Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 7 46
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 46 Kronrod extension for:
P2 : 3/2*t^9 - 151/50*t^7 + 1281/650*t^5 - 651/1430*t^3 + 56/2145*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^55 - 1890910177113072367994621685885991139733434213774890709316941315348398427674268569672205696148594497/92718420867004995722685612627912441943424758433028818731071019677729960534351916804347306025214850*t^53 + 281778513355359762365474737759833911604829355061170189269778690230182004683256180538758078650357969018838/2149722947011944328328327271584463922679274736648989676689247126738007999969216367067194463847618904675*t^51 - 6230350189986290835765368600891427412039419240737346872952496609833689230667418002208628650433675916210443/11762842997239715888852949737336528233327108430792164025781675303740792492139250582875366630386714724555*t^49 + 78328322787436056414957726922106941577136234893440049045395510953769141129785505272477367496923568517021420742/51882539648539461152619260448609329886282067542958294899429889286142424027828480249468134959027116731519375*t^47 - 1507375119061285223523677209165777524460955966557558510165767257081913595825016029571390199250522850714743832576/466942856836855150373573344037483968976538607886624654094869003575281816250456322245213214631244050583674375*t^45 + 65933057960848377452128748489255946776400362133967916707663792888327512028671715405578567616751677219336826393/12263145735109327181528188833307659791303034146517415158047064740360936588395822604419740990315500318359125*t^43 - 5899155497833166612961350306233501345016541462675987314161476203290416760624298325874103993179055829885080524313/825219977638210577898445682709654472297684663664428010269557356552581074326440843063269887616596716545190875*t^41 + 221574177151220923878850685759537914154415688505808006939922086957858396265634266264763045415218870375105429615671/28717655221809728110865909758295975635959426295522094757380596008029821386560141338601792089057565735772642450*t^39 - 6624962300772168852248732962247274953270640143836472384881395127257444839399142695362559141349352831838109804173/968881755121785698747162947310930352090398997824632076834702969231775350423756455418414038092360517401236250*t^37 + 6502978572245440071616688423003275979111674371499494347848709928324452211007668318380418339935336394301785907169/1297051381856584080580879429464632568121018013216846167375489458810279904599544932253683309059127789424235625*t^35 - 663502218096577043447033597445321349080869778049391206794785614504928830622232277062567540624694759847017937376346/217126401322792175089239216492379491903458415412500048418656935404840856029963821659266585936497991949617043625*t^33 + 22015609549301696117831727786607016574084004832543219162543775507485125831818906638209678502940015238056712577104/14187746653846635096815465759220827014369904729187348076984200080217061725696560720497982042169843973548177375*t^31 - 92793963365595664957872461528449301206405348875687578979972194260148516564967214099362823133010153584695498412/141333874712648472228813068865801341905600583509145996169191265166913258570157309859366870918167028088985675*t^29 + 