Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 58
-------------------------------------------------
Trying to find an order 58 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^60 - 7100056248952808251326215218100848843/4063740125999662721849503071001624*t^58 + 5791527230493455445334986465437072379759/4063740125999662721849503071001624*t^56 - 209544792278338545268124721947505750328545/290267151857118765846393076500116*t^54 + 73958940429153327335161553593069567418585265/290267151857118765846393076500116*t^52 - 38694393945555743669385549187155812489343638235/580534303714237531692786153000232*t^50 + 7791197202028914847874454612828453310723387265775/580534303714237531692786153000232*t^48 - 309486498646990861776617058169250251882004349502425/145133575928559382923196538250058*t^46 + 39472189964977110901679716161182062178025142554078375/145133575928559382923196538250058*t^44 - 16357207867757684885206703110642059944799959947622830125/580534303714237531692786153000232*t^42 + 1387807392178377928695548102693462423100128802484999751625/580534303714237531692786153000232*t^40 - 48475552991609043965651966940786450830151146441552072136375/290267151857118765846393076500116*t^38 + 2797179923141512100472082555990429212104206947634333073925375/290267151857118765846393076500116*t^36 - 266974650941614531758849853950902288190384202573488703195801875/580534303714237531692786153000232*t^34 + 10532294825069122620301580737365197707016287119407151363621294375/580534303714237531692786153000232*t^32 - 42848340510803620120034421618789046816868243358951098536619934375/72566787964279691461598269125029*t^30 + 1146311884307804189570481540160240328341255467599587348441765976250/72566787964279691461598269125029*t^28 - 200595174188110594726684845970611295397593555310949395128681924689375/580534303714237531692786153000232*t^26 + 3562030571506248739281040164397943200815761152382733235697279955421875/580534303714237531692786153000232*t^24 - 25437059406158723869170737412125921704884884354799234922288603790109375/290267151857118765846393076500116*t^22 + 288779202391539686349420354323588703604933370659923458053398614870109375/290267151857118765846393076500116*t^20 - 5134711432568548693512814418290797351286171631825142192698012631737765625/580534303714237531692786153000232*t^18 + 35077993157232416753588844267452849679164746181689207530417388967529703125/580534303714237531692786153000232*t^16 - 44930089905251287769789439235341900660264697963937453113966552287476015625/145133575928559382923196538250058*t^14 + 167236295333582233454784506864121225615485993842446815538087891293511796875/145133575928559382923196538250058*t^12 - 1733029757638995208262679637987150582562065683476421121481195510528429484375/580534303714237531692786153000232*t^10 + 2942384255576588130997214221423582539157960278421045161138778077110840296875/580534303714237531692786153000232*t^8 - 1496078334397705381994991141402369261385888464530449531019768188751825015625/290267151857118765846393076500116*t^6 + 785612112686584460193819891583289376321955023546619889268345022084261640625/290267151857118765846393076500116*t^4 - 318518767898765749373335667107812800294204251487497105917203917321792265625/580534303714237531692786153000232*t^2 + 10398555386079770047503022980751344714023432533006199393077801080060703125/580534303714237531692786153000232
-------------------------------------------------
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: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (12.647335763017280188 - 3.513229708024183347e-1311j)  +/-  (5.5e-498, 5.5e-498j)
