3.74e-237, 3.74e-237j)
| (-0.74289300837461692886 + 3.69383754139706416e-1009j)  +/-  (3.08e-239, 3.08e-239j)
| (-0.8071760988284091133 - 1.0116605929806403668e-1007j)  +/-  (2.73e-238, 2.73e-238j)
| (0.96049126870802028342 - 3.2387887230212119189e-1004j)  +/-  (1.63e-236, 1.63e-236j)
| (0.8071760988284091133 + 8.7595296998119582385e-1016j)  +/-  (2.55e-238, 2.55e-238j)
| (0.89649714092533581661 - 9.1222337032136942916e-1014j)  +/-  (3.59e-237, 3.59e-237j)
| (-0.83911234808857255807 - 3.5132532726878890769e-1017j)  +/-  (6.86e-238, 6.86e-238j)
| (-0.77459666924148337704 + 2.4636519469680050444e-1019j)  +/-  (9.03e-239, 9.03e-239j)
| (-0.9945606278002295985 - 1.3451310840034908589e-1014j)  +/-  (1.14e-236, 1.14e-236j)
| (-0.96049126870802028342 - 1.7793136379043234736e-1015j)  +/-  (1.45e-236, 1.45e-236j)
| (0.77459666924148337704 + 2.9999314401973526871e-1022j)  +/-  (9.05e-239, 9.05e-239j)
| (-0.94235998510772295663 + 5.5426524546456218917e-1018j)  +/-  (1.22e-236, 1.22e-236j)
| (-0.67242224729723229726 - 1.9380199010676802257e-1025j)  +/-  (1.12e-240, 1.12e-240j)
| (-0.71005241704422017889 + 8.0719649658385112005e-1024j)  +/-  (7.17e-240, 7.17e-240j)
| (0.86909747750776410279 - 5.820824911000908354e-1022j)  +/-  (1.62e-237, 1.62e-237j)
| (0.74289300837461692886 + 8.5878286045225123918e-1029j)  +/-  (2.94e-239, 2.94e-239j)
| (0.71005241704422017889 + 8.5920429595404131461e-1030j)  +/-  (6.92e-240, 6.92e-240j)
| (-0.049533121846925956131 - 1.9516118045943591528e-1042j)  +/-  (1.46e-254, 1.46e-254j)
| (-0.63022206698533544489 - 2.8958075826994408042e-1030j)  +/-  (1.33e-241, 1.33e-241j)
| (-0.86909747750776410279 - 2.9491120864827559391e-1025j)  +/-  (1.46e-237, 1.46e-237j)
| (0.67242224729723229726 - 2.6399215317071077219e-1031j)  +/-  (1.06e-240, 1.06e-240j)
| (0.63022206698533544489 + 2.5374917030916918002e-1033j)  +/-  (1.35e-241, 1.35e-241j)
| (-0.97528003238311993722 + 1.9343089463356573263e-1037j)  +/-  (1.75e-236, 1.75e-236j)
| (-0.53657499352412296393 + 9.6888532159903714012e-1046j)  +/-  (1.36e-243, 1.36e-243j)
| (-0.58469104119450947156 + 1.7541543923983124394e-1047j)  +/-  (1.53e-242, 1.53e-242j)
| (0.21372528681388302214 - 7.8062617699491119215e-1056j)  +/-  (8.85e-251, 8.85e-251j)
| (0.58469104119450947156 - 2.7390040205366442449e-1047j)  +/-  (1.47e-242, 1.47e-242j)
| (0.27002159285246639447 - 6.8732527567326810234e-1055j)  +/-  (1.84e-249, 1.84e-249j)
| (-0.27002159285246639447 - 8.614083281335327941e-1055j)  +/-  (1.66e-249, 1.66e-249j)
| (-0.48631750354619633507 + 1.1084131696272295293e-1049j)  +/-  (1.12e-244, 1.12e-244j)
| (-0.21372528681388302214 + 1.7587874153394130818e-1056j)  +/-  (9.71e-251, 9.71e-251j)
| (0.434243749346802558 + 2.8718309985591551266e-1050j)  +/-  (8.47e-246, 8.47e-246j)
| (0.53657499352412296393 - 1.2705652152203771279e-1049j)  +/-  (1.51e-243, 1.51e-243j)