3636792189780408794178751866327361921563966879159861869008362886284873012509643642993085695523869178265242746018362/15741060296121223594484055544928624454736264988331135323343677157964964173251270385586985248510852753410779553125*t^27 - 2866544076463614895666445312877375689721219962609902574329778814261509480238485068597799893785369436714545281833546/42559163022846271199901335362214429081323975709191588096447719723386754986938619931401849005233046333295811384375*t^25 + 300678423003152444062282883377662289441470014888042016955387504494721447355942623905289582474522551863378452107709/18595080459212832339649198835182919783224629386785247722140234463756674486600873939258654026901823321009246820250*t^23 - 208984236588142491715343138454892496436244374561355555898822123931785891253738449191593213672668404046045375488259/65928012537209132840574432233830351958705504189511332833042649462410027725221280330098864277197373592669147817250*t^21 + 73877466421684169665468520255863141506945405774741485140433241789587757965158774333295678386862647252346446281412/147239227999767063343949565322221119374442292689908643327128583799382395252994192737220796885740801023627763458525*t^19 - 3023513519237923021782968847255586605014916061587419710342628833221128366171948381707730752761071437010373395596069/47852749099924295586783608729721863796693745124220309081316789734799278457223112639596758987865760332679023124020625*t^17 + 4184145826080702674201781228134787696085169457773596346363369312956098069295629197304746894565335807876614444538/673982381689074585729346601827068504178785142594652240581926615983088428974973417459109281519236061023648213014375*t^15 - 493268137329395404130257106528524695775633414192504533379154395321131934163313036917429636653784081614643001676/1063394424442762124150746860660485862148749891649340201807039771884428410160513614213261310841461340726200513867125*t^13 + 67454555694632493521303971779579455971300591179909896525914672966163050507071371098949183132966350518623598111383/2649569907855808304874372427973369043143089056954906036671678865469886202577630498306288239958905714420181603436157375*t^11 - 88616453669058045867280513642650096244979079287863207464223711756647064557069487602620364444365505764844484751551/90615290848668644026703537036689221275493645747857786454171417199070108128154963042075057806594575433170210837516582225*t^9 + 12332338356513849571882190006238549597759021704863105343119184550747865552742002972012115181467921305520356310317/503418282492603577926130761314940118197186920821432146967618984439278378489749794678194765592192085739834504652869901250*t^7 - 152478145851904812415462586801839962804461775620752200704413854026010702916615931707990570903407184040567339933/425969315955279950552879874958795484628388933002750278203369909910158627952865210881549417039547149472167657783197608750*t^5 + 4152853463545501720401516495117868365742355041412972417878405378551298138699379950411117928862382120203668861/1661280332225591807156231512339302390050716838710726084993142648649618649016174322438042726454233882941453865354470674125*t^3 - 2921273733394831723708093550207050235718861350639502923114392281284340151020730893498172618323193166556688/553760110741863935718743837446434130016905612903575361664380882883206216338724774146014242151411294313817955118156891375*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:
