Starting with polynomial:
P : t
Extension levels are: 1 74
-------------------------------------------------
Trying to find an order 74 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^75 - 2775*t^73 + 3646350*t^71 - 3020393250*t^69 + 1771460641125*t^67 - 783339895505475*t^65 + 271557830441898000*t^63 - 75764634693289542000*t^61 + 17331160186089982732500*t^59 - 3294846119822217828367500*t^57 + 525857440723625965407453000*t^55 - 70990754497689505330006155000*t^53 + 8152104974818011528729040132500*t^51 - 799533372530228053779194320687500*t^49 + 67160803292539156517452322937750000*t^47 - 4840055223948988546357730739713850000*t^45 + 299478416981843666305884589519794468750*t^43 - 15907588854976754745541987313904376781250*t^41 + 724679047837829938408023866522310497812500*t^39 - 28262482865675367597912930794370109414687500*t^37 + 941140679426989741010500595452524643509093750*t^35 - 26665652583764709328630850204488198232757656250*t^33 + 639975662010353023887140404907716757586183750000*t^31 - 12938638384122354613370447316612534446851106250000*t^29 + 218878632664736498876183400439362041059231214062500*t^27 - 3073056002612900444221614942168643056471606245437500*t^25 + 35458338491687312817941710871176650651595456678125000*t^23 - 332257764385070005294046401866951578327912982946875000*t^21 + 2491933232888025039705348014002136837459347372101562500*t^19 - 14693813200822492475503948634288462041570634504460937500*t^17 + 66611953177061965888951233808774361255120209753556250000*t^15 - 225621131728758271559350953223267997799600710455593750000*t^13 + 549951508588848286925917948481715744636526731735509765625*t^11 - 916585847648080478209863247469526241060877886225849609375*t^9 + 970502662215614623986914026732439549358576585415605468750*t^7 - 582301597329368774392148416039463729615145951249363281250*t^5 + 161750443702602437331152337788739924893096097569267578125*t^3 - 13114900840751548972796135496384318234575359262373046875*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
-------------------------------------------------
The nodes are:
| (-14.649231488377466584 + 8.8901460550412703514e-1291j)  +/-  (4.59e-495, 4.59e-495j)
| (-15.366113578843672881 + 4.7692372515429047933e-1292j)  +/-  (3.72e-496, 3.72e-496j)
| (-13.421465202006966352 + 3.1242713482869344671e-1289j)  +/-  (1.5e-493, 1.5e-493j)
| (16.233277100611433587 + 2.9810886163721380108e-1287j)  +/-  (1.66e-497, 1.66e-497j)
| (-14.01022598478736488 - 2.9801009795058601368e-1292j)  +/-  (3.53e-494, 3.53e-494j)
| (13.421465202006966352 + 1.3611488463351585056e-1295j)  +/-  (1.56e-493, 1.56e-493j)
| (5.517429288090624187 - 3.4346737035137628983e-1311j)  +/-  (3.02e-495, 3.02e-495j)
| (11.35458872821159597 + 2.6214983400119672553e-1332j)  +/-  (6.4e-492, 6.4e-492j)
| (-8.2789098103041333113 - 2.6901776282566129564e-1347j)  +/-  (3.66e-492, 3.66e-492j)
| (2.175007555551530875 + 2.1277459082206060478e-1363j)  +/-  (1.73e-502, 1.73e-502j)
| (-16.233277100611433587 + 3.9829369607822667387e-1358j)  +/-  (1.71e-497, 1.71e-497j)
| (-9.1142429327466782564 + 4.0394471364373931857e-1351j)  +/-  (6.17e-492, 6.17e-492j)
