Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 28
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^30 - 166298445234613824167539415014206970253269379271738/389613955679202646378402598698717016939418184777*t^29 + 861213881758050676906477922731882897178642219764041161/5064981423829634402919233783083321220212436402101*t^28 - 212947833205813303294063435036965568519170953885483071856/5064981423829634402919233783083321220212436402101*t^27 + 36672750958436395081122984012317203632204570167006998035900/5064981423829634402919233783083321220212436402101*t^26 - 359911966236193272793231594117393971330046176313370720660016/389613955679202646378402598698717016939418184777*t^25 + 35329936652464877803356824576765593670478392262920670589149000/389613955679202646378402598698717016939418184777*t^24 - 2735681887286975753148521135886566584239143125447507976235456000/389613955679202646378402598698717016939418184777*t^23 + 169978157874103816814321044077385758446785044795353799074293176000/389613955679202646378402598698717016939418184777*t^22 - 8576416095416360085889200713137797185004127335822145316420580960000/389613955679202646378402598698717016939418184777*t^21 + 354314493493123079401654928944406312580739924995371983933257265008000/389613955679202646378402598698717016939418184777*t^20 - 12051048373454887665406084386146052178129786934309352593524459280640000/389613955679202646378402598698717016939418184777*t^19 + 338561071545472397291906316535841840712706812727583547481429943828160000/389613955679202646378402598698717016939418184777*t^18 - 7867584362412874554900014856513345896800181566767426640354521203823360000/389613955679202646378402598698717016939418184777*t^17 + 151194632738586116820853489484680833569211921418866805325424424501315200000/389613955679202646378402598698717016939418184777*t^16 - 2398544702991412894357368748169274150721629563988922898399845416295956480000/389613955679202646378402598698717016939418184777*t^15 + 31306729898308011593105912380690029592454777628554921497294292194552166400000/389613955679202646378402598698717016939418184777*t^14 - 334563893609879787163631281692966951628215504229434243927840408996550041600000/389613955679202646378402598698717016939418184777*t^13 + 2908009637668901895606109111992406839188726567122710151070885866433775513600000/389613955679202646378402598698717016939418184777*t^12 - 20382681597722665773699328534868702477080708652220616469235736839561289728000000/389613955679202646378402598698717016939418184777*t^11 + 113957504428136421304617110625363684834514640067444456853117892528398726348800000/389613955679202646378402598698717016939418184777*t^10 - 501270175380015552319549904452141058808839772030917176647802454093514252288000000/389613955679202646378402598698717016939418184777*t^9 + 1704908352937020697022950149511210057385592490339699915536511728618647580672000000/389613955679202646378402598698717016939418184777*t^8 - 4385180850438675461122796707660197484476509208256601278434778164389366464512000000/389613955679202646378402598698717016939418184777*t^7 + 8286730535998583078081070742198917955144726628804203237633300894273284833280000000/389613955679202646378402598698717016939418184777*t^6 - 11069013670672144562895780389607222205215150557972584106752857621037018644480000000/389613955679202646378402598698717016939418184777*t^5 + 9904612304607942929882824887541655436328047797844232781039385387649233518592000000/389613955679202646378402598698717016939418184777*t^4 - 5486177407520403353267130683233470200060663134378522289901004463879249461248000000/389613955679202646378402598698717016939418184777*t^3 + 1657755921408477340038976151593677261390299053333607634842264416464406315008000000/389613955679202646378402598698717016939418184777*t^2 - 216499046074730221598209528834748884477324158162424536937437500126763417600000000/389613955679202646378402598698717016939418184777*t + 6891957032657182031106696629818458537019911338308736006117941998210514944000000/389613955679202646378402598698717016939418184777
-------------------------------------------------
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
Positive weights:   30 out of 30
Indefinite weights: 0 out of 30
Negative weights:   0 out of 30
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (100.73414877582065858 - 8.4362379801382409934e-711j)  +/-  (2.66e-244, 2.66e-244j)
| (63.328775874307352081 + 9.535508646282095339e-734j)  +/-  (6.01e-241, 6.01e-241j)
| (56.96976333499831537 + 7.082118128379936581e-752j)  +/-  (1.42e-240, 1.42e-240j)
| (78.62552549690034895 + 6.2752059336882801031e-758j)  +/-  (4.39e-242, 4.39e-242j)
| (70.462910842055458116 + 7.4952899200150954978e-757j)  +/-  (2e-241, 2e-241j)
| (1.0820126235403278963 + 3.1214786194728455839e-766j)  +/-  (2.12e-250, 2.12e-250j)
| (19.679323904714225075 + 2.6702631726967747051e-755j)  +/-  (3.03e-241, 3.03e-241j)
| (88.300997735070623403 + 2.0897235697750504883e-759j)  +/-  (5.76e-243, 5.76e-243j)
| (22.566502573945450542 - 5.2991033593869677105e-756j)  +/-  (6.57e-241, 6.57e-241j)
| (17.033308931352764771 - 9.3777990227677062924e-761j)  +/-  (1.13e-241, 1.13e-241j)
| (10.434947282192086461 - 4.7690658740083028109e-768j)  +/-  (2.7e-243, 2.7e-243j)
| (7.0740307920492629068 + 4.3897208929798690624e-768j)  +/-  (1.08e-244, 1.08e-244j)
| (25.709052226589063535 - 1.6246555462190153885e-763j)  +/-  (1.35e-240, 1.35e-240j)
| (36.860977386772434906 - 1.0124906178211420862e-774j)  +/-  (3.69e-240, 3.69e-240j)
| (51.232021836295382465 - 1.059810326541994754e-790j)  +/-  (2.49e-240, 2.49e-240j)
| (5.6832305012356973682 - 8.9414212299492885807e-815j)  +/-  (1.75e-245, 1.75e-245j)
| (3.4142135623730950488 + 2.1409641323517438994e-817j)  +/-  (3.66e-247, 3.66e-247j)
| (8.6551417861799342125 - 3.3565062393347672849e-811j)  +/-  (5.32e-244, 5.32e-244j)
| (46.013168159016807493 - 3.3184007965698321503e-809j)  +/-  (3.73e-240, 3.73e-240j)
| (32.832888670837534794 + 3.2889497107034465611e-837j)  +/-  (3.12e-240, 3.12e-240j)
| (2.5007865181729025515 - 6.427478545775141571e-860j)  +/-  (3.72e-248, 3.72e-248j)
| (1.722431507669741952 + 9.4960160303821761592e-858j)  +/-  (2.9e-249, 2.9e-249j)
| (41.240710019480684766 + 5.5940944761835303894e-869j)  +/-  (3.94e-240, 3.94e-240j)
| (29.124188215765578435 + 5.622479612280880123e-890j)  +/-  (2.09e-240, 2.09e-240j)
| (0.0454668075919932409 + 3.9243594038027678644e-914j)  +/-  (6.55e-255, 6.55e-255j)
