Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 61
-------------------------------------------------
Trying to find an order 61 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^63 - 16856937805381518160301638383184185661427/8912577376109714820850333034596236377*t^61 + 14921464975626998397066557360068758335894295/8912577376109714820850333034596236377*t^59 - 139382041306855774215418784128731872318634555/151060633493384996963564966688071803*t^57 + 53674778551877575006418477996942833208726079075/151060633493384996963564966688071803*t^55 - 15365628418828949741962803754576929860608140299385/151060633493384996963564966688071803*t^53 + 3396735000579976312712103721952868853305591197732685/151060633493384996963564966688071803*t^51 - 594604872819336055603658068792260869928096981578704875/151060633493384996963564966688071803*t^49 + 83866252968355934574608895069636632211603308264846592375/151060633493384996963564966688071803*t^47 - 9647995821387032884721548711442511198202471712985675238125/151060633493384996963564966688071803*t^45 + 913049558587912093148192273592568023615914460593872867217625/151060633493384996963564966688071803*t^43 - 71496874578657514675471177813759243369512286555159453539306375/151060633493384996963564966688071803*t^41 + 4649446524598304365552951491332301754692133545179829080220639375/151060633493384996963564966688071803*t^39 - 251556577320335678012076232427290147110652868018154443609554558125/151060633493384996963564966688071803*t^37 + 11326505144563306627640314077085259767126203325576074810327911390625/151060633493384996963564966688071803*t^35 - 423882146731882234717343732858467433927543501878777833194784852474375/151060633493384996963564966688071803*t^33 + 13149826450070859115763515241754245604049670970820255064136564252980625/151060633493384996963564966688071803*t^31 - 336756885703833299171907623183427390479296409796058315251354776120746875/151060633493384996963564966688071803*t^29 + 7078550048192278984653656169716495655515262281841938007095945634805809375/151060633493384996963564966688071803*t^27 - 121212519458617453562256525178830805249848655026191936796651477530827640625/151060633493384996963564966688071803*t^25 + 1674872109877873667172879979914537335059256707949031598249009917122061515625/151060633493384996963564966688071803*t^23 - 18451608392988135205748274132528237410324202304657694693843174325441534796875/151060633493384996963564966688071803*t^21 + 159647685775636200384858581203549102483465704402053719447460823925755862734375/151060633493384996963564966688071803*t^19 - 1064410929612021415923429725052202453914730939052953297760448318558856910390625/151060633493384996963564966688071803*t^17 + 5337297455171395836715045643943551855679489733951294440795680724070345086328125/151060633493384996963564966688071803*t^15 - 19500318498673615329428755952883417184537117415730584815985048100490104257859375/151060633493384996963564966688071803*t^13 + 49751963056882104433962960603611749725661133846597198941884711479654277459421875/151060633493384996963564966688071803*t^11 - 83524569776884628088154849413760319791633346278894273665547604673374196962578125/151060633493384996963564966688071803*t^9 + 84474704753488293947257096911638620658897063690354516006471977189581970271953125/151060633493384996963564966688071803*t^7 - 44578421230021496117400590900596325286192287084991182182828886751080670118359375/151060633493384996963564966688071803*t^5 + 9328501511701064389848680886093975089222003602667169315726021960706407944296875/151060633493384996963564966688071803*t^3 - 367502833554351297473919174708629846746443049387478506823459516553476695078125/151060633493384996963564966688071803*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: 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
Positive weights:   63 out of 63
Indefinite weights: 0 out of 63
Negative weights:   0 out of 63
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-1.3968491165222961633 + 1.6261470543348207982e-1413j)  +/-  (8.37e-506, 8.37e-506j)
| (-2.1953112441718457501 - 4.9703261879908585411e-1410j)  +/-  (1.14e-503, 1.14e-503j)
| (-1.7953297748411636392 - 1.6511167100706543179e-1411j)  +/-  (1.06e-504, 1.06e-504j)
| (-1 + 8.657343230437010748e-1414j)  +/-  (6.51e-507, 6.51e-507j)
| (-9.5610986836557816565 - 1.8196796934010120568e-1401j)  +/-  (2.52e-495, 2.52e-495j)
| (1.1385873772619376665e-1427 - 3.4547382519849822397e-1427j)  +/-  (2.29e-1425, 2.29e-1425j)
| (14.629220417673895979 + 2.3194006265269870539e-1407j)  +/-  (7.29e-500, 7.29e-500j)
| (-12.989209416424786707 - 1.0287244411420347056e-1422j)  +/-  (1.44e-497, 1.44e-497j)
| (11.139733534821377749 - 2.2057063365112703339e-1463j)  +/-  (6.75e-496, 6.75e-496j)
| (12.32624039189638351 - 3.9918589784364197893e-1496j)  +/-  (7.9e-497, 7.9e-497j)
| (9.5610986836557816565 - 5.5426434957308430895e-1521j)  +/-  (2.85e-495, 2.85e-495j)
| (5.477189074385718281 - 6.1448757882565797033e-1534j)  +/-  (1.77e-497, 1.77e-497j)
| (-2.596916484702306224 - 9.0562072398559175862e-1543j)  +/-  (1.11e-502, 1.11e-502j)
| (-13.732002620184482463 + 2.4668604442590375616e-1538j)  +/-  (1.78e-498, 1.78e-498j)
| (-10.592752190737217687 - 2.1207672297111157037e-1534j)  +/-  (1.41e-495, 1.41e-495j)
| (12.989209416424786707 + 7.044112081876939422e-1538j)  +/-  (1.54e-497, 1.54e-497j)
| (-5.903024129599718185 + 4.7594049602332191564e-1548j)  +/-  (5.69e-497, 5.69e-497j)
| (-11.71463354970820781 + 9.7071806324675675586e-1548j)  +/-  (2.53e-496, 2.53e-496j)
| (13.732002620184482463 + 2.2361846622662607726e-1550j)  +/-  (1.64e-498, 1.64e-498j)
| (2.1953112441718457501 + 3.4228261163261561512e-1575j)  +/-  (1.15e-503, 1.15e-503j)
| (-8.1223108429355707155 - 3.1205487365319570824e-1565j)  +/-  (2.14e-495, 2.14e-495j)
| (8.5903582054369502039 - 2.8127345244323112361e-1598j)  +/-  (2.44e-495, 2.44e-495j)
| (-14.629220417673895979 - 5.3272449641361408541e-1624j)  +/-  (8.25e-500, 8.25e-500j)
| (10.592752190737217687 - 5.4626519499873903191e-1645j)  +/-  (1.44e-495, 1.44e-495j)
| (-12.32624039189638351 + 2.3644978617780318104e-1670j)  +/-  (7.64e-497, 7.64e-497j)