| (12.343460677058588425 - 1.0267291866222951157e-1367j)  +/-  (1.56e-492, 1.56e-492j)
| (-5.1375802711046107365 - 8.1415777432036813898e-1386j)  +/-  (7.45e-496, 7.45e-496j)
| (-11.840066370001286069 - 7.1380866661334840576e-1381j)  +/-  (3.4e-492, 3.4e-492j)
| (12.868720405524555785 + 1.4857200858158463807e-1388j)  +/-  (6.2e-493, 6.2e-493j)
| (-10.426434490376407201 + 4.9755373501643262471e-1394j)  +/-  (9.17e-492, 9.17e-492j)
| (-8.6932257561750679984 - 1.2710465029763456427e-1394j)  +/-  (4.85e-492, 4.85e-492j)
| (14.649231488377466584 + 7.1860492825354369581e-1396j)  +/-  (4.81e-495, 4.81e-495j)
| (-4.013033550011849763 + 4.6081840476725855508e-1403j)  +/-  (6.52e-498, 6.52e-498j)
| (15.366113578843672881 - 9.4029869883461270613e-1400j)  +/-  (3.39e-496, 3.39e-496j)
| (1.4478875919404804897 + 8.1937711179046380935e-1411j)  +/-  (8.7e-505, 8.7e-505j)
| (-9.5427764059401307103 - 5.7489200913118086165e-1396j)  +/-  (8.52e-492, 8.52e-492j)
| (-6.2863027207039867538 + 3.1463053316987686493e-1401j)  +/-  (4.28e-494, 4.28e-494j)
| (14.01022598478736488 - 3.749538164423333898e-1398j)  +/-  (3.35e-494, 3.35e-494j)
| (-1.8110468094728801151 + 2.5119551274301560432e-1415j)  +/-  (1.14e-503, 1.14e-503j)
| (5.9002336364869002995 + 4.6501891545968344685e-1402j)  +/-  (1.38e-494, 1.38e-494j)
| (7.0696291535639913609 + 1.1174183289200339016e-1416j)  +/-  (3.11e-493, 3.11e-493j)
| (6.2863027207039867538 - 6.9128062132610609012e-1455j)  +/-  (4.12e-494, 4.12e-494j)
| (-3.6423712491727554255 - 1.2875759287732497753e-1486j)  +/-  (7.99e-499, 7.99e-499j)
| (-12.343460677058588425 - 1.1313288838992312005e-1482j)  +/-  (1.58e-492, 1.58e-492j)
| (2.5399403369940129509 + 2.9807913578783711075e-1520j)  +/-  (1.63e-501, 1.63e-501j)
| (10.426434490376407201 - 1.8601768583453102831e-1524j)  +/-  (8.59e-492, 8.59e-492j)
| (4.3856349862626040773 + 2.4100636151037822816e-1557j)  +/-  (3.14e-497, 3.14e-497j)
| (-2.175007555551530875 + 9.473464373735254459e-1568j)  +/-  (1.7e-502, 1.7e-502j)
| (9.5427764059401307103 + 8.1622984322902001888e-1556j)  +/-  (8.38e-492, 8.38e-492j)
| (-6.6759761260812720721 + 1.2527312446220369999e-1570j)  +/-  (1.15e-493, 1.15e-493j)
| (4.013033550011849763 + 1.6018748127645356928e-1574j)  +/-  (6.56e-498, 6.56e-498j)
| (7.8705963542516114839 - 1.7011189133306070044e-1567j)  +/-  (1.17e-492, 1.17e-492j)
| (11.840066370001286069 - 4.0930462843771929553e-1579j)  +/-  (3.58e-492, 3.58e-492j)
| (9.1142429327466782564 - 5.8587714451417199245e-1602j)  +/-  (6.18e-492, 6.18e-492j)
| (8.2789098103041333113 + 8.5014826673627926661e-1629j)  +/-  (3.26e-492, 3.26e-492j)
| (-10.884118784597433379 - 2.1234591865842660929e-1638j)  +/-  (6.61e-492, 6.61e-492j)
| (-12.868720405524555785 + 1.1824687104934864042e-1647j)  +/-  (6.07e-493, 6.07e-493j)
| (-5.517429288090624187 - 4.2651310194983336728e-1661j)  +/-  (3e-495, 3e-495j)
| (-7.0696291535639913609 + 3.4553457450496087404e-1664j)  +/-  (3.26e-493, 3.26e-493j)
| (9.9797889894026804144 - 1.3431240366776516271e-1689j)  +/-  (8.91e-492, 8.91e-492j)