| (10.788224797712877847 + 1.159455924443243322e-1309j)  +/-  (2.39e-496, 2.39e-496j)
| (9.7108571459931936861 + 4.8611607628908879498e-1309j)  +/-  (7.01e-496, 7.01e-496j)
| (13.393984628391886333 - 9.6335259086238310993e-1313j)  +/-  (7.06e-499, 7.06e-499j)
| (7.7555642324473114448 - 7.4798559135514782133e-1309j)  +/-  (5.17e-496, 5.17e-496j)
| (8.7072562137171810682 - 7.5916643667012425144e-1309j)  +/-  (8.49e-496, 8.49e-496j)
| (8.2258900827628561865 + 1.5020203406051119603e-1310j)  +/-  (7e-496, 7e-496j)
| (4.6754803083725200582 + 1.9268138666240894839e-1313j)  +/-  (7.36e-499, 7.36e-499j)
| (14.295823400414208428 + 2.2930957044358111635e-1315j)  +/-  (3.32e-500, 3.32e-500j)
| (6.842439237146984574 + 6.6022479046277137588e-1311j)  +/-  (1.65e-496, 1.65e-496j)
| (11.980912326760506776 - 7.4836289163524540477e-1312j)  +/-  (2.96e-497, 2.96e-497j)
| (3.8409589797882882261 - 1.7745553575644655897e-1315j)  +/-  (3.28e-500, 3.28e-500j)
| (2.2066493062692059191 + 1.6327682405524092891e-1318j)  +/-  (9.52e-504, 9.52e-504j)
| (11.366116412516882823 + 2.2233538243046048711e-1311j)  +/-  (9.51e-497, 9.51e-497j)
| (10.238410310600275013 - 2.7296413718171339134e-1311j)  +/-  (4.48e-496, 4.48e-496j)
| (5.5261800009579592622 - 3.7842093889257720473e-1312j)  +/-  (8.93e-498, 8.93e-498j)
| (5.0985574237917571227 + 1.0595216766270143167e-1312j)  +/-  (3e-498, 3e-498j)
| (9.2014770517910558685 - 2.4989168067275658364e-1311j)  +/-  (8.8e-496, 8.8e-496j)
| (3.4286243635738085537 + 1.2555539832237806012e-1315j)  +/-  (5.49e-501, 5.49e-501j)
| (7.294815381007186963 - 6.557607835005274834e-1310j)  +/-  (3.32e-496, 3.32e-496j)
| (2.6118289504804400943 - 1.7110994020573176593e-1318j)  +/-  (8.91e-503, 8.91e-503j)
| (5.9589208180340749597 - 4.3571513402680568135e-1313j)  +/-  (2.8e-497, 2.8e-497j)
| (4.2564357177187983427 + 6.6768046333172925813e-1317j)  +/-  (1.58e-499, 1.58e-499j)
| (6.3974270947529783494 - 7.8078323406891932694e-1311j)  +/-  (7.12e-497, 7.12e-497j)
| (3.0190374689043681296 - 2.2196055415571291789e-1319j)  +/-  (7.66e-502, 7.66e-502j)
| (-13.393984628391886333 + 2.0607773808488864966e-1312j)  +/-  (6.5e-499, 6.5e-499j)
| (-10.788224797712877847 + 7.1274522863859988869e-1333j)  +/-  (2.2e-496, 2.2e-496j)
| (-6.3974270947529783494 - 8.5831984039806640003e-1347j)  +/-  (6.9e-497, 6.9e-497j)
| (-11.980912326760506776 - 4.8779838001849104325e-1358j)  +/-  (2.97e-497, 2.97e-497j)
| (-6.842439237146984574 - 5.8651892114111603016e-1367j)  +/-  (1.74e-496, 1.74e-496j)
| (-5.9589208180340749597 - 4.821437173042805778e-1382j)  +/-  (2.67e-497, 2.67e-497j)
| (-12.647335763017280188 + 1.0861648079499120626e-1401j)  +/-  (5.55e-498, 5.55e-498j)
| (-14.295823400414208428 + 6.3199005518492669932e-1429j)  +/-  (3.43e-500, 3.43e-500j)
| (-11.366116412516882823 - 3.2248057151912692028e-1467j)  +/-  (9.18e-497, 9.18e-497j)
| (-1.4010525171555368454 + 4.0757877075418806484e-1502j)  +/-  (8.6e-506, 8.6e-506j)
| (1.8031645350997978587 + 5.2406082292129227909e-1501j)  +/-  (8.63e-505, 8.63e-505j)
| (-9.7108571459931936861 + 1.0230073217811473447e-1491j)  +/-  (7.12e-496, 7.12e-496j)
| (-3.8409589797882882261 + 5.6327989765881853984e-1514j)  +/-  (3.47e-500, 3.47e-500j)
| (-8.2258900827628561865 - 3.4101022661970105358e-1508j)  +/-  (7.43e-496, 7.43e-496j)
| (-1 + 5.0225393304772596934e-1535j)  +/-  (5.46e-507, 5.46e-507j)
| (-4.6754803083725200582 + 1.9147108273052857436e-1524j)  +/-  (7.87e-499, 7.87e-499j)
| (-4.2564357177187983427 - 1.3611526659351968724e-1528j)  +/-  (1.7e-499, 1.7e-499j)