| (12.419912335463270406 + 1.1801152950074288393e-899j)  +/-  (1e-242, 1e-242j)
| (0.5857864376269049512 - 1.1048534121633166851e-918j)  +/-  (9.98e-252, 9.98e-252j)
| (0.23914583006679425775 + 1.0233599469469235065e-921j)  +/-  (3.08e-253, 3.08e-253j)
| (14.616723682853384996 - 2.7024834651030073519e-918j)  +/-  (3.75e-242, 3.75e-242j)
| (4.4694451028295798284 - 1.1442143826036308834e-933j)  +/-  (2.82e-246, 2.82e-246j)
-------------------------------------------------
The weights are:
| (2.6486723227245421211e-43 + 1.1289306593292321609e-753j)  +/-  (9.85e-93, 3.75e-210j)
| (2.1071971758204299279e-27 + 6.8267412274931691703e-747j)  +/-  (3.12e-87, 1.19e-204j)
| (1.0927479058011873599e-24 - 1.4074703158417038219e-745j)  +/-  (2.91e-86, 1.11e-203j)
| (6.2829107135757016228e-34 + 5.6139064186877408515e-750j)  +/-  (1.82e-90, 6.91e-208j)
| (1.9002180017112290207e-30 - 2.3913081348324909455e-748j)  +/-  (5.1e-89, 1.94e-206j)
| (0.19296683532820802663 + 4.5902833556865419791e-734j)  +/-  (1.92e-48, 7.3e-166j)
| (7.8521205879289546482e-09 + 1.1872439422920136922e-737j)  +/-  (2.64e-78, 1.01e-195j)
| (4.8031617573174014576e-38 - 8.2053267775793259538e-752j)  +/-  (2.27e-92, 8.65e-210j)
| (4.7685445607091724234e-10 - 2.7932457725374626205e-738j)  +/-  (7.14e-80, 2.72e-197j)
| (1.0129024519905541053e-07 - 4.5102293519454065995e-737j)  +/-  (1.08e-77, 4.12e-195j)
| (5.5287471172440958288e-05 + 1.3171657657461101191e-735j)  +/-  (1.16e-74, 4.42e-192j)
| (0.0012568779818455004941 + 7.3997716911299226026e-735j)  +/-  (4.71e-72, 1.79e-189j)
| (2.2387378418184238891e-11 + 5.8349504441988234751e-739j)  +/-  (9.52e-82, 3.62e-199j)
| (4.1163534246767228773e-16 - 2.3851134766345340597e-741j)  +/-  (5.5e-86, 2.09e-203j)
| (3.0742766892310055295e-22 + 2.2122898616430825196e-744j)  +/-  (9.66e-89, 3.68e-206j)
| (0.0044217800409851141402 - 1.4644231213618511629e-734j)  +/-  (2.9e-74, 1.1e-191j)
| (0.032316712755334981121 - 3.6910017771044626019e-734j)  +/-  (2.94e-72, 1.12e-189j)
| (0.00029258501380429487175 - 3.3002711453384597959e-735j)  +/-  (2.03e-76, 7.74e-194j)
| (5.1812625171617675252e-20 - 2.7573398010457117724e-743j)  +/-  (2.6e-88, 9.91e-206j)
| (2.1274130726880236478e-14 + 1.72328017251499924e-740j)  +/-  (4.91e-86, 1.87e-203j)
| (0.069368882995651959602 + 4.6291303230233182822e-734j)  +/-  (3.94e-75, 1.5e-192j)
| (0.12689151323932298527 - 4.981614007577520159e-734j)  +/-  (2.61e-74, 9.93e-192j)
| (5.6123802083800304062e-18 + 2.8062070335615243405e-742j)  +/-  (8.05e-88, 3.06e-205j)
| (7.993540008179460664e-13 - 1.0736103820087663382e-739j)  +/-  (2.52e-85, 9.58e-203j)
| (0.11145173645551543037 - 6.3095417378870880847e-735j)  +/-  (5.21e-78, 1.98e-195j)
| (8.4368980812849613203e-06 - 4.7383768385617731293e-736j)  +/-  (3.58e-82, 1.36e-199j)
| (0.23500872897750115323 - 3.5223601481809171998e-734j)  +/-  (2.92e-78, 1.11e-195j)
| (0.21300276894845658433 + 2.0516245060152577476e-734j)  +/-  (2.88e-78, 1.1e-195j)
| (1.0345575987061456289e-06 + 1.5394423632790882818e-736j)  +/-  (8.31e-83, 3.16e-200j)
| (0.012956709694092870971 + 2.5131909431923277342e-734j)  +/-  (4.33e-80, 1.64e-197j)
Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 28
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^30 - 166298445234613824167539415014206970253269379271738/389613955679202646378402598698717016939418184777*t^29 + 861213881758050676906477922731882897178642219764041161/5064981423829634402919233783083321220212436402101*t^28 - 212947833205813303294063435036965568519170953885483071856/5064981423829634402919233783083321220212436402101*t^27 + 36672750958436395081122984012317203632204570167006998035900/5064981423829634402919233783083321220212436402101*t^26 - 359911966236193272793231594117393971330046176313370720660016/389613955679202646378402598698717016939418184777*t^25 + 35329936652464877803356824576765593670478392262920670589149000/389613955679202646378402598698717016939418184777*t^24 - 2735681887286975753148521135886566584239143125447507976235456000/389613955679202646378402598698717016939418184777*t^23 + 169978157874103816814321044077385758446785044795353799074293176000/389613955679202646378402598698717016939418184777*t^22 - 8576416095416360085889200713137797185004127335822145316420580960000/389613955679202646378402598698717016939418184777*t^21 + 354314493493123079401654928944406312580739924995371983933257265008000/389613955679202646378402598698717016939418184777*t^20 - 12051048373454887665406084386146052178129786934309352593524459280640000/389613955679202646378402598698717016939418184777*t^19 + 338561071545472397291906316535841840712706812727583547481429943828160000/389613955679202646378402598698717016939418184777*t^18 - 7867584362412874554900014856513345896800181566767426640354521203823360000/389613955679202646378402598698717016939418184777*t^17 + 151194632738586116820853489484680833569211921418866805325424424501315200000/389613955679202646378402598698717016939418184777*t^16 - 2398544702991412894357368748169274150721629563988922898399845416295956480000/389613955679202646378402598698717016939418184777*t^15 + 31306729898308011593105912380690029592454777628554921497294292194552166400000/389613955679202646378402598698717016939418184777*t^14 - 334563893609879787163631281692966951628215504229434243927840408996550041600000/389613955679202646378402598698717016939418184777*t^13 + 2908009637668901895606109111992406839188726567122710151070885866433775513600000/389613955679202646378402598698717016939418184777*t^12 - 20382681597722665773699328534868702477080708652220616469235736839561289728000000/389613955679202646378402598698717016939418184777*t^11 + 113957504428136421304617110625363684834514640067444456853117892528398726348800000/389613955679202646378402598698717016939418184777*t^10 - 501270175380015552319549904452141058808839772030917176647802454093514252288000000/389613955679202646378402598698717016939418184777*t^9 + 1704908352937020697022950149511210057385592490339699915536511728618647580672000000/389613955679202646378402598698717016939418184777*t^8 - 4385180850438675461122796707660197484476509208256601278434778164389366464512000000/389613955679202646378402598698717016939418184777*t^7 + 8286730535998583078081070742198917955144726628804203237633300894273284833280000000/389613955679202646378402598698717016939418184777*t^6 - 11069013670672144562895780389607222205215150557972584106752857621037018644480000000/389613955679202646378402598698717016939418184777*t^5 + 9904612304607942929882824887541655436328047797844232781039385387649233518592000000/389613955679202646378402598698717016939418184777*t^4 - 5486177407520403353267130683233470200060663134378522289901004463879249461248000000/389613955679202646378402598698717016939418184777*t^3 + 1657755921408477340038976151593677261390299053333607634842264416464406315008000000/389613955679202646378402598698717016939418184777*t^2 - 216499046074730221598209528834748884477324158162424536937437500126763417600000000/389613955679202646378402598698717016939418184777*t + 6891957032657182031106696629818458537019911338308736006117941998210514944000000/389613955679202646378402598698717016939418184777
-------------------------------------------------
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
Positive weights:   30 out of 30
Indefinite weights: 0 out of 30
Negative weights:   0 out of 30
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (100.73414877582065858 - 8.4362379801382409934e-711j)  +/-  (2.66e-244, 2.66e-244j)
| (63.328775874307352081 + 9.535508646282095339e-734j)  +/-  (6.01e-241, 6.01e-241j)
| (56.96976333499831537 + 7.082118128379936581e-752j)  +/-  (1.42e-240, 1.42e-240j)
| (78.62552549690034895 + 6.2752059336882801031e-758j)  +/-  (4.39e-242, 4.39e-242j)
| (70.462910842055458116 + 7.4952899200150954978e-757j)  +/-  (2e-241, 2e-241j)
| (1.0820126235403278963 + 3.1214786194728455839e-766j)  +/-  (2.12e-250, 2.12e-250j)
| (19.679323904714225075 + 2.6702631726967747051e-755j)  +/-  (3.03e-241, 3.03e-241j)
| (88.300997735070623403 + 2.0897235697750504883e-759j)  +/-  (5.76e-243, 5.76e-243j)
| (22.566502573945450542 - 5.2991033593869677105e-756j)  +/-  (6.57e-241, 6.57e-241j)
| (17.033308931352764771 - 9.3777990227677062924e-761j)  +/-  (1.13e-241, 1.13e-241j)
| (10.434947282192086461 - 4.7690658740083028109e-768j)  +/-  (2.7e-243, 2.7e-243j)
| (7.0740307920492629068 + 4.3897208929798690624e-768j)  +/-  (1.08e-244, 1.08e-244j)
| (25.709052226589063535 - 1.6246555462190153885e-763j)  +/-  (1.35e-240, 1.35e-240j)
| (36.860977386772434906 - 1.0124906178211420862e-774j)  +/-  (3.69e-240, 3.69e-240j)
| (51.232021836295382465 - 1.059810326541994754e-790j)  +/-  (2.49e-240, 2.49e-240j)
| (5.6832305012356973682 - 8.9414212299492885807e-815j)  +/-  (1.75e-245, 1.75e-245j)
| (3.4142135623730950488 + 2.1409641323517438994e-817j)  +/-  (3.66e-247, 3.66e-247j)
| (8.6551417861799342125 - 3.3565062393347672849e-811j)  +/-  (5.32e-244, 5.32e-244j)
| (46.013168159016807493 - 3.3184007965698321503e-809j)  +/-  (3.73e-240, 3.73e-240j)
| (32.832888670837534794 + 3.2889497107034465611e-837j)  +/-  (3.12e-240, 3.12e-240j)
| (2.5007865181729025515 - 6.427478545775141571e-860j)  +/-  (3.72e-248, 3.72e-248j)
| (1.722431507669741952 + 9.4960160303821761592e-858j)  +/-  (2.9e-249, 2.9e-249j)
| (41.240710019480684766 + 5.5940944761835303894e-869j)  +/-  (3.94e-240, 3.94e-240j)
| (29.124188215765578435 + 5.622479612280880123e-890j)  +/-  (2.09e-240, 2.09e-240j)
| (0.0454668075919932409 + 3.9243594038027678644e-914j)  +/-  (6.55e-255, 6.55e-255j)