| (-4.7604028116585082927 + 1.5684944683460333378e-1711j)  +/-  (1.69e-496, 1.69e-496j)
| (0.36157880978360518116 + 5.5812849175720385025e-1723j)  +/-  (1.18e-508, 1.18e-508j)
| (1.8110468094728801151 + 1.6230182889245777576e-1718j)  +/-  (1.14e-503, 1.14e-503j)
| (-0.36157880978360518116 + 9.8559917119855348499e-1723j)  +/-  (1.33e-508, 1.33e-508j)
| (-2.5399403369940129509 + 1.6277310381261694955e-1716j)  +/-  (1.62e-501, 1.62e-501j)
| (-9.9797889894026804144 + 5.3366597860906768316e-1705j)  +/-  (8.62e-492, 8.62e-492j)
| (-1.4478875919404804897 + 2.7175841085357251026e-1733j)  +/-  (9.53e-505, 9.53e-505j)
| (-11.35458872821159597 + 3.4783186649175800281e-1718j)  +/-  (6.33e-492, 6.33e-492j)
| (2.9060215125326179993 - 6.7909532049329773795e-1752j)  +/-  (1.74e-500, 1.74e-500j)
| (-1.0853641253687033217 - 1.9209701257729532866e-1758j)  +/-  (7.3e-506, 7.3e-506j)
| (-3.2734345220241972895 - 7.6569612333890387629e-1751j)  +/-  (1.09e-499, 1.09e-499j)
| (10.884118784597433379 + 3.9127614161967753006e-1741j)  +/-  (6.5e-492, 6.5e-492j)
| (6.6759761260812720721 + 3.8932262383523638935e-1757j)  +/-  (1.27e-493, 1.27e-493j)
| (1.0853641253687033217 + 1.6169948959066829758e-1776j)  +/-  (6.73e-506, 6.73e-506j)
| (-7.8705963542516114839 + 1.1249517306034622408e-1762j)  +/-  (1.11e-492, 1.11e-492j)
| (-5.9002336364869002995 - 7.8510328814237368963e-1766j)  +/-  (1.38e-494, 1.38e-494j)
| (-4.3856349862626040773 - 7.7231161042178755794e-1769j)  +/-  (3.26e-497, 3.26e-497j)
| (8.6932257561750679984 + 6.4425890948052108534e-1762j)  +/-  (4.65e-492, 4.65e-492j)
| (3.2734345220241972895 - 7.9201723680753281589e-1782j)  +/-  (1.13e-499, 1.13e-499j)
| (-3.4847322393709407114e-1820 - 1.7378004059395807224e-1819j)  +/-  (1.33e-1817, 1.33e-1817j)
| (4.7604028116585082927 + 2.8972801691938646902e-1778j)  +/-  (1.72e-496, 1.72e-496j)
| (-2.9060215125326179993 + 3.1464360756284415309e-1783j)  +/-  (1.7e-500, 1.7e-500j)
| (7.4676796256647639057 + 9.4521733554633068533e-1774j)  +/-  (6.82e-493, 6.82e-493j)
| (0.72331432227767647704 - 1.6031900130735997073e-1797j)  +/-  (4.82e-507, 4.82e-507j)
| (5.1375802711046107365 - 4.107414875358045633e-1786j)  +/-  (8.07e-496, 8.07e-496j)
| (-7.4676796256647639057 + 3.2483288204688612139e-1784j)  +/-  (6.76e-493, 6.76e-493j)
| (-0.72331432227767647704 - 4.0376950945450574178e-1798j)  +/-  (4.82e-507, 4.82e-507j)
| (3.6423712491727554255 + 2.2326442498826281709e-1789j)  +/-  (7.68e-499, 7.68e-499j)
-------------------------------------------------
The weights are:
| (6.73196777064783938e-48 - 8.703946113451934122e-1333j)  +/-  (2.12e-167, 1.16e-412j)
| (1.6462690981313147968e-52 + 2.717659137356641859e-1335j)  +/-  (3.49e-169, 1.91e-414j)
| (1.7379568545505588668e-40 + 3.6438449275628417224e-1328j)  +/-  (1.86e-165, 1.02e-410j)
| (2.3964180523247840393e-58 + 2.1500743772783467393e-1339j)  +/-  (7.34e-175, 4.01e-420j)
| (5.8043087959232874624e-44 + 1.68527640689079506e-1330j)  +/-  (1.72e-166, 9.39e-412j)
| (1.7379568545505588668e-40 + 2.0226960223426269639e-1330j)  +/-  (4.46e-169, 2.44e-414j)
| (3.7303464887411851309e-08 + 4.2008176783363605155e-1314j)  +/-  (2.57e-143, 1.41e-388j)
