Starting with polynomial:
P : 2*t
Extension levels are: 1 62
-------------------------------------------------
Trying to find an order 62 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^63 - 1953*t^61 + 1786995/2*t^59 - 1019182815/4*t^57 + 406653943185/8*t^55 - 120776221125945/16*t^53 + 27738272118592035/32*t^51 - 5052328135886406375/64*t^49 + 742692235975301737125/128*t^47 - 89205589676589019759125/256*t^45 + 8831353377982312956153375/512*t^43 - 724973827301638963582408875/1024*t^41 + 49539878198945329178131273125/2048*t^39 - 2823773057339883763153482568125/4096*t^37 + 134330918299168756161444242169375/8192*t^35 - 5328459759200360661070621606051875/16384*t^33 + 175839172053611901815330512999711875/32768*t^31 - 4809718529701737314360511090874471875/65536*t^29 + 108485873503272519423909305716390865625/131072*t^27 - 2004133768402560753568008752971220728125/262144*t^25 + 30062006526038411303520131294568310921875/524288*t^23 - 362175602432748479037647296072656317296875/1048576*t^21 + 3457130750494417299904815098875355756015625/2097152*t^19 - 25703015579762841664509712256855905838203125/4194304*t^17 + 145650421618656102765555036122183466416484375/8388608*t^15 - 611731770798355631615331151713170558949234375/16777216*t^13 + 1835195312395066894845993455139511676847703125/33554432*t^11 - 3738360821545506637649245927136042304689765625/67108864*t^9 + 4806463913415651391263316192032054391743984375/134217728*t^7 - 3480542833852713076432056552850798007814609375/268435456*t^5 + 1160180944617571025477352184283599335938203125/536870912*t^3 - 112275575285571389562324404930670903477890625/1073741824*t
-------------------------------------------------
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
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:
| (-9.8028759912974963635 - 1.6179545132716086104e-1311j)  +/-  (3.91e-498, 3.91e-498j)
| (-4.8979018644975742351 - 1.4527397463371271329e-1308j)  +/-  (1.19e-495, 1.19e-495j)
| (-3.9875699104197157485 + 2.5646016270512976326e-1310j)  +/-  (4.2e-497, 4.2e-497j)
| (-1.9613138583081485294 + 2.4561452999150298434e-1315j)  +/-  (5.3e-502, 5.3e-502j)
| (-3.3973817713303911853 + 3.894515007617877595e-1311j)  +/-  (4.21e-498, 4.21e-498j)
| (-2.2450734604812066299 - 4.3733539373545175337e-1315j)  +/-  (4.56e-501, 4.56e-501j)
| (-5.2097979830408354862 - 3.0506638331759850407e-1308j)  +/-  (2.42e-495, 2.42e-495j)
| (-3.1062230279282566329 + 5.5022499821763613294e-1312j)  +/-  (9.47e-499, 9.47e-499j)
| (-10.435499877854168053 - 1.8092737768030569209e-1312j)  +/-  (1.91e-499, 1.91e-499j)
| (-9.2792019543050391319 + 4.7895302820692398793e-1310j)  +/-  (3.46e-497, 3.46e-497j)
| (-7.9755950801420373182 - 7.9232960448052399609e-1309j)  +/-  (1.21e-495, 1.21e-495j)
| (-8.8118581437284546443 + 1.2499225397988556304e-1309j)  +/-  (1.91e-496, 1.91e-496j)
| (-5.8497884000810673463 - 4.7215150964030843436e-1309j)  +/-  (7.1e-495, 7.1e-495j)
| (-7.5901395198641066762 - 6.3218293392592246247e-1308j)  +/-  (2.9e-495, 2.9e-495j)
| (-6.1794379922705969862 - 1.2744995179817660292e-1308j)  +/-  (8.78e-495, 8.78e-495j)
| (-3.6910577000963465117 + 3.095902010086126045e-1311j)  +/-  (1.46e-497, 1.46e-497j)
| (-7.2203167078889678461 + 5.2368647122389910482e-1308j)  +/-  (4.88e-495, 4.88e-495j)