| (-0.9879055305434337762 + 4.6059934886572701294e-850j)  +/-  (3.64e-236, 3.64e-236j)
| (-0.99906727175437545512 + 4.2583149710749565412e-884j)  +/-  (8.52e-237, 8.52e-237j)
| (-0.94712756612829870844 + 1.6811222333372234769e-898j)  +/-  (1.88e-236, 1.88e-236j)
| (0.99906727175437545512 - 1.8452868178237741955e-908j)  +/-  (8.07e-237, 8.07e-237j)
| (0.94712756612829870844 - 7.0185466415850342456e-908j)  +/-  (2.06e-236, 2.06e-236j)
| (0.92713939652541071478 - 8.5911729370861430422e-908j)  +/-  (1.12e-236, 1.12e-236j)
| (-0.99508290628120056183 + 1.8377563439367080789e-905j)  +/-  (2.43e-236, 2.43e-236j)
| (-0.8777772225794059094 - 9.0421595455974841309e-920j)  +/-  (2.2e-237, 2.2e-237j)
| (-0.74406485301822495592 - 9.9356585103222754345e-922j)  +/-  (1.54e-239, 1.54e-239j)
| (0.99508290628120056183 + 1.6208674843871742257e-917j)  +/-  (2.48e-236, 2.48e-236j)
| (0.8777772225794059094 - 1.8837810032727523732e-920j)  +/-  (2.02e-237, 2.02e-237j)
| (-0.059103046634552776294 - 8.0984824091205494507e-939j)  +/-  (2.1e-254, 2.1e-254j)
| (-0.84854472834515751128 + 1.5723597911130329311e-919j)  +/-  (7.74e-238, 7.74e-238j)
| (-0.90400283342309525552 + 1.8548444215061134042e-919j)  +/-  (4.99e-237, 4.99e-237j)
| (0.90400283342309525552 - 1.0179894977039861975e-918j)  +/-  (5.17e-237, 5.17e-237j)
| (0.84854472834515751128 + 7.3025473653717087871e-921j)  +/-  (7.1e-238, 7.1e-238j)
| (0.6626528689105408911 - 1.9911669851640996841e-923j)  +/-  (6.91e-241, 6.91e-241j)
| (0.96392874096524810675 + 9.6639066696019143245e-918j)  +/-  (2.91e-236, 2.91e-236j)
| (-0.78152450684568851664 + 4.5079114000350339513e-922j)  +/-  (6.7e-239, 6.7e-239j)
| (-0.97752291183323911041 - 2.7958982889051852453e-917j)  +/-  (3.79e-236, 3.79e-236j)
| (0.11795604714665053388 + 1.1372275751222249028e-946j)  +/-  (4.55e-253, 4.55e-253j)
| (0.74406485301822495592 - 2.5766191851960641024e-933j)  +/-  (1.51e-239, 1.51e-239j)
| (-0.92713939652541071478 + 2.0502949792443066847e-928j)  +/-  (1.15e-236, 1.15e-236j)
| (-0.70430054623785234203 - 2.1746828458516396375e-936j)  +/-  (3.38e-240, 3.38e-240j)
| (-0.81641357233552832956 + 5.6235669509210501116e-935j)  +/-  (2.31e-238, 2.31e-238j)
| (0.97752291183323911041 - 1.2590260471595008178e-930j)  +/-  (3.62e-236, 3.62e-236j)
| (0.78152450684568851664 + 6.163285344617289472e-938j)  +/-  (7.36e-239, 7.36e-239j)
| (0.81641357233552832956 - 1.949619104122942673e-937j)  +/-  (2.33e-238, 2.33e-238j)
| (-0.17630301016452293915 + 6.1471406064368475905e-951j)  +/-  (1.17e-251, 1.17e-251j)
| (-0.6626528689105408911 + 6.4665149188152251447e-941j)  +/-  (7.38e-241, 7.38e-241j)
| (0.9879055305434337762 - 2.2621501190654313251e-937j)  +/-  (3.62e-236, 3.62e-236j)
| (0.70430054623785234203 - 2.3793709363443419534e-945j)  +/-  (3.65e-240, 3.65e-240j)
| (0.57735026918962576451 - 3.9209551177912013906e-947j)  +/-  (2.28e-242, 2.28e-242j)
| (-0.96392874096524810675 + 8.4613867004343241117e-949j)  +/-  (2.98e-236, 2.98e-236j)
| (-0.61987957090620921788 - 1.0278753862362465565e-979j)  +/-  (1.25e-241, 1.25e-241j)
| (-0.57735026918962576451 + 3.3185267265226439915e-981j)  +/-  (2.49e-242, 2.49e-242j)