| (12.419912335463270406 + 1.1801152950074288393e-899j)  +/-  (1e-242, 1e-242j)
| (0.5857864376269049512 - 1.1048534121633166851e-918j)  +/-  (9.98e-252, 9.98e-252j)
| (0.23914583006679425775 + 1.0233599469469235065e-921j)  +/-  (3.08e-253, 3.08e-253j)
| (14.616723682853384996 - 2.7024834651030073519e-918j)  +/-  (3.75e-242, 3.75e-242j)
| (4.4694451028295798284 - 1.1442143826036308834e-933j)  +/-  (2.82e-246, 2.82e-246j)
-------------------------------------------------
The weights are:
| (2.6486723227245421211e-43 + 1.1289306593292321609e-753j)  +/-  (9.85e-93, 3.75e-210j)
| (2.1071971758204299279e-27 + 6.8267412274931691703e-747j)  +/-  (3.12e-87, 1.19e-204j)
| (1.0927479058011873599e-24 - 1.4074703158417038219e-745j)  +/-  (2.91e-86, 1.11e-203j)
| (6.2829107135757016228e-34 + 5.6139064186877408515e-750j)  +/-  (1.82e-90, 6.91e-208j)
| (1.9002180017112290207e-30 - 2.3913081348324909455e-748j)  +/-  (5.1e-89, 1.94e-206j)
| (0.19296683532820802663 + 4.5902833556865419791e-734j)  +/-  (1.92e-48, 7.3e-166j)
| (7.8521205879289546482e-09 + 1.1872439422920136922e-737j)  +/-  (2.64e-78, 1.01e-195j)
| (4.8031617573174014576e-38 - 8.2053267775793259538e-752j)  +/-  (2.27e-92, 8.65e-210j)
| (4.7685445607091724234e-10 - 2.7932457725374626205e-738j)  +/-  (7.14e-80, 2.72e-197j)
| (1.0129024519905541053e-07 - 4.5102293519454065995e-737j)  +/-  (1.08e-77, 4.12e-195j)
| (5.5287471172440958288e-05 + 1.3171657657461101191e-735j)  +/-  (1.16e-74, 4.42e-192j)
| (0.0012568779818455004941 + 7.3997716911299226026e-735j)  +/-  (4.71e-72, 1.79e-189j)
| (2.2387378418184238891e-11 + 5.8349504441988234751e-739j)  +/-  (9.52e-82, 3.62e-199j)
| (4.1163534246767228773e-16 - 2.3851134766345340597e-741j)  +/-  (5.5e-86, 2.09e-203j)
| (3.0742766892310055295e-22 + 2.2122898616430825196e-744j)  +/-  (9.66e-89, 3.68e-206j)
| (0.0044217800409851141402 - 1.4644231213618511629e-734j)  +/-  (2.9e-74, 1.1e-191j)
| (0.032316712755334981121 - 3.6910017771044626019e-734j)  +/-  (2.94e-72, 1.12e-189j)
| (0.00029258501380429487175 - 3.3002711453384597959e-735j)  +/-  (2.03e-76, 7.74e-194j)
| (5.1812625171617675252e-20 - 2.7573398010457117724e-743j)  +/-  (2.6e-88, 9.91e-206j)
| (2.1274130726880236478e-14 + 1.72328017251499924e-740j)  +/-  (4.91e-86, 1.87e-203j)
| (0.069368882995651959602 + 4.6291303230233182822e-734j)  +/-  (3.94e-75, 1.5e-192j)
| (0.12689151323932298527 - 4.981614007577520159e-734j)  +/-  (2.61e-74, 9.93e-192j)
| (5.6123802083800304062e-18 + 2.8062070335615243405e-742j)  +/-  (8.05e-88, 3.06e-205j)
| (7.993540008179460664e-13 - 1.0736103820087663382e-739j)  +/-  (2.52e-85, 9.58e-203j)
| (0.11145173645551543037 - 6.3095417378870880847e-735j)  +/-  (5.21e-78, 1.98e-195j)
| (8.4368980812849613203e-06 - 4.7383768385617731293e-736j)  +/-  (3.58e-82, 1.36e-199j)
| (0.23500872897750115323 - 3.5223601481809171998e-734j)  +/-  (2.92e-78, 1.11e-195j)
| (0.21300276894845658433 + 2.0516245060152577476e-734j)  +/-  (2.88e-78, 1.1e-195j)
| (1.0345575987061456289e-06 + 1.5394423632790882818e-736j)  +/-  (8.31e-83, 3.16e-200j)
| (0.012956709694092870971 + 2.5131909431923277342e-734j)  +/-  (4.33e-80, 1.64e-197j)