| (11.71463354970820781 + 4.4375542563144145868e-1686j)  +/-  (2.5e-496, 2.5e-496j)
| (-4.2246177419336521449 - 4.5296945926620214748e-1701j)  +/-  (2.64e-499, 2.64e-499j)
| (-11.139733534821377749 + 2.4987034639042535293e-1696j)  +/-  (6.49e-496, 6.49e-496j)
| (-3.0003637609000710707 + 3.5971573479955340069e-1716j)  +/-  (1e-501, 1e-501j)
| (-10.067898021150950339 + 9.5211500434544253165e-1709j)  +/-  (2.21e-495, 2.21e-495j)
| (3.8138940104475027126 - 1.7601547819006763715e-1719j)  +/-  (4.54e-500, 4.54e-500j)
| (9.0693511133551014369 - 1.3067197268130202324e-1736j)  +/-  (2.86e-495, 2.86e-495j)
| (-3.4059215168866259405 + 8.5672390707638103692e-1771j)  +/-  (6.87e-501, 6.87e-501j)
| (-4.6384626621802307105 - 7.2730938834242838703e-1766j)  +/-  (1.15e-498, 1.15e-498j)
| (7.2134738716480872189 + 5.867775981410999185e-1772j)  +/-  (7.19e-496, 7.19e-496j)
| (10.067898021150950339 + 2.4032437866583750822e-1798j)  +/-  (2.06e-495, 2.06e-495j)
| (5.0558361406489537415 - 3.7408042796131451531e-1810j)  +/-  (4.85e-498, 4.85e-498j)
| (5.903024129599718185 - 1.9332706589148386936e-1815j)  +/-  (5.88e-497, 5.88e-497j)
| (-9.0693511133551014369 + 5.575476608509581105e-1820j)  +/-  (3.14e-495, 3.14e-495j)
| (8.1223108429355707155 - 3.7327995110609332656e-1827j)  +/-  (2.16e-495, 2.16e-495j)
| (6.3339064738120881906 + 8.0415173102717223402e-1845j)  +/-  (1.4e-496, 1.4e-496j)
| (-6.3339064738120881906 - 4.0593076186641414531e-1853j)  +/-  (1.4e-496, 1.4e-496j)
| (2.596916484702306224 - 3.1038729541060889524e-1861j)  +/-  (1.13e-502, 1.13e-502j)
| (-3.8138940104475027126 + 6.3179913166829971022e-1858j)  +/-  (4.37e-500, 4.37e-500j)
| (-8.5903582054369502039 - 2.3301682233730365417e-1853j)  +/-  (2.51e-495, 2.51e-495j)
| (1.3968491165222961633 - 7.8564258304939707334e-1866j)  +/-  (7.95e-506, 7.95e-506j)
| (4.2246177419336521449 - 2.3162389799297499932e-1856j)  +/-  (2.5e-499, 2.5e-499j)
| (7.6637497319341614913 + 1.7146086117196335283e-1864j)  +/-  (1.26e-495, 1.26e-495j)
| (-5.477189074385718281 - 2.4555153139313885476e-1873j)  +/-  (1.68e-497, 1.68e-497j)
| (1 - 2.5720174722405174247e-1883j)  +/-  (6.01e-507, 6.01e-507j)
| (0.22461862387670325177 - 1.0576039521873943287e-1885j)  +/-  (2.68e-509, 2.68e-509j)
| (-7.2134738716480872189 + 1.3535871495043888562e-1871j)  +/-  (6.97e-496, 6.97e-496j)
| (1.7953297748411636392 - 1.6080788955769518317e-1883j)  +/-  (1.03e-504, 1.03e-504j)
| (3.4059215168866259405 - 1.9331376952712300529e-1880j)  +/-  (6.68e-501, 6.68e-501j)
| (3.0003637609000710707 - 7.152162242698887895e-1881j)  +/-  (9.9e-502, 9.9e-502j)
| (-7.6637497319341614913 - 6.7456209503863794864e-1873j)  +/-  (1.36e-495, 1.36e-495j)
| (-0.60593496054742584285 + 7.6965067309676011021e-1891j)  +/-  (3.91e-508, 3.91e-508j)
| (-6.7704776798845270494 - 2.5090668975800188017e-1877j)  +/-  (3.57e-496, 3.57e-496j)
| (4.6384626621802307105 - 7.6380157490925178941e-1879j)  +/-  (1.23e-498, 1.23e-498j)
| (0.60593496054742584285 - 2.6668037404847963464e-1903j)  +/-  (3.91e-508, 3.91e-508j)