| (-7.294815381007186963 + 1.0043150610636847121e-1530j)  +/-  (3.23e-496, 3.23e-496j)
| (-10.238410310600275013 + 2.3585221868644180361e-1567j)  +/-  (4.46e-496, 4.46e-496j)
| (1 - 2.6531013419795931478e-1602j)  +/-  (5.46e-507, 5.46e-507j)
| (-3.0190374689043681296 + 1.2819811808956283339e-1591j)  +/-  (7.64e-502, 7.64e-502j)
| (-0.59970008632913004351 + 6.9712702993669182572e-1617j)  +/-  (3.39e-508, 3.39e-508j)
| (-3.4286243635738085537 - 2.281056682982830838e-1605j)  +/-  (5.78e-501, 5.78e-501j)
| (-7.7555642324473114448 + 3.9365499919031005573e-1653j)  +/-  (5.69e-496, 5.69e-496j)
| (-0.19985012197265887452 - 9.4581473598020250671e-1707j)  +/-  (2.14e-509, 2.14e-509j)
| (-1.8031645350997978587 - 1.7739483579694683806e-1694j)  +/-  (9.03e-505, 9.03e-505j)
| (1.4010525171555368454 + 1.1489419596494029359e-1701j)  +/-  (8.3e-506, 8.3e-506j)
| (-8.7072562137171810682 - 1.2755787185683943745e-1713j)  +/-  (8.41e-496, 8.41e-496j)
| (-5.0985574237917571227 + 4.8875543381736476915e-1757j)  +/-  (2.9e-498, 2.9e-498j)
| (0.19985012197265887452 - 5.0734218091637251682e-1799j)  +/-  (2.14e-509, 2.14e-509j)
| (-9.2014770517910558685 + 3.2135795166880961473e-1784j)  +/-  (8.85e-496, 8.85e-496j)
| (-2.2066493062692059191 - 7.187308291237639066e-1805j)  +/-  (1.09e-503, 1.09e-503j)
| (-2.6118289504804400943 - 3.5840126236481523194e-1804j)  +/-  (9.11e-503, 9.11e-503j)
| (-5.5261800009579592622 + 9.5475416657609066589e-1798j)  +/-  (9.53e-498, 9.53e-498j)
| (0.59970008632913004351 + 1.1592197188902734902e-1819j)  +/-  (3.15e-508, 3.15e-508j)
-------------------------------------------------
The weights are:
| (5.1534310098637738118e-36 - 3.7929912362647097239e-1334j)  +/-  (3.09e-154, 5.55e-401j)
| (1.1976401236464140107e-26 + 2.561785805734853573e-1329j)  +/-  (1.89e-150, 3.39e-397j)
| (6.8865380007423514399e-22 + 6.9937278443884734239e-1327j)  +/-  (3.63e-148, 6.52e-395j)
| (3.5494911965018798159e-40 + 2.7663833471270011856e-1336j)  +/-  (2.57e-156, 4.61e-403j)
| (1.612570174455528539e-14 + 7.8735627364277943391e-1322j)  +/-  (5.41e-144, 9.7e-391j)
| (6.6917958786921302007e-18 + 6.8925144984530357822e-1325j)  +/-  (1.46e-146, 2.63e-393j)
| (3.8441852102570564331e-16 + 7.3813991548443666374e-1324j)  +/-  (2.42e-145, 4.34e-392j)
| (3.0082044503836238592e-06 + 4.124184229361518477e-1318j)  +/-  (5.23e-136, 9.38e-383j)
| (1.7387339200018362547e-45 - 5.2827304932579011493e-1339j)  +/-  (2.32e-160, 4.16e-407j)
| (1.2192700413315395882e-11 + 8.8869052441677490498e-1321j)  +/-  (1.93e-143, 3.46e-390j)
| (1.7199985069606263743e-32 + 2.4708694235918309302e-1332j)  +/-  (4.84e-155, 8.68e-402j)
| (0.00010331755855941275776 + 1.0950966186403301164e-1317j)  +/-  (6.73e-135, 1.21e-381j)
| (0.014133003807973406996 + 8.3883353582473130497e-1317j)  +/-  (2.15e-125, 3.86e-372j)
| (2.0995609811764439806e-29 - 9.6657541014012563164e-1331j)  +/-  (7.85e-154, 1.41e-400j)
| (3.7079323598082713395e-24 - 4.9196803460977552511e-1328j)  +/-  (1.99e-151, 3.57e-398j)
| (4.0093406822393543229e-08 + 4.7101062531395841708e-1319j)  +/-  (2.23e-142, 4.01e-389j)
| (3.8437875155632205841e-07 - 3.2174422489561655294e-1318j)  +/-  (4.56e-141, 8.18e-388j)
| (8.2379801552026701234e-20 - 6.9222496430855105253e-1326j)  +/-  (5.72e-150, 1.03e-396j)
| (0.00045917322576623160306 - 2.2468424611267139679e-1317j)  +/-  (6.62e-137, 1.19e-383j)
| (5.0686378086712269744e-13 - 1.9025920664981506215e-1321j)  +/-  (1.35e-146, 2.42e-393j)
| (0.0053490950724115713305 - 5.8130528514851315523e-1317j)  +/-  (1.51e-134, 2.71e-381j)
