Starting with polynomial:
P : 2*t
Extension levels are: 1 68
-------------------------------------------------
Trying to find an order 68 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^69 - 2346*t^67 + 2593503/2*t^65 - 449540520*t^63 + 109744079445*t^61 - 20083166538435*t^59 + 11454099315754095/4*t^57 - 652883660997983415/2*t^55 + 969532236582005371275/32*t^53 - 74223079000555744534275/32*t^51 + 18926885145141714856240125/128*t^49 - 252932010575984734897027125/32*t^47 + 91139834477546499474562107375/256*t^45 - 3470324466645039787685249473125/256*t^43 + 447671856197210132611397182033125/1024*t^41 - 6118182034695205145689094821119375/512*t^39 + 4533572887709147012955619262449456875/16384*t^37 - 88804692447479173842013012611509949375/16384*t^35 + 5870976889583345381777526944872046653125/65536*t^33 - 10196959860855284084139915220040923134375/8192*t^31 + 948317267059541419825012115463805851496875/65536*t^29 - 9167066914908900391641783782816789897803125/65536*t^27 + 292512771557547639769660555251699386738990625/262144*t^25 - 953845994209394477509762680168584956757578125/131072*t^23 + 80441012178325600936656652694217331353222421875/2097152*t^21 - 337852251148967523933957941315712791683534171875/2097152*t^19 + 4444056534344111276362062151152837490606487953125/8388608*t^17 - 2798109669772218211042779872948082864455936859375/2097152*t^15 + 41971645046583273165641698094221242966839052890625/16777216*t^13 - 56444626097129229429656076747400981920921484921875/16777216*t^11 + 206963629022807174575405614740470267043378778046875/67108864*t^9 - 60086214877589179715440339763362335593239000078125/33554432*t^7 + 1261810512429372774024247135030609047458019001640625/2147483648*t^5 - 191183410974147390003673808337971067796669545703125/2147483648*t^3 + 33738248995437774706530672059641953140588743359375/8589934592*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:
| (10.96871671227272066 - 2.3266922425942691232e-1448j)  +/-  (1.23e-498, 1.23e-498j)
| (10.346335043862190691 + 2.7738042673936565779e-1445j)  +/-  (3.45e-497, 3.45e-497j)
| (9.8315026740330877716 + 2.6995264740583979764e-1443j)  +/-  (3.83e-496, 3.83e-496j)
| (-9.8315026740330877716 - 4.9654790185694970175e-1446j)  +/-  (3.83e-496, 3.83e-496j)
| (8.9490694985983320076 - 8.1658699641141272213e-1442j)  +/-  (9.28e-495, 9.28e-495j)
| (-9.3723455663368829416 - 6.7390804963377384517e-1450j)  +/-  (2.13e-495, 2.13e-495j)
| (-10.96871671227272066 - 6.8654584893227232125e-1454j)  +/-  (1.22e-498, 1.22e-498j)
| (9.3723455663368829416 - 3.4285349752072587065e-1447j)  +/-  (2.18e-495, 2.18e-495j)
| (-3.5168876985063169805 - 4.3374829816538496508e-1454j)  +/-  (4.23e-497, 4.23e-497j)
| (-7.4612754898399771593 - 3.9074020406335008563e-1451j)  +/-  (1.52e-493, 1.52e-493j)
| (1.8731503781015580668 + 6.0831159008632367672e-1459j)  +/-  (7.58e-502, 7.58e-502j)
| (-3.2387596283073630946 - 8.7440580720304165633e-1455j)  +/-  (9.9e-498, 9.9e-498j)
| (-1.8731503781015580668 + 2.0051264864472794566e-1459j)  +/-  (7.65e-502, 7.65e-502j)
| (-8.5514820514248042555 + 1.2852310039795447214e-1451j)  +/-  (3.07e-494, 3.07e-494j)
| (4.3652936245432167645 + 9.7065085322807517243e-1451j)  +/-  (2.59e-495, 2.59e-495j)
| (-5.2408902012860349472 - 2.2124362838693150128e-1458j)  +/-  (3.7e-494, 3.7e-494j)
| (-1.3351739542940309502 + 4.2292990780586809435e-1477j)  +/-  (6.01e-504, 6.01e-504j)
| (5.2408902012860349472 - 2.4641427958668524369e-1465j)  +/-  (3.36e-494, 3.36e-494j)
| (-10.346335043862190691 + 4.9673764593146017903e-1479j)  +/-  (3.47e-497, 3.47e-497j)
| (1.3351739542940309502 + 2.9666288070423355461e-1486j)  +/-  (6.24e-504, 6.24e-504j)
| (-7.1221736773103954472 - 1.3578778384043277003e-1474j)  +/-  (2.03e-493, 2.03e-493j)
| (3.7971816649246473504 - 2.0813693382655159252e-1480j)  +/-  (1.69e-496, 1.69e-496j)
| (-4.9454294985999852187 + 2.0578461518345479712e-1477j)  +/-  (1.59e-494, 1.59e-494j)
| (2.1435714896364329484 + 1.6220556633371985518e-1484j)  +/-  (7.52e-501, 7.52e-501j)
