Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 20 24
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P2 : 3/2*t^22 - 30461783/3830466*t^20 + 66155815/3643614*t^18 - 14341808855/614151382*t^16 + 39940250075/2149529837*t^14 - 670092247/70863621*t^12 + 2251326473/732257417*t^10 - 13150594545/21235465093*t^8 + 27599544115/382238371674*t^6 - 544763725/127412790558*t^4 + 4285838227/43957412742510*t^2 - 333527539/923105667592710
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^46 - 611464710537289982894552150300481150516323264482925704234208735183188016947092141616892141366015675/36712728616675335949789753139109488060403111865313510564913043944400695867132503513070741950187522*t^44 + 5803721115917221385689629537233759717780552770020440441795509982716679757305740246751787580856153994235/67294431554365890795964617503987691614718904049119664865485609550086475524453878939458669994693727826*t^42 - 5598957493848065014900705011784405406687919856030852739038695022084956226646741231146749895361752417205/20243040386272666336997486566240199916622759754613232520511931328074793450445475778536347884582666094*t^40 + 16077344926925166337633264257978803205715767461439552239416408868130743602332986709070235100875082344632445/26127536510866851420652371314995716492385637378665802189359207365674381485001895237543183165800965722402*t^38 - 113183230107826893648039135222342097557538113454727400407160744096594680856218957504147896428069686836513583/112277792033184577726587217272549160061873414681293582381300377598438558273386522777550435766550095942214*t^36 + 107951113875560516057134223691355253720909540791517388217362280839306122630467655050178712124891252941617900945/85689341567421391772572063391768828014840248433194868801195292941436893973693609550276230191928494650755418*t^34 - 135257708854211045206504332578982018582011763965050772309330243381120355139533670083805326164451214165481345199595/110167930141848102688936816167350789884412946068944202988736748291707366685512084011805139950089401289321215742*t^32 + 2139177199222870686017105985680058068152748620368626521628001020882273485793795243498285519889417886219433180543980505/2261653430000891258696735518959955755167903042696365551185242812627793197885267405077639754265378073981565623305287*t^30 - 306843703940045582747315120287509214701915531428355374629705019355694187672012641369950815267001361312000234770627065/528585667548101022147512899067269352740391132584208040698466710997300325942533761339984770153977251007185835331887*t^28 + 55432163999926655781107423738909343162662629611944223012785415489199791193227946191219637099889445859572599137325950905167/194684519898214404826483649097392548027855044594516629629739485327510677262878772211475519234204548412565916123591583585*t^26 - 638368122184156801883397223533149970919064903455870407952003868706875669365585530020783285143271550001706268679469702659945/5723724885007503501898619283463340912018938311078788911114340868628813911528635903017380265485613723329437934033592557399*t^24 + 1696759742463485298524212130529068533805872306468053876855438294657594584821144885601016370346450438787006516454517802588262225/48847678361741645429543864450986569847452290879373751805297450824976365889630248170413385438763115274796272610852513248226773*t^22 - 2319503796655913733723101271534909257272144496388689995220786669456641514643071344730048461356140974879444022862792178914593/271879471401159436528073457055583876701960802668128488712230709600981628328183199464267451421687098004431944030718997671021*t^20 + 