| (0.049533121846925956131 - 7.0235217561920719293e-1062j)  +/-  (1.46e-254, 1.46e-254j)
| (-0.38064000825613705824 + 9.7264507200695686515e-1055j)  +/-  (5.13e-247, 5.13e-247j)
| (-0.32579293603171046543 + 3.2021371683633489095e-1057j)  +/-  (2.69e-248, 2.69e-248j)
| (0.10225086942592806394 + 1.1039780522798176497e-1060j)  +/-  (2.35e-253, 2.35e-253j)
| (0.48631750354619633507 + 1.4204226308268840644e-1053j)  +/-  (1.15e-244, 1.15e-244j)
| (0.15748196067160482019 + 4.6144032394012209411e-1060j)  +/-  (4.69e-252, 4.69e-252j)
| (-0.15748196067160482019 - 3.812651471113017732e-1060j)  +/-  (4.85e-252, 4.85e-252j)
| (-0.434243749346802558 + 4.699828328699971057e-1055j)  +/-  (7.42e-246, 7.42e-246j)
| (-0.10225086942592806394 - 1.6971449460417546822e-1061j)  +/-  (2.38e-253, 2.38e-253j)
| (0.32579293603171046543 - 1.0649088504470910249e-1056j)  +/-  (2.69e-248, 2.69e-248j)
| (0.38064000825613705824 + 3.1770961856522314879e-1056j)  +/-  (4.86e-247, 4.86e-247j)
-------------------------------------------------
The weights are:
| (0.0096474814543814148977 - 1.1794247564204819966e-912j)  +/-  (4.72e-46, 8.16e-159j)
| (0.0096474814543814148977 - 1.8763411867863014316e-912j)  +/-  (1.96e-46, 3.4e-159j)
| (0.025983610379168538016 + 2.5650945855016459957e-912j)  +/-  (8.19e-47, 1.42e-159j)
| (0.0026511683097546702811 + 4.8349269912282143319e-913j)  +/-  (9.09e-47, 1.57e-159j)
| (0.022957801452241373332 - 3.7328136842107332097e-912j)  +/-  (2.12e-47, 3.67e-160j)
| (0.019772518264465307785 + 3.8100048869714427435e-912j)  +/-  (2.09e-47, 3.61e-160j)
| (0.013091600034806328255 + 6.4846980844777603471e-912j)  +/-  (2.21e-47, 3.83e-160j)
| (0.022957801452241373332 - 2.396589527380108107e-912j)  +/-  (2.45e-50, 4.23e-163j)
| (0.048709591285374252492 + 8.1635061552339321353e-912j)  +/-  (2.78e-51, 4.82e-164j)
| (0.0061602551893151194599 - 2.6964198959104151501e-912j)  +/-  (3.35e-47, 5.8e-160j)
| (0.031107509551345270332 + 5.3777670405906164824e-912j)  +/-  (3.3e-50, 5.71e-163j)
| (0.0026511683097546702811 + 2.9856604186092079626e-913j)  +/-  (8.33e-53, 1.44e-165j)
| (0.031486540008112702226 - 7.3025240804770849601e-912j)  +/-  (1.7e-52, 2.94e-165j)
| (0.032551948253083088531 - 4.6920423559711412989e-912j)  +/-  (1.55e-52, 2.67e-165j)
| (0.016473947718604246065 - 4.3592373784914067837e-912j)  +/-  (4.49e-48, 7.76e-161j)
| (0.032551948253083088531 - 6.9084765028851768873e-912j)  +/-  (3.09e-51, 5.35e-164j)
| (0.025983610379168538016 + 3.9470016747325814882e-912j)  +/-  (1.27e-49, 2.2e-162j)
| (0.031107509551345270332 + 3.5954758518687665874e-912j)  +/-  (8.17e-53, 1.41e-165j)
| (0.032268905542861532611 + 6.2328881350152736164e-912j)  +/-  (7.38e-53, 1.28e-165j)
| (0.0061602551893151194599 - 1.6687731686821305655e-912j)  +/-  (8.34e-54, 1.44e-166j)
| (0.016473947718604246065 - 2.7442347714552044018e-912j)  +/-  (2.5e-54, 4.32e-167j)
| (0.032268905542861532611 + 9.03166949176576038e-912j)  +/-  (7.25e-56, 1.25e-168j)