| (-1.6788312791720137521 + 1.070701756529309095e-1316j)  +/-  (6.78e-503, 6.78e-503j)
| (-2.5303236304712010927 - 3.2121368285956322963e-1313j)  +/-  (3.12e-500, 3.12e-500j)
| (-2.8172919672837977751 + 2.8675039026194843189e-1312j)  +/-  (1.43e-499, 1.43e-499j)
| (-8.3807683451863219343 - 4.5547020206293160585e-1309j)  +/-  (7.22e-496, 7.22e-496j)
| (-1.1168987050996462691 + 2.7765738206592066357e-1318j)  +/-  (4.3e-505, 4.3e-505j)
| (-4.2872733352824404032 + 8.0175344093869521849e-1310j)  +/-  (1.96e-496, 1.96e-496j)
| (-6.8632544331795368527 - 1.4895140571515333379e-1307j)  +/-  (8.54e-495, 8.54e-495j)
| (-5.5268572526403031425 - 1.6693902404264416811e-1308j)  +/-  (3.63e-495, 3.63e-495j)
| (-0.83707109558947615978 - 6.2231787814194972791e-1319j)  +/-  (3.69e-506, 3.69e-506j)
| (-4.5905665744435190229 - 9.7496452896406541404e-1311j)  +/-  (5.26e-496, 5.26e-496j)
| (-1.3974237486049625108 + 6.6645440382233718448e-1317j)  +/-  (4.53e-504, 4.53e-504j)
| (-6.5168348106821160605 + 1.2508550260024722707e-1307j)  +/-  (8.15e-495, 8.15e-495j)
| (6.8632544331795368527 + 1.9254448631566330829e-1306j)  +/-  (7.76e-495, 7.76e-495j)
| (8.8118581437284546443 + 8.1748559804316200039e-1321j)  +/-  (1.89e-496, 1.89e-496j)
| (6.5168348106821160605 + 2.402887077190240652e-1332j)  +/-  (8.37e-495, 8.37e-495j)
| (10.435499877854168053 - 8.7838887522181060012e-1347j)  +/-  (1.88e-499, 1.88e-499j)
| (0.83707109558947615978 - 3.1886479482827765933e-1359j)  +/-  (3.94e-506, 3.94e-506j)
| (7.9755950801420373182 - 3.7498169313295817113e-1348j)  +/-  (1.25e-495, 1.25e-495j)
| (3.9875699104197157485 - 1.0818421630864129949e-1360j)  +/-  (4.25e-497, 4.25e-497j)
| (3.1062230279282566329 - 2.0391962055417789302e-1367j)  +/-  (9.22e-499, 9.22e-499j)
| (8.3807683451863219343 - 8.2681866685384431723e-1378j)  +/-  (7.22e-496, 7.22e-496j)
| (9.2792019543050391319 + 4.3735335478656446643e-1410j)  +/-  (3.27e-497, 3.27e-497j)
| (5.8497884000810673463 + 1.2303085487861559833e-1444j)  +/-  (7.02e-495, 7.02e-495j)
| (9.8028759912974963635 + 3.6211680015980158519e-1472j)  +/-  (3.86e-498, 3.86e-498j)
| (7.2203167078889678461 + 3.2427309681775928577e-1487j)  +/-  (5.47e-495, 5.47e-495j)
| (2.2450734604812066299 + 3.3741446348183023077e-1507j)  +/-  (4.73e-501, 4.73e-501j)
| (1.1168987050996462691 - 3.3625582318340574858e-1517j)  +/-  (4.38e-505, 4.38e-505j)
| (1.9613138583081485294 + 5.3694565833870761763e-1512j)  +/-  (5.17e-502, 5.17e-502j)
| (3.6910577000963465117 - 2.6077011190305840189e-1530j)  +/-  (1.43e-497, 1.43e-497j)
| (4.8979018644975742351 + 7.2081706310359212282e-1592j)  +/-  (1.17e-495, 1.17e-495j)
| (5.2097979830408354862 + 4.7802471364711446325e-1646j)  +/-  (2.29e-495, 2.29e-495j)
| (2.5303236304712010927 - 5.4849609443468610137e-1672j)  +/-  (2.93e-500, 2.93e-500j)
| (7.5901395198641066762 - 2.0684792170313052866e-1682j)  +/-  (3.16e-495, 3.16e-495j)
| (-0.27879538567115223987 + 1.2008904745158783015e-1729j)  +/-  (6.53e-509, 6.53e-509j)
| (2.8172919672837977751 + 1.799872217508046129e-1711j)  +/-  (1.36e-499, 1.36e-499j)
| (-8.4193053081586502879e-1747 - 1.5361093716113693198e-1746j)  +/-  (1.1e-1744, 1.1e-1744j)
| (6.1794379922705969862 - 9.6978210481788131825e-1741j)  +/-  (7.93e-495, 7.93e-495j)