| (1.9224696335568582429e-29 + 7.2890356668584297937e-1325j)  +/-  (2.77e-164, 1.52e-409j)
| (2.1459659314638432789e-16 - 1.1733015271561818625e-1317j)  +/-  (5.16e-155, 2.82e-400j)
| (0.013654017656194762919 - 3.085919388412589371e-1311j)  +/-  (2.2e-118, 1.2e-363j)
| (2.3964180523247840393e-58 - 2.2676555669966010728e-1338j)  +/-  (1.97e-173, 1.07e-418j)
| (1.5510392996203341843e-19 - 3.7660932791583474989e-1319j)  +/-  (6.46e-158, 3.53e-403j)
| (1.6854799461897554852e-34 + 2.0754074740763832641e-1327j)  +/-  (5.63e-168, 3.08e-413j)
| (2.8015351120256180515e-07 - 2.6317331136413388249e-1313j)  +/-  (1.52e-144, 8.33e-390j)
| (7.1330216612233448644e-32 - 6.9561755526334578577e-1325j)  +/-  (3.65e-165, 1.99e-410j)
| (2.3504511766040101569e-37 - 7.5953545776483893743e-1329j)  +/-  (2.22e-169, 1.22e-414j)
| (4.4644186836303139056e-25 + 9.1887740682064194577e-1322j)  +/-  (3.37e-162, 1.85e-407j)
| (6.4762025047971534469e-18 + 2.2168577947407435652e-1318j)  +/-  (3.87e-157, 2.12e-402j)
| (6.73196777064783938e-48 + 3.8071248727881462154e-1334j)  +/-  (9.51e-175, 5.2e-420j)
| (4.7200416271767593941e-05 + 3.0076947844440058039e-1312j)  +/-  (6.11e-143, 3.34e-388j)
| (1.6462690981313147968e-52 - 1.8357874930865096274e-1336j)  +/-  (1.27e-176, 6.96e-422j)
| (0.050742442003969058946 - 6.2398429284387655032e-1311j)  +/-  (1.97e-121, 1.08e-366j)
| (2.9011639637145324892e-21 + 5.7197625964423807052e-1320j)  +/-  (5.86e-161, 3.21e-406j)
| (4.0587560354841126466e-10 + 1.1629746671096219582e-1314j)  +/-  (2.08e-153, 1.14e-398j)
| (5.8043087959232874624e-44 - 3.6174839042124734454e-1332j)  +/-  (2.74e-173, 1.5e-418j)
| (0.028134132060466145086 + 5.9504179166915334317e-1311j)  +/-  (3.01e-129, 1.65e-374j)
| (4.2284372216695220929e-09 - 1.3860746658467494898e-1314j)  +/-  (1.58e-155, 8.65e-401j)
| (2.2152228704211189204e-12 + 2.9916549482316434599e-1316j)  +/-  (1.49e-160, 8.15e-406j)
| (4.0587560354841126466e-10 + 4.2103516262796141103e-1315j)  +/-  (2.14e-157, 1.17e-402j)
| (0.00019407605941249404897 - 5.8676678350915434177e-1312j)  +/-  (2.9e-146, 1.59e-391j)
| (1.6854799461897554852e-34 + 4.9603865133162975464e-1326j)  +/-  (9.73e-171, 5.32e-416j)
| (0.0057928040339243874553 + 1.964058874777687452e-1311j)  +/-  (5.13e-141, 2.81e-386j)
| (4.4644186836303139056e-25 + 1.1539982750144687131e-1322j)  +/-  (1.15e-169, 6.29e-415j)
| (9.9266904057990784813e-06 - 7.2878166776797672623e-1313j)  +/-  (8.66e-153, 4.73e-398j)
| (0.013654017656194762919 - 4.279499321730681788e-1311j)  +/-  (1.11e-140, 6.07e-386j)
| (2.9011639637145324892e-21 + 9.6606574428485771207e-1321j)  +/-  (2.35e-168, 1.28e-413j)
| (3.2793584144169020244e-11 - 3.4967015784236845169e-1315j)  +/-  (1.52e-160, 8.32e-406j)
| (4.7200416271767593941e-05 + 1.6231138019130008652e-1312j)  +/-  (3.13e-152, 1.71e-397j)
| (5.7208165983180591026e-15 + 1.4631270107665297404e-1317j)  +/-  (8.24e-165, 4.51e-410j)
| (7.1330216612233448644e-32 - 4.3546068866791216962e-1326j)  +/-  (1.06e-172, 5.81e-418j)
| (1.5510392996203341843e-19 - 7.1980123933456071877e-1320j)  +/-  (4.77e-168, 2.61e-413j)