| (1.8538251798624958171e-992 + 1.1967342812017409485e-992j)  +/-  (1.21e-990, 1.21e-990j)
| (0.61987957090620921788 - 1.36634462052117183e-984j)  +/-  (1.29e-241, 1.29e-241j)
| (0.17630301016452293915 - 1.0525885674403411092e-994j)  +/-  (1.27e-251, 1.27e-251j)
| (-0.39843844371375730799 + 6.2442891416082168136e-988j)  +/-  (2.62e-246, 2.62e-246j)
| (-0.53630770882601270453 + 5.0129109046266926348e-986j)  +/-  (3.96e-243, 3.96e-243j)
| (-0.2338729523990239282 - 6.5258586998717701402e-994j)  +/-  (2.83e-250, 2.83e-250j)
| (0.53630770882601270453 - 2.3251505269515450462e-987j)  +/-  (3.85e-243, 3.85e-243j)
| (0.494579454576344586 - 1.005205835223048277e-990j)  +/-  (5.11e-244, 5.11e-244j)
| (0.059103046634552776294 - 1.1652472673932979239e-999j)  +/-  (2.1e-254, 2.1e-254j)
| (-0.494579454576344586 - 4.5245083587641755051e-989j)  +/-  (5.05e-244, 5.05e-244j)
| (-0.34539614352544860815 - 1.2056734587551005796e-992j)  +/-  (1.37e-247, 1.37e-247j)
| (0.2338729523990239282 - 2.9627626387182713503e-998j)  +/-  (2.82e-250, 2.82e-250j)
| (0.44860360377869240256 + 3.9076092280263416424e-992j)  +/-  (3.95e-245, 3.95e-245j)
| (0.29036229308829455553 - 2.6993493052767799317e-996j)  +/-  (6.47e-249, 6.47e-249j)
| (-0.29036229308829455553 - 9.3742482409021448327e-995j)  +/-  (6.62e-249, 6.62e-249j)
| (-0.44860360377869240256 - 6.2991558713693458957e-991j)  +/-  (3.81e-245, 3.81e-245j)
| (-0.11795604714665053388 + 8.1883072949259157836e-1001j)  +/-  (4.91e-253, 4.91e-253j)
| (0.39843844371375730799 - 1.1139851472189903459e-993j)  +/-  (2.61e-246, 2.61e-246j)
| (0.34539614352544860815 + 2.562629322346264571e-994j)  +/-  (1.42e-247, 1.42e-247j)
-------------------------------------------------
The weights are:
| (0.0087783171232489692019 + 1.5575509388452317222e-850j)  +/-  (1.13e-55, 3.8e-169j)
| (0.0023939930170561392885 - 5.4375608300182784082e-851j)  +/-  (4.59e-56, 1.54e-169j)
| (0.018399473854033808229 - 2.7633222915310457146e-850j)  +/-  (1.15e-56, 3.85e-170j)
| (0.0023939930170561392885 + 3.0545283122763444976e-853j)  +/-  (3.4e-58, 1.14e-171j)
| (0.018399473854033808229 - 5.8232935790823041886e-852j)  +/-  (4.55e-58, 1.53e-171j)
| (0.02157046551907644063 + 7.3218411108174794365e-852j)  +/-  (2.68e-58, 8.99e-172j)
| (0.0055784646042651801355 + 2.9254642399385926583e-850j)  +/-  (5.32e-56, 1.79e-169j)
| (0.027744775655166966767 + 1.8498431258814703764e-850j)  +/-  (7.71e-58, 2.59e-171j)
| (0.038665525007908174303 + 1.7666779888809011819e-850j)  +/-  (3.82e-59, 1.28e-172j)
| (0.0055784646042651801355 - 1.0588642710928974308e-852j)  +/-  (9.46e-59, 3.17e-172j)
| (0.027744775655166966767 + 1.0919331977058870561e-851j)  +/-  (2.45e-59, 8.22e-173j)
| (0.059019969483060911482 + 5.2327538694828414561e-851j)  +/-  (1.28e-60, 4.3e-174j)
| (0.030702274731250576425 - 1.7419887670584102795e-850j)  +/-  (2.24e-58, 7.5e-172j)
| (0.024692801505158503268 - 2.0280995051795065623e-850j)  +/-  (4.06e-58, 1.36e-171j)
| (0.024692801505158503268 - 8.9942526685713741799e-852j)  +/-  (2.88e-59, 9.66e-173j)
| (0.030702274731250576425 - 1.3219250062594462025e-851j)  +/-  (2.49e-60, 8.36e-174j)
| (0.042379295849733523661 + 4.2958183136615616161e-851j)  +/-  (1.28e-62, 4.29e-176j)
| (0.015199591714681275611 + 4.4522274655273366512e-852j)  +/-  (9.35e-60, 3.14e-173j)