| (6.7704776798845270494 - 2.9150463567060867056e-1889j)  +/-  (3.48e-496, 3.48e-496j)
| (-5.0558361406489537415 + 1.7886840701055975098e-1900j)  +/-  (5.26e-498, 5.26e-498j)
| (-0.22461862387670325177 + 4.3783209457310105976e-1914j)  +/-  (2.68e-509, 2.68e-509j)
-------------------------------------------------
The weights are:
| (0.059813296116338843111 - 2.4321620895280155432e-1411j)  +/-  (6.87e-124, 1.06e-369j)
| (0.014364139968373510799 - 1.1124726897476823631e-1411j)  +/-  (2.13e-136, 3.29e-382j)
| (0.031784440298759398894 + 3.052396017457940069e-1411j)  +/-  (5.14e-131, 7.93e-377j)
| (0.095779767519096499659 + 2.8350061776829280493e-1411j)  +/-  (5.66e-125, 8.73e-371j)
| (2.8082911787971278439e-21 - 2.5910805861840430552e-1421j)  +/-  (7.85e-177, 1.21e-422j)
| (0.042742810561430109139 - 1.0809354679224374225e-1410j)  +/-  (5.84e-126, 9.01e-372j)
| (1.3929953877996334341e-47 + 9.2962287830230777007e-1437j)  +/-  (5.04e-189, 7.77e-435j)
| (6.4071400202740982952e-38 + 2.9708698543873719555e-1431j)  +/-  (9.07e-186, 1.4e-431j)
| (2.5254227063724265978e-28 - 7.0607766938979637614e-1427j)  +/-  (3.37e-182, 5.2e-428j)
| (2.5736400655309369267e-34 - 5.7572918984000183174e-1430j)  +/-  (8.05e-185, 1.24e-430j)
| (2.8082911787971278439e-21 + 3.2382384842534125438e-1423j)  +/-  (6.31e-179, 9.73e-425j)
| (5.1693820162312443751e-08 - 4.2318972703337942488e-1416j)  +/-  (2.13e-166, 3.28e-412j)
| (0.0055109197204371896688 - 9.4994416796812971112e-1412j)  +/-  (8.31e-148, 1.28e-393j)
| (3.6048374925351136361e-42 - 1.5494705045383673118e-1433j)  +/-  (2.73e-189, 4.21e-435j)
| (9.2056572072086761391e-26 + 2.1307391811929496302e-1424j)  +/-  (5.59e-183, 8.62e-429j)
| (6.4071400202740982952e-38 + 8.1277862918239867025e-1432j)  +/-  (1.51e-187, 2.32e-433j)
| (4.6341484157727748058e-09 - 6.8274540467046979214e-1416j)  +/-  (5.12e-171, 7.9e-417j)
| (3.7422323525469325213e-31 + 1.5457499571911786305e-1427j)  +/-  (1.1e-185, 1.69e-431j)
| (3.6048374925351136361e-42 - 5.4150604681179270301e-1434j)  +/-  (1.63e-189, 2.52e-435j)
| (0.014364139968373510799 - 1.125545101904502876e-1412j)  +/-  (3.75e-153, 5.78e-399j)
| (8.7286580316955139717e-16 + 3.1034529299237527471e-1419j)  +/-  (1.1e-178, 1.7e-424j)
| (1.7855964963781132675e-17 + 3.218380111543478779e-1421j)  +/-  (2.4e-180, 3.7e-426j)
| (1.3929953877996334341e-47 + 2.0615913212794803323e-1436j)  +/-  (1.03e-192, 1.59e-438j)
| (9.2056572072086761391e-26 + 1.4980953402923711179e-1425j)  +/-  (5.05e-184, 7.78e-430j)
| (2.5736400655309369267e-34 - 2.7240389252511050372e-1429j)  +/-  (2.68e-187, 4.13e-433j)
| (3.7422323525469325213e-31 + 2.4447891097589844766e-1428j)  +/-  (4.85e-186, 7.48e-432j)
| (2.1904141272918115855e-05 - 8.814711193844983973e-1414j)  +/-  (2.44e-169, 3.76e-415j)
| (2.5254227063724265978e-28 - 6.3256033549923613473e-1426j)  +/-  (3.4e-185, 5.25e-431j)
| (0.0017905261375143425353 + 2.4277403945283870991e-1412j)  +/-  (6.59e-164, 1.02e-409j)
| (2.0059852113815812472e-23 - 7.3821410507483030175e-1423j)  +/-  (1.73e-183, 2.67e-429j)