| (2.1459659314638432789e-16 - 2.7804536368984312826e-1318j)  +/-  (3.07e-166, 1.68e-411j)
| (3.4918525679334391583e-27 - 9.5923340300100038674e-1323j)  +/-  (8.99e-174, 4.91e-419j)
| (2.3504511766040101569e-37 - 3.6126312357841352038e-1327j)  +/-  (6.9e-178, 3.77e-423j)
| (3.7303464887411851309e-08 + 1.0064761252265087941e-1313j)  +/-  (2.21e-163, 1.21e-408j)
| (2.2152228704211189204e-12 + 9.6513245904886746942e-1316j)  +/-  (6.35e-167, 3.47e-412j)
| (4.1583350763978992287e-23 - 1.134993583621079763e-1321j)  +/-  (1.96e-172, 1.07e-417j)
| (1.7994911753710221612e-06 + 6.3794264156764435773e-1313j)  +/-  (4.76e-162, 2.6e-407j)
| (0.13514066563165885894 + 1.0985687633845225638e-1310j)  +/-  (2.42e-150, 1.32e-395j)
| (0.028134132060466145086 + 4.5355043401924787549e-1311j)  +/-  (7.34e-153, 4.01e-398j)
| (0.13514066563165885894 + 1.1593983337846311078e-1310j)  +/-  (1.09e-150, 5.95e-396j)
| (0.0057928040339243874553 + 2.8809323169967003174e-1311j)  +/-  (3.7e-156, 2.02e-401j)
| (4.1583350763978992287e-23 - 7.7173171783563734101e-1321j)  +/-  (2.45e-172, 1.34e-417j)
| (0.050742442003969058946 - 7.748906630592598055e-1311j)  +/-  (9.06e-153, 4.95e-398j)
| (1.9224696335568582429e-29 + 8.7375756227557547442e-1324j)  +/-  (2.53e-175, 1.38e-420j)
| (0.0021450616332283533694 - 1.1683753295764875562e-1311j)  +/-  (2.42e-160, 1.33e-405j)
| (0.080191351631714854551 + 9.4550675803231724643e-1311j)  +/-  (6.68e-153, 3.65e-398j)
| (0.00069200902322717366738 + 1.0677076147187121934e-1311j)  +/-  (3.37e-160, 1.84e-405j)
| (3.4918525679334391583e-27 - 1.0013701356229921684e-1323j)  +/-  (6.14e-176, 3.36e-421j)
| (3.2793584144169020244e-11 - 1.173596379351013784e-1315j)  +/-  (1.1e-168, 6e-414j)
| (0.080191351631714854551 + 8.0402776065989556161e-1311j)  +/-  (1.04e-155, 5.7e-401j)
| (5.7208165983180591026e-15 + 5.612357830170528058e-1317j)  +/-  (9.19e-170, 5.02e-415j)
| (4.2284372216695220929e-09 - 3.5610552074504998762e-1314j)  +/-  (3.93e-166, 2.15e-411j)
| (9.9266904057990784813e-06 - 1.4361909542376926584e-1312j)  +/-  (8.53e-164, 4.66e-409j)
| (6.4762025047971534469e-18 + 4.7397054819617236487e-1319j)  +/-  (6.2e-173, 3.39e-418j)
| (0.00069200902322717366738 + 6.4901496756926790796e-1312j)  +/-  (2.74e-165, 1.5e-410j)
| (0.14423866742684052088 - 1.1655210309827218836e-1310j)  +/-  (1.8e-160, 9.84e-406j)
| (1.7994911753710221612e-06 + 3.038998856612821459e-1313j)  +/-  (5.35e-168, 2.92e-413j)
| (0.0021450616332283533694 - 1.8141391587904696885e-1311j)  +/-  (1.82e-164, 9.95e-410j)
| (1.2414235683278477463e-13 - 6.9471865524449234577e-1317j)  +/-  (1.24e-171, 6.79e-417j)
| (0.11113485782850290627 - 9.7075250941076238691e-1311j)  +/-  (9.42e-164, 5.17e-409j)
| (2.8015351120256180515e-07 - 1.1747729212306978192e-1313j)  +/-  (1.22e-168, 6.66e-414j)
| (1.2414235683278477463e-13 - 2.4374976431335174708e-1316j)  +/-  (7.59e-172, 4.34e-417j)
| (0.11113485782850290627 - 1.0813432571574208074e-1310j)  +/-  (5.16e-165, 2.99e-410j)
| (0.00019407605941249404897 - 3.3627385278936957018e-1312j)  +/-  (4.05e-167, 2.19e-412j)