3432700977022091578210981229005526529771345483132850269687364389885109946930320875409803227392891369263367341094291701698785/2103488541893180903664568325640569993430959894327099360036732332176015756012785806381437650473052810876394514342931192507373*t^18 - 1750260377213817476583438039358604379122411112801753964809930900022875691756341685776207079046138793809030683218549936620029/7327839168817421056556960245532181741821579239714666398036459693136054888593561011773243579752530380373322066305766834028953*t^16 + 42506710451282900221560334102733545454091043428027870396695671861170498120371115562212282795519045166324792494426460645055/1628408704181649123679324499007151498182573164381036977341435487363567753020791335949609684389451195638516014734614852006434*t^14 - 36811904342016975979584116567380366385694378884334726446585627568332378255268782103278730113086741929396358483061519069075/17876706543708433786325771148441146666861435068314900443561473097540705332612863127622638183572107081789862623295387221477226*t^12 + 274273944687289292330121443976979700286170186059737471248094025971122190552007676078305480002949108903828559042315905583/2453665604038412480476086236060549542510393048592241237351574738878136026044902782222715044804014697500569379667994324516482*t^10 - 2750985671947347262606961417081525463110606306072697467272917997197563087959972100961979459354568659444354668702918205/706988394383949358781245186661514274960621725865561034491131704422513770216327920301460267146919489110333550073828873165766*t^8 + 3914372705346251713488753926866494798975613112972560228538272624278085178925759718071844189706167118695647021279823561/50379809350451040670554445963788686061154953374341992159127787820341987755545341541481980335521392685044158302014273078708546*t^6 - 27354477052439709563420409712768278257035783197785279652730705742795271247856364985107703606560268599883748987607476755/37499371426519057939116025945713378658186336961635222830444116734274552886044249220709754029739756621901201829465957261585394406*t^4 + 62912747634570273692739690609352224435795696499289154318983961802024874958328480191568589122506112464370184032536625/30681303894424683768367657591947309811243366604974273224908822782588270543127112998762526024332528145191892405926692304933504514*t^2 - 206816191340520678508635062631779212285962476421606309684134604609496502651643636208010108314559669924153744831633/2421155068190469610416839066494972491626378712522969821878674493495552653729378699684955858007110373196664552902475936237143943170
-------------------------------------------------
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:
| (0.96888548864291551998 - 3.9325934471752763461e-856j)  +/-  (8.24e-240, 8.24e-240j)
| (-0.96888548864291551998 - 1.8807123578702417611e-851j)  +/-  (8.17e-240, 8.17e-240j)
| (-0.92419486526088066841 + 9.4476078208884140723e-863j)  +/-  (3.03e-240, 3.03e-240j)
| (0.99406617535715816159 + 3.7968246539321466712e-872j)  +/-  (7.46e-240, 7.46e-240j)
| (0.94888061826907397424 - 1.3421952264421983854e-876j)  +/-  (5.43e-240, 5.43e-240j)
| (0.92419486526088066841 + 2.8818526569970447564e-878j)  +/-  (3.05e-240, 3.05e-240j)
| (-0.99406617535715816159 - 1.5735188359952863954e-879j)  +/-  (7.55e-240, 7.55e-240j)
| (-0.94888061826907397424 - 6.4165259990589936162e-908j)  +/-  (5.81e-240, 5.81e-240j)
| (0.06741352924250103978 + 5.6666212663817417869e-936j)  +/-  (2.35e-254, 2.35e-254j)
| (0.99901200552661851907 - 5.2334279136574911632e-921j)  +/-  (3.07e-240, 3.07e-240j)
| (0.89487055542882490333 + 6.1267844185831977387e-926j)  +/-  (1.31e-240, 1.31e-240j)