| (3.3828479834464532881e-09 - 3.1361751673048822031e-1320j)  +/-  (1.91e-144, 3.43e-391j)
| (1.9370052406144784588e-05 - 4.9698483192115814273e-1318j)  +/-  (1.49e-140, 2.67e-387j)
| (2.284359966384415009e-10 + 4.6655265916942508098e-1320j)  +/-  (1.81e-145, 3.24e-392j)
| (0.0017089224298964096489 + 3.8350083192614413463e-1317j)  +/-  (1.5e-137, 2.68e-384j)
| (3.5494911965018798159e-40 + 1.2199251870272039284e-1336j)  +/-  (7.51e-179, 1.35e-425j)
| (1.1976401236464140107e-26 + 9.5838635308313058203e-1330j)  +/-  (1.57e-174, 2.82e-421j)
| (2.284359966384415009e-10 - 2.3999009339070567496e-1321j)  +/-  (6.39e-165, 1.15e-411j)
| (1.7199985069606263743e-32 + 9.958289718519919464e-1333j)  +/-  (6.7e-177, 1.2e-423j)
| (1.2192700413315395882e-11 + 5.1940755090416905903e-1322j)  +/-  (1.46e-166, 2.62e-413j)
| (3.3828479834464532881e-09 + 9.8588078461807843668e-1321j)  +/-  (2.46e-164, 4.42e-411j)
| (5.1534310098637738118e-36 - 1.5969583289951959925e-1334j)  +/-  (2.17e-178, 3.9e-425j)
| (1.7387339200018362547e-45 - 2.4517184650403331683e-1339j)  +/-  (3.17e-182, 5.69e-429j)
| (2.0995609811764439806e-29 - 3.7411000481249320802e-1331j)  +/-  (2.33e-176, 4.19e-423j)
| (0.060031612279458387483 - 8.5560830195191567739e-1317j)  +/-  (2.49e-149, 4.46e-396j)
| (0.031616060661762463528 - 1.1334596258915270177e-1316j)  +/-  (3.74e-148, 6.71e-395j)
| (6.8865380007423514399e-22 + 2.6321951815709882591e-1327j)  +/-  (8.4e-175, 1.51e-421j)
| (0.00010331755855941275776 - 2.3905261527162530846e-1318j)  +/-  (2.28e-163, 4.09e-410j)
| (3.8441852102570564331e-16 - 2.3974235495161064267e-1324j)  +/-  (8.36e-173, 1.5e-419j)
| (0.096939638665822614521 + 1.1626824318077025899e-1316j)  +/-  (2.62e-150, 4.7e-397j)
| (3.0082044503836238592e-06 - 3.5777381014892755287e-1319j)  +/-  (4.87e-166, 8.73e-413j)
| (1.9370052406144784588e-05 + 9.6936815162020885353e-1319j)  +/-  (5.11e-165, 9.17e-412j)
| (5.0686378086712269744e-13 - 9.9210466290467380495e-1323j)  +/-  (3.38e-171, 6.07e-418j)
| (3.7079323598082713395e-24 - 1.8057691450140485425e-1328j)  +/-  (1.55e-176, 2.77e-423j)
| (0.096939638665822614521 - 1.6683289512841145096e-1316j)  +/-  (1.38e-156, 2.49e-403j)
| (0.0017089224298964096489 - 1.1085958737413082086e-1317j)  +/-  (1.89e-164, 3.4e-411j)
| (0.13332207321399164034 - 1.4594850159170823449e-1316j)  +/-  (2.05e-157, 3.68e-404j)
| (0.00045917322576623160306 + 5.381334065018374958e-1318j)  +/-  (5.27e-165, 9.46e-412j)
| (1.612570174455528539e-14 + 1.6577144426392387676e-1323j)  +/-  (1.09e-172, 1.95e-419j)
| (0.15631429673134289349 + 1.6939241480286168126e-1316j)  +/-  (3.61e-160, 6.5e-407j)
| (0.031616060661762463528 + 5.8100914611042877012e-1317j)  +/-  (2.91e-163, 5.24e-410j)
| (0.060031612279458387483 + 1.426895433991635334e-1316j)  +/-  (5.35e-161, 9.62e-408j)
| (6.6917958786921302007e-18 + 2.9622110520886653418e-1325j)  +/-  (5.69e-175, 1.02e-421j)
| (3.8437875155632205841e-07 + 1.1978033805643595573e-1319j)  +/-  (8.29e-170, 1.53e-416j)
| (0.15631429673134289349 - 1.8193162923345400479e-1316j)  +/-  (1.41e-164, 2.46e-411j)
| (8.2379801552026701234e-20 - 3.076855352849182884e-1326j)  +/-  (5.21e-176, 9.26e-423j)
| (0.014133003807973406996 - 3.6362843899305237777e-1317j)  +/-  (5e-167, 8.71e-414j)
| (0.0053490950724115713305 + 2.0945463127005147167e-1317j)  +/-  (1.53e-167, 2.63e-414j)
| (4.0093406822393543229e-08 - 3.6234104719402922371e-1320j)  +/-  (1.21e-170, 2.31e-417j)
| (0.13332207321399164034 + 1.8096177290152132217e-1316j)  +/-  (2.54e-166, 3.09e-413j)