| (0.019772518264465307785 + 2.4202668348203218828e-912j)  +/-  (3.61e-54, 6.24e-167j)
| (0.040152078378836624841 - 5.3687338015785044411e-912j)  +/-  (5.96e-57, 1.03e-169j)
| (0.034966474339073395544 + 6.7977702405695855669e-912j)  +/-  (4.86e-56, 8.4e-169j)
| (0.028763717647483354159 - 4.4579992786352039891e-912j)  +/-  (1.94e-55, 3.36e-168j)
| (0.031486540008112702226 - 1.0418762209773890653e-911j)  +/-  (7.09e-58, 1.23e-170j)
| (0.034966474339073395544 + 9.5444695103543751401e-912j)  +/-  (6.68e-59, 1.16e-171j)
| (0.050978523586183076162 - 7.3528679969213657849e-912j)  +/-  (1.22e-62, 2.1e-175j)
| (0.044029532436293616557 + 4.1956891309847134108e-912j)  +/-  (4.03e-60, 6.97e-173j)
| (0.028763717647483354159 - 2.9367480182243829403e-912j)  +/-  (1.47e-57, 2.55e-170j)
| (0.040152078378836624841 - 7.4012919066799289603e-912j)  +/-  (2.05e-60, 3.54e-173j)
| (0.044029532436293616557 + 5.6669746414870921431e-912j)  +/-  (1.64e-61, 2.83e-174j)
| (0.013091600034806328255 + 4.0522057811949198945e-912j)  +/-  (8.68e-59, 1.5e-171j)
| (0.049247036534649652257 + 3.0422430176216112122e-912j)  +/-  (3.53e-63, 6.11e-176j)
| (0.046913984487643166094 - 3.4666134733054011917e-912j)  +/-  (3.62e-62, 6.27e-175j)
| (0.056388939605747759791 + 4.1674922271181810881e-912j)  +/-  (8.95e-67, 1.55e-179j)
| (0.046913984487643166094 - 4.5803057433464172895e-912j)  +/-  (1.22e-64, 2.11e-177j)
| (0.056110658653857366708 - 3.6875534630182712898e-912j)  +/-  (7.51e-67, 1.3e-179j)
| (0.056110658653857366708 - 3.2444871630306734621e-912j)  +/-  (2.13e-67, 3.68e-180j)
| (0.051214916398111582984 - 2.8159455583625198017e-912j)  +/-  (8.61e-66, 1.49e-178j)
| (0.056388939605747759791 + 3.7661299542597190254e-912j)  +/-  (1.13e-67, 1.96e-180j)
| (0.052885466692156046358 + 3.3585723454014878631e-912j)  +/-  (4.83e-68, 8.35e-181j)
| (0.049247036534649652257 + 3.9274695479457929045e-912j)  +/-  (6.55e-67, 1.13e-179j)
| (0.050978523586183076162 - 7.5273351543552503674e-912j)  +/-  (2.19e-68, 3.78e-181j)
| (0.054274726063310766821 - 2.7702631914745522259e-912j)  +/-  (3e-68, 5.18e-181j)
| (0.055366964902350441904 + 2.9320031448826622423e-912j)  +/-  (2.69e-68, 4.65e-181j)
| (0.054255738040637461724 + 6.1393148288352119313e-912j)  +/-  (1.59e-69, 2.74e-182j)
| (0.051214916398111582984 - 3.5485947345577430709e-912j)  +/-  (1.3e-69, 2.25e-182j)
| (0.055943160432838970059 - 4.9535863269636303012e-912j)  +/-  (7.41e-70, 1.28e-182j)
| (0.055943160432838970059 - 4.5975494708791848511e-912j)  +/-  (2.63e-70, 4.55e-183j)
| (0.052885466692156046358 + 2.7324843953049417418e-912j)  +/-  (4.05e-70, 7e-183j)
| (0.054255738040637461724 + 5.8491533026037827754e-912j)  +/-  (2.27e-70, 3.93e-183j)
| (0.055366964902350441904 + 3.4220060157364138777e-912j)  +/-  (6.35e-72, 1.1e-184j)
| (0.054274726063310766821 - 3.3188947664852292931e-912j)  +/-  (5.59e-72, 9.64e-185j)