| (-0.99901200552661851907 - 1.8604256834397384582e-925j)  +/-  (2.91e-240, 2.91e-240j)
| (-0.89487055542882490333 - 2.1756167750601933795e-941j)  +/-  (1.39e-240, 1.39e-240j)
| (-0.780839931409340531 - 6.0244583843824017811e-950j)  +/-  (4.15e-242, 4.15e-242j)
| (0.98403747204090030929 + 6.0366414425768193071e-952j)  +/-  (9.41e-240, 9.41e-240j)
| (0.780839931409340531 + 4.1517093985318202152e-959j)  +/-  (4.36e-242, 4.36e-242j)
| (0.82291735288005035859 - 9.1403380345589224363e-960j)  +/-  (1.66e-241, 1.66e-241j)
| (-0.98403747204090030929 + 3.2124837416166182657e-957j)  +/-  (9.05e-240, 9.05e-240j)
| (-0.82291735288005035859 - 1.9710306698134815854e-972j)  +/-  (1.68e-241, 1.68e-241j)
| (-0.86102168810005007167 - 2.9413029986638932926e-975j)  +/-  (5.06e-241, 5.06e-241j)
| (0.86102168810005007167 + 1.2589455806113545082e-978j)  +/-  (4.81e-241, 4.81e-241j)
| (0.73497729426405810948 - 1.2016489552443318447e-977j)  +/-  (1e-242, 1e-242j)
| (0.51926561395367323531 - 7.0086221861278125027e-983j)  +/-  (4.23e-246, 4.23e-246j)
| (-0.73497729426405810948 - 4.4324043547188627578e-978j)  +/-  (9.96e-243, 9.96e-243j)
| (-0.68553363455588642792 + 3.0671592373956314426e-981j)  +/-  (1.83e-243, 1.83e-243j)
| (-0.0065031748063020905837 - 1.0282932357226397208e-993j)  +/-  (8.07e-256, 8.07e-256j)
| (0.68553363455588642792 + 1.4144874425533991555e-980j)  +/-  (1.84e-243, 1.84e-243j)
| (0.26762420896476965748 + 1.2468809072438279689e-989j)  +/-  (1.42e-250, 1.42e-250j)
| (-0.20139298243596146919 - 1.1498278470302376708e-991j)  +/-  (8.32e-252, 8.32e-252j)
| (-0.63285971887272298318 - 7.5411891971529404023e-985j)  +/-  (2.91e-244, 2.91e-244j)
| (-0.26762420896476965748 - 2.2087831135817921733e-992j)  +/-  (1.65e-250, 1.65e-250j)
| (0.4588223560349795942 - 1.4022873636694731347e-986j)  +/-  (4.27e-247, 4.27e-247j)
| (0.63285971887272298318 - 1.0369146153658997741e-983j)  +/-  (2.62e-244, 2.62e-244j)
| (0.0065031748063020905837 + 1.3161685448966493918e-996j)  +/-  (8.07e-256, 8.07e-256j)
| (-0.57735026918962576451 + 3.5445804635392825749e-988j)  +/-  (3.86e-245, 3.86e-245j)
| (-0.39643773053455804602 - 5.4620223396861556397e-992j)  +/-  (2.92e-248, 2.92e-248j)
| (0.20139298243596146919 + 1.6301535874095980212e-993j)  +/-  (8.06e-252, 8.06e-252j)
| (0.57735026918962576451 + 1.0640551440572454877e-988j)  +/-  (3.77e-245, 3.77e-245j)
| (0.13431784608604247473 - 1.5336116536578096257e-996j)  +/-  (4.63e-253, 4.63e-253j)
| (-0.33263121197918282965 + 4.0091595228618069196e-993j)  +/-  (2.36e-249, 2.36e-249j)
| (-0.51926561395367323531 + 1.6161625890203959015e-991j)  +/-  (4.29e-246, 4.29e-246j)
| (-0.13431784608604247473 + 4.9898341632950884421e-998j)  +/-  (4.8e-253, 4.8e-253j)
| (0.33263121197918282965 + 2.8056177815776175831e-994j)  +/-  (2.23e-249, 2.23e-249j)
| (0.39643773053455804602 - 9.9450612198405237361e-993j)  +/-  (3.14e-248, 3.14e-248j)
| (-0.06741352924250103978 - 3.0541308385477414677e-999j)  +/-  (2.35e-254, 2.35e-254j)
| (-0.4588223560349795942 + 4.9155955265067907412e-993j)  +/-  (4.08e-247, 4.08e-247j)
-------------------------------------------------
The weights are:
| (0.017622393996969540937 + 1.7110789070072878174e-853j)  +/-  (6.28e-69, 2.64e-184j)
| (0.017622393996969540937 - 3.4888064023358513505e-852j)  +/-  (1.98e-69, 8.33e-185j)
| (0.027010768855305178983 - 1.28706448554843078e-851j)  +/-  (1.96e-69, 8.24e-185j)
| (0.0074183855204735864409 + 7.0882609442983523864e-854j)  +/-  (7.63e-70, 3.21e-185j)
| (0.022358239957962816975 - 2.3301406234903451005e-853j)  +/-  (1.06e-69, 4.45e-185j)