| (0.00011333469137823870295 - 3.8896021427511240711e-1414j)  +/-  (2.34e-171, 3.6e-417j)
| (2.6646599993534535004e-19 - 3.5174564982705883923e-1422j)  +/-  (2.08e-183, 3.21e-429j)
| (0.00049116035540357845383 - 7.7920425930578743383e-1413j)  +/-  (2.71e-167, 4.18e-413j)
| (3.5279701349582889218e-06 + 2.8514819719511025677e-1414j)  +/-  (1.25e-172, 1.93e-418j)
| (8.9460258685065668587e-13 - 1.0257617605980215528e-1418j)  +/-  (8.01e-182, 1.24e-427j)
| (2.0059852113815812472e-23 - 2.4587116036405443461e-1424j)  +/-  (3.36e-185, 5.17e-431j)
| (4.7077539415219887975e-07 + 1.4879111005209334489e-1415j)  +/-  (1.68e-177, 2.59e-423j)
| (4.6341484157727748058e-09 + 1.0963900086641020659e-1416j)  +/-  (1.53e-179, 2.36e-425j)
| (2.6646599993534535004e-19 + 1.1713509811452027543e-1420j)  +/-  (2.57e-186, 3.97e-432j)
| (8.7286580316955139717e-16 - 2.5223719596754840534e-1420j)  +/-  (1.11e-183, 1.72e-429j)
| (3.3606121514942149968e-10 - 2.5727774049451204495e-1417j)  +/-  (7.26e-181, 1.12e-426j)
| (3.3606121514942149968e-10 + 1.7081217456430038162e-1416j)  +/-  (1.02e-182, 1.57e-428j)
| (0.0055109197204371896688 + 5.2900353924497200529e-1413j)  +/-  (5.34e-174, 8.23e-420j)
| (0.00011333469137823870295 + 2.6306987073601221873e-1413j)  +/-  (8.68e-176, 1.34e-421j)
| (1.7855964963781132675e-17 - 5.640116331384712049e-1420j)  +/-  (2.93e-186, 4.52e-432j)
| (0.059813296116338843111 - 4.6048940991332903255e-1412j)  +/-  (1.46e-170, 2.25e-416j)
| (2.1904141272918115855e-05 + 1.4193772018140833839e-1414j)  +/-  (5.49e-179, 8.47e-425j)
| (3.194993792582361939e-14 + 1.7165212748636738337e-1419j)  +/-  (6.13e-184, 9.45e-430j)
| (5.1693820162312443751e-08 + 2.5323560478048935529e-1415j)  +/-  (1.3e-181, 2.01e-427j)
| (0.095779767519096499659 + 9.3482759714015338971e-1412j)  +/-  (3.28e-172, 5.06e-418j)
| (0.13899651166722258633 + 6.4766659884878524375e-1411j)  +/-  (2.19e-171, 3.38e-417j)
| (8.9460258685065668587e-13 + 8.4402175660246176397e-1418j)  +/-  (2.03e-185, 3.13e-431j)
| (0.031784440298759398894 + 2.3006662253873144509e-1412j)  +/-  (5.56e-175, 8.58e-421j)
| (0.00049116035540357845383 + 9.9089241680121961609e-1414j)  +/-  (4.46e-179, 6.87e-425j)
| (0.0017905261375143425353 - 2.3600110605033108288e-1413j)  +/-  (2.35e-178, 3.63e-424j)
| (3.194993792582361939e-14 - 1.6703907323861026923e-1418j)  +/-  (1.66e-186, 2.56e-432j)
| (0.12995853867349734873 - 3.978370232052131913e-1411j)  +/-  (4.97e-177, 7.61e-423j)
| (1.9504143184166445271e-11 - 3.9511419692408062969e-1417j)  +/-  (3.88e-185, 5.97e-431j)
| (3.5279701349582889218e-06 - 4.7904095707830992691e-1415j)  +/-  (2.23e-182, 3.41e-428j)
| (0.12995853867349734873 - 2.0856339268138407046e-1411j)  +/-  (1.84e-178, 2.48e-424j)
| (1.9504143184166445271e-11 + 5.4340160124177130035e-1418j)  +/-  (1.87e-185, 2.85e-431j)
| (4.7077539415219887975e-07 - 8.7640439647143969917e-1415j)  +/-  (3.73e-183, 5.94e-429j)
| (0.13899651166722258633 + 8.1911243201234604048e-1411j)  +/-  (3.41e-178, 3.73e-424j)