| (1.3974237486049625108 - 3.0849771018803485546e-1772j)  +/-  (4.68e-504, 4.68e-504j)
| (3.3973817713303911853 - 2.4717248492449758701e-1763j)  +/-  (4.57e-498, 4.57e-498j)
| (-0.55776166427908221669 - 2.7951801729698998262e-1785j)  +/-  (2.43e-507, 2.43e-507j)
| (5.5268572526403031425 + 4.614377246372494631e-1771j)  +/-  (3.46e-495, 3.46e-495j)
| (0.55776166427908221669 - 2.192781777451853036e-1791j)  +/-  (2.48e-507, 2.48e-507j)
| (4.2872733352824404032 + 1.1683628032536210268e-1778j)  +/-  (2.14e-496, 2.14e-496j)
| (1.6788312791720137521 - 2.0572468317512694617e-1796j)  +/-  (6.83e-503, 6.83e-503j)
| (4.5905665744435190229 + 1.1237925890175469555e-1787j)  +/-  (4.96e-496, 4.96e-496j)
| (0.27879538567115223987 + 7.7093166829653835697e-1831j)  +/-  (6.53e-509, 6.53e-509j)
-------------------------------------------------
The weights are:
| (5.8680109554960143265e-43 - 8.4828025886316918178e-1336j)  +/-  (7.71e-157, 2.24e-402j)
| (6.6624706976357767418e-12 - 3.2959022689997153629e-1319j)  +/-  (2.17e-138, 6.29e-384j)
| (2.0898499538350775514e-08 + 3.4506030239709648951e-1318j)  +/-  (3.25e-133, 9.44e-379j)
| (0.0034097386806714308008 - 3.2814803472615079996e-1315j)  +/-  (4.13e-116, 1.2e-361j)
| (1.6019099444515148973e-06 + 2.2624439864742620427e-1316j)  +/-  (1.34e-129, 3.88e-375j)
| (0.0010386291644793544391 + 2.6614520951573987075e-1315j)  +/-  (6.97e-120, 2.02e-365j)
| (2.8923214197654518893e-13 - 1.1462202572087184076e-1319j)  +/-  (6.79e-141, 1.97e-386j)
| (1.0555486674155470532e-05 - 1.0446528482896730198e-1316j)  +/-  (8.17e-128, 2.37e-373j)
| (2.093098582846016693e-48 + 1.4534371114444946427e-1338j)  +/-  (7.29e-161, 2.11e-406j)
| (1.1169151003963276417e-38 + 1.2788717688875754672e-1333j)  +/-  (1.22e-157, 3.54e-403j)
| (5.2716654443737682728e-29 - 1.1446580296385262756e-1328j)  +/-  (1.11e-154, 3.23e-400j)
| (4.7779793052799765668e-35 - 9.1217817431722173714e-1332j)  +/-  (7.22e-157, 2.09e-402j)
| (2.5307885261102354053e-16 - 5.1685312568800260168e-1322j)  +/-  (9.8e-148, 2.84e-393j)
| (2.0326298829658879104e-26 + 2.4712651391501766739e-1327j)  +/-  (4.87e-154, 1.41e-399j)
| (4.9042482496257813033e-18 + 5.9690670384215972842e-1323j)  +/-  (1.14e-149, 3.31e-395j)
| (2.0161164101245637805e-07 + 5.8148144875661952332e-1317j)  +/-  (4.16e-139, 1.21e-384j)
| (4.6807347381047564859e-24 - 4.149943318804665642e-1326j)  +/-  (2.23e-153, 6.46e-399j)
| (0.0094949153068523089996 + 4.2964767906960784304e-1315j)  +/-  (4.09e-128, 1.19e-373j)
| (0.00026749188751006891552 - 1.9621684536738266209e-1315j)  +/-  (6.99e-134, 2.03e-379j)
| (5.8026226157771469059e-05 + 5.3883645797994377422e-1316j)  +/-  (1.5e-135, 4.35e-381j)
| (7.3746946495350049249e-32 + 3.9115140731937691692e-1330j)  +/-  (1.41e-157, 4.08e-403j)
| (0.045398692864748827383 + 6.7610832939718206878e-1315j)  +/-  (7.22e-127, 2.09e-372j)
| (1.7699715859657334523e-09 + 1.1004655933400410764e-1317j)  +/-  (1.46e-143, 4.24e-389j)
| (6.9207048199740978517e-22 + 5.6251898209098732313e-1325j)  +/-  (3.41e-153, 9.88e-399j)
| (9.7806879129363705437e-15 + 1.240839175328852251e-1321j)  +/-  (8.64e-149, 2.5e-394j)
| (0.078264101548096858352 - 7.8188253015243465642e-1315j)  +/-  (2.6e-131, 7.54e-377j)
| (1.2134983535332409183e-10 + 1.2502093571073978711e-1318j)  +/-  (1.17e-145, 3.39e-391j)