| (0.027010768855305178983 + 3.0411088216055070754e-853j)  +/-  (4.27e-70, 1.8e-185j)
| (0.0074183855204735864409 + 5.5346493622715069759e-852j)  +/-  (7.64e-72, 3.22e-187j)
| (0.022358239957962816975 + 2.2293200937920737663e-851j)  +/-  (2.4e-71, 1.01e-186j)
| (0.066359335552166308997 + 5.4322084497079406753e-851j)  +/-  (6.29e-74, 2.65e-189j)
| (0.0026579598649831917257 - 2.3841135797012308833e-854j)  +/-  (3.87e-71, 1.63e-186j)
| (0.031620521803917607338 - 3.8741873709024489386e-853j)  +/-  (1.32e-71, 5.54e-187j)
| (0.0026579598649831917257 - 1.5594589547724076349e-852j)  +/-  (2.58e-72, 1.09e-187j)
| (0.031620521803917607338 + 9.7503921829062750419e-852j)  +/-  (4.92e-73, 2.07e-188j)
| (0.043996013579439080883 - 7.2302684325219845856e-852j)  +/-  (1.2e-74, 5.05e-190j)
| (0.012630137110670662354 - 1.1814893694791144596e-853j)  +/-  (9.28e-72, 3.91e-187j)
| (0.043996013579439080883 + 7.7719699243665238895e-853j)  +/-  (3.36e-75, 1.42e-190j)
| (0.040130024113852322791 - 6.1649474585980116226e-853j)  +/-  (7.81e-75, 3.29e-190j)
| (0.012630137110670662354 - 1.5269239734835059357e-851j)  +/-  (6.78e-73, 2.85e-188j)
| (0.040130024113852322791 + 7.5657296672585734893e-852j)  +/-  (2.31e-75, 9.71e-191j)
| (0.036029159615539624609 - 8.2925460959206605771e-852j)  +/-  (7.99e-75, 3.36e-190j)
| (0.036029159615539624609 + 4.8897657170559478354e-853j)  +/-  (3.64e-75, 1.53e-190j)
| (0.047698270692378312899 - 9.8102511683493459431e-853j)  +/-  (3.31e-77, 1.39e-192j)
| (0.059311220924273843825 - 2.7111561554616675762e-852j)  +/-  (6.84e-80, 2.88e-195j)
| (0.047698270692378312899 + 7.1450357910997138397e-852j)  +/-  (7.63e-78, 3.21e-193j)
| (0.051128391524035011927 - 7.2754225017495973599e-852j)  +/-  (9.7e-79, 4.08e-194j)
| (0.034373483291464390479 + 3.0802543611928058045e-850j)  +/-  (2.71e-81, 1.14e-196j)
| (0.051128391524035011927 + 1.2462070398871321651e-852j)  +/-  (4.16e-79, 1.75e-194j)
| (0.065625939290629445763 - 9.6207718235397293542e-852j)  +/-  (7.98e-82, 3.36e-197j)
| (0.066777557127164693556 - 2.2063540690523362239e-851j)  +/-  (2.58e-82, 1.09e-197j)
| (0.054149490255303734186 + 7.6236406147945211918e-852j)  +/-  (4.11e-81, 1.73e-196j)
| (0.065625939290629445763 + 1.6963549071535954989e-851j)  +/-  (1.25e-82, 5.25e-198j)
| (0.061504153602782322973 + 3.5977736993045765318e-852j)  +/-  (2.22e-82, 9.35e-198j)
| (0.054149490255303734186 - 1.599495220397612373e-852j)  +/-  (1.53e-81, 6.43e-197j)
| (0.034373483291464390479 - 3.0391823225436428859e-850j)  +/-  (8.26e-82, 3.48e-197j)
| (0.056827795441800787782 - 8.1852433740924789985e-852j)  +/-  (5.45e-83, 2.29e-198j)
| (0.063169379058442314531 + 1.1627444197060930563e-851j)  +/-  (5.76e-84, 2.42e-199j)
| (0.066777557127164693556 + 1.4469983212485262715e-851j)  +/-  (1e-83, 4.22e-199j)
| (0.056827795441800787782 + 2.0728137474921287536e-852j)  +/-  (4.48e-83, 1.88e-198j)
| (0.067194693904348288889 - 2.4471851532801662847e-851j)  +/-  (1.09e-83, 4.58e-199j)
| (0.064406684916096931156 - 1.3819362102957212715e-851j)  +/-  (1.51e-84, 6.34e-200j)
| (0.059311220924273843825 + 8.9728157660359259939e-852j)  +/-  (7e-85, 2.95e-200j)
| (0.067194693904348288889 + 3.2348617027178083979e-851j)  +/-  (1.22e-84, 5.13e-200j)
| (0.064406684916096931156 + 6.7558982879816801515e-852j)  +/-  (2.49e-85, 1.05e-200j)
| (0.063169379058442314531 - 4.8753129407184213173e-852j)  +/-  (2.01e-85, 8.45e-201j)
| (0.066359335552166308997 - 6.2446305771665421674e-851j)  +/-  (5.48e-85, 2.36e-200j)
| (0.061504153602782322973 - 1.0069944588998836168e-851j)  +/-  (4.16e-86, 1.63e-201j)