| (0.036210598794952789569 - 1.6979095503207862509e-850j)  +/-  (3.92e-61, 1.31e-174j)
| (0.011988069541662003645 - 6.039181788546241612e-850j)  +/-  (4.58e-60, 1.54e-173j)
| (0.058643505691689985931 - 4.5490155568680330072e-851j)  +/-  (6.14e-65, 2.06e-178j)
| (0.038665525007908174303 + 2.4872709248740804566e-851j)  +/-  (4.21e-63, 1.41e-176j)
| (0.02157046551907644063 + 2.3074784833138051203e-850j)  +/-  (3.77e-60, 1.27e-173j)
| (0.040795666984684477629 - 1.9164858938075062763e-850j)  +/-  (3.87e-63, 1.3e-176j)
| (0.033536791161640054246 + 1.6920250259219975585e-850j)  +/-  (2.13e-61, 7.16e-175j)
| (0.011988069541662003645 - 3.19027243526631547e-852j)  +/-  (1.86e-61, 6.25e-175j)
| (0.036210598794952789569 - 1.9803908814526401107e-851j)  +/-  (3.67e-63, 1.23e-176j)
| (0.033536791161640054246 + 1.6081893971479529424e-851j)  +/-  (8.88e-63, 2.98e-176j)
| (0.058005523977802253216 + 6.576244166442665505e-851j)  +/-  (1.47e-67, 4.93e-181j)
| (0.042379295849733523661 + 2.1799972257091702385e-850j)  +/-  (4.27e-65, 1.43e-178j)
| (0.0087783171232489692019 + 2.0463936206942673416e-852j)  +/-  (3.82e-62, 1.28e-175j)
| (0.040795666984684477629 - 3.2119312138919556601e-851j)  +/-  (1.22e-64, 4.1e-178j)
| (0.041835277676277749186 + 8.1279383244389639596e-851j)  +/-  (4.59e-67, 1.54e-180j)
| (0.015199591714681275611 + 3.6243426683256857346e-850j)  +/-  (1.19e-63, 3.98e-177j)
| (0.04293720426004624408 - 2.5941984672793722374e-850j)  +/-  (2.47e-67, 8.3e-181j)
| (0.041835277676277749186 + 3.0988039369532955269e-850j)  +/-  (2.93e-68, 9.81e-182j)
| (0.059144541925447085929 - 4.8643373734017245872e-851j)  +/-  (6.22e-71, 2.09e-184j)
| (0.04293720426004624408 - 5.9381840244015408169e-851j)  +/-  (5.98e-69, 2.01e-182j)
| (0.058005523977802253216 + 4.5844847838569885014e-851j)  +/-  (1.34e-71, 4.49e-185j)
| (0.051793337062960961285 + 1.5840256966671538307e-850j)  +/-  (1.18e-71, 3.96e-185j)
| (0.040637008502974588236 - 3.3143612549700611514e-850j)  +/-  (4.21e-70, 1.41e-183j)
| (0.057084344443397361833 - 7.7197748366770986171e-851j)  +/-  (4.42e-72, 1.48e-185j)
| (0.040637008502974588236 - 9.8198748342344362734e-851j)  +/-  (1.58e-71, 5.32e-185j)
| (0.043555025373817172658 + 9.6648135712256587067e-851j)  +/-  (2.19e-72, 7.35e-186j)
| (0.059019969483060911482 + 4.6419818305206312524e-851j)  +/-  (1.02e-72, 3.44e-186j)
| (0.043555025373817172658 + 2.9043550911506549675e-850j)  +/-  (6.02e-72, 2.02e-185j)
| (0.054148279295409263509 - 1.192349909276207306e-850j)  +/-  (4.74e-73, 1.59e-186j)
| (0.057084344443397361833 - 4.7643347825009322046e-851j)  +/-  (2.17e-74, 7.27e-188j)
| (0.048298939380350946671 - 8.1794139725703341577e-851j)  +/-  (2.18e-74, 7.33e-188j)
| (0.055833208824970136339 + 5.1272375425774053912e-851j)  +/-  (5.5e-75, 1.85e-188j)
| (0.055833208824970136339 + 9.3958086364715338746e-851j)  +/-  (1.78e-74, 5.99e-188j)
| (0.048298939380350946671 - 2.1787058977308099642e-850j)  +/-  (4.94e-74, 1.66e-187j)
| (0.058643505691689985931 - 5.7826133777475632332e-851j)  +/-  (5.97e-75, 2e-188j)
| (0.051793337062960961285 + 6.7352044674052333867e-851j)  +/-  (5.45e-76, 1.84e-189j)
| (0.054148279295409263509 - 5.7458565020929190987e-851j)  +/-  (4.58e-76, 1.53e-189j)