| (0.02248761738279060688 - 5.527722664381040556e-1315j)  +/-  (7.93e-134, 2.3e-379j)
| (6.9330073798860006421e-20 - 6.2637594494767951352e-1324j)  +/-  (2.79e-152, 8.1e-398j)
| (6.9207048199740978517e-22 - 1.8638688121753548235e-1325j)  +/-  (1.1e-172, 3.2e-418j)
| (4.7779793052799765668e-35 + 3.8956143165726833126e-1332j)  +/-  (8.48e-179, 2.46e-424j)
| (6.9330073798860006421e-20 + 1.87454137802371219e-1324j)  +/-  (4.85e-172, 1.41e-417j)
| (2.093098582846016693e-48 - 7.2096816856446943873e-1339j)  +/-  (1.16e-183, 3.36e-429j)
| (0.078264101548096858352 - 4.6083845692726075645e-1315j)  +/-  (5.8e-141, 1.68e-386j)
| (5.2716654443737682728e-29 + 4.3799984626190942583e-1329j)  +/-  (5.7e-177, 1.65e-422j)
| (2.0898499538350775514e-08 + 1.3570119696597609589e-1318j)  +/-  (1.16e-165, 3.37e-411j)
| (1.0555486674155470532e-05 - 3.4637887086421054595e-1317j)  +/-  (1.1e-161, 3.19e-407j)
| (7.3746946495350049249e-32 - 1.5847361140470555927e-1330j)  +/-  (4.31e-178, 1.25e-423j)
| (1.1169151003963276417e-38 - 5.7409119472568426092e-1334j)  +/-  (3.94e-181, 1.14e-426j)
| (2.5307885261102354053e-16 + 1.1974004983806521711e-1322j)  +/-  (2.13e-173, 6.18e-419j)
| (5.8680109554960143265e-43 + 3.9984001461920828793e-1336j)  +/-  (4.48e-183, 1.3e-428j)
| (4.6807347381047564859e-24 + 1.3778803342807995624e-1326j)  +/-  (5.32e-176, 1.54e-421j)
| (0.0010386291644793544391 + 3.9644416133560572381e-1316j)  +/-  (2.2e-162, 6.39e-408j)
| (0.045398692864748827383 + 3.2873730647266731263e-1315j)  +/-  (4.75e-155, 1.38e-400j)
| (0.0034097386806714308008 - 7.5678998874826019109e-1316j)  +/-  (4.97e-161, 1.44e-406j)
| (2.0161164101245637805e-07 - 4.3911079407891475904e-1318j)  +/-  (2.03e-168, 5.89e-414j)
| (6.6624706976357767418e-12 - 2.1586106551099275197e-1320j)  +/-  (9.49e-173, 2.75e-418j)
| (2.8923214197654518893e-13 + 4.3372500149640923189e-1321j)  +/-  (1.48e-173, 4.3e-419j)
| (0.00026749188751006891552 - 1.9142172020009460813e-1316j)  +/-  (2.31e-166, 6.71e-412j)
| (2.0326298829658879104e-26 - 8.8702685932190623073e-1328j)  +/-  (6.7e-179, 1.94e-424j)
| (0.14556029162597161507 - 8.6347622163632392489e-1315j)  +/-  (1.72e-161, 4.98e-407j)
| (5.8026226157771469059e-05 + 8.5009439003692752315e-1317j)  +/-  (1.09e-167, 3.16e-413j)
| (0.15727740877813796956 + 8.2041326311393036962e-1315j)  +/-  (1.84e-163, 5.32e-409j)
| (4.9042482496257813033e-18 - 1.6150990382287216825e-1323j)  +/-  (7.61e-176, 2.21e-421j)
| (0.02248761738279060688 - 2.1757238145052516568e-1315j)  +/-  (8.1e-166, 2.35e-411j)
| (1.6019099444515148973e-06 + 1.2913465713312289277e-1317j)  +/-  (6.39e-170, 1.85e-415j)
| (0.11536940911860985222 + 8.4912696223647436123e-1315j)  +/-  (1.79e-164, 5.19e-410j)
| (9.7806879129363705437e-15 - 7.7000279460858179687e-1322j)  +/-  (7.37e-175, 2.14e-420j)
| (0.11536940911860985222 + 6.0017033904362898798e-1315j)  +/-  (4.73e-167, 1.36e-412j)
| (1.7699715859657334523e-09 - 3.795607897406754608e-1319j)  +/-  (5.7e-173, 1.65e-418j)
| (0.0094949153068523089996 + 1.3341418973191581114e-1315j)  +/-  (6.06e-169, 1.67e-414j)
| (1.2134983535332409183e-10 + 9.563265054092624685e-1320j)  +/-  (1.29e-173, 3.76e-419j)
| (0.14556029162597161507 - 7.2707727018402323599e-1315j)  +/-  (5.84e-168, 1.55e-413j)