| (3.5168876985063169805 - 9.3339703015968114366e-1482j)  +/-  (4.7e-497, 4.7e-497j)
| (-7.8110131087611867601 - 1.2685077570934993648e-1475j)  +/-  (9.2e-494, 9.2e-494j)
| (-2.4151642892936242479 - 5.9076167957649266976e-1485j)  +/-  (5.41e-500, 5.41e-500j)
| (3.2387596283073630946 + 7.5366109284780798224e-1483j)  +/-  (9.88e-498, 9.88e-498j)
| (-8.9490694985983320076 - 4.3303849490647993485e-1479j)  +/-  (9.33e-495, 9.33e-495j)
| (-4.3652936245432167645 + 2.2757381222247629419e-1480j)  +/-  (2.66e-495, 2.66e-495j)
| (-8.1734720117891596127 + 2.0824427886808600275e-1477j)  +/-  (7.53e-494, 7.53e-494j)
| (-6.7921138299353222519 + 1.0118077169591558362e-1479j)  +/-  (2.46e-493, 2.46e-493j)
| (-1.6037367745786485213 - 1.4107226564564958046e-1496j)  +/-  (9.46e-503, 9.46e-503j)
| (2.4151642892936242479 + 3.8891523980157583561e-1493j)  +/-  (5.36e-500, 5.36e-500j)
| (5.5405131730790885288 + 1.2258801854354953652e-1485j)  +/-  (6.38e-494, 6.38e-494j)
| (-5.844803327699797846 - 8.8840950175983696131e-1496j)  +/-  (1.28e-493, 1.28e-493j)
| (-5.5405131730790885288 + 2.5121845119428796732e-1498j)  +/-  (6.65e-494, 6.65e-494j)
| (1.067311311962256223 - 4.5462448270540954806e-1509j)  +/-  (5.57e-505, 5.57e-505j)
| (4.9454294985999852187 + 2.122962378083564439e-1496j)  +/-  (1.67e-494, 1.67e-494j)
| (-2.1435714896364329484 + 1.8150500326061515266e-1514j)  +/-  (7.39e-501, 7.39e-501j)
| (-2.9625681999937007656 + 1.8212855874427111044e-1511j)  +/-  (2.22e-498, 2.22e-498j)
| (4.6536923643912965965 + 1.9040045337079941976e-1505j)  +/-  (6.2e-495, 6.2e-495j)
| (-3.1686872715395051378e-1559 - 1.4918721115791859861e-1558j)  +/-  (1.05e-1556, 1.05e-1556j)
| (-1.067311311962256223 + 2.4941635380336958935e-1520j)  +/-  (5.17e-505, 5.17e-505j)
| (1.6037367745786485213 - 3.5067498636565746341e-1519j)  +/-  (9.04e-503, 9.04e-503j)
| (4.0798918452871911585 - 6.2965639466279653689e-1509j)  +/-  (9.04e-496, 9.04e-496j)
| (0.53310762988307845661 - 8.5537516253137983418e-1523j)  +/-  (2.98e-507, 2.98e-507j)
| (-4.6536923643912965965 - 4.2802586775572240225e-1510j)  +/-  (6.36e-495, 6.36e-495j)
| (-0.80000315987311327285 - 2.6308223988066048033e-1522j)  +/-  (4.37e-506, 4.37e-506j)
| (-2.6881019184401618579 + 1.3208257502052819205e-1514j)  +/-  (2.87e-499, 2.87e-499j)
| (-0.53310762988307845661 - 1.3625121297300750487e-1522j)  +/-  (2.89e-507, 2.89e-507j)
| (0.80000315987311327285 - 8.0535422793935340376e-1522j)  +/-  (4.62e-506, 4.62e-506j)
| (-4.0798918452871911585 - 8.9297163823456600994e-1511j)  +/-  (9.23e-496, 9.23e-496j)
| (-6.4698421035199564134 + 5.2278854875850679799e-1508j)  +/-  (2.13e-493, 2.13e-493j)
| (-6.1543485281550765809 - 4.8261593037360789243e-1521j)  +/-  (1.74e-493, 1.74e-493j)
| (-3.7971816649246473504 + 1.8301981891818164879e-1535j)  +/-  (1.68e-496, 1.68e-496j)
| (2.9625681999937007656 + 1.556308708114283775e-1535j)  +/-  (2.24e-498, 2.24e-498j)
| (2.6881019184401618579 - 4.0612525251670826642e-1541j)  +/-  (2.92e-499, 2.92e-499j)
| (-0.26648565380755117484 + 2.4816076144794697242e-1566j)  +/-  (8.78e-509, 8.78e-509j)
| (0.26648565380755117484 + 4.5732386091280686288e-1566j)  +/-  (8.78e-509, 8.78e-509j)
| (6.4698421035199564134 + 9.0210616303150884685e-1567j)  +/-  (2.19e-493, 2.19e-493j)
| (7.8110131087611867601 - 3.914538792168954363e-1621j)  +/-  (9.18e-494, 9.18e-494j)
| (6.7921138299353222519 + 1.4416338309654355773e-1671j)  +/-  (2.41e-493, 2.41e-493j)
| (8.5514820514248042555 + 4.5844712554827664512e-1731j)  +/-  (3.06e-494, 3.06e-494j)
| (5.844803327699797846 - 3.5874490993708726715e-1796j)  +/-  (1.34e-493, 1.34e-493j)
| (7.4612754898399771593 - 1.9440937190981069198e-1852j)  +/-  (1.47e-493, 1.47e-493j)
| (7.1221736773103954472 - 6.357919944468108437e-1892j)  +/-  (1.95e-493, 1.95e-493j)
| (8.1734720117891596127 + 3.96762145572579932e-1916j)  +/-  (7.9e-494, 7.9e-494j)
| (6.1543485281550765809 - 4.3850756756574782313e-1933j)  +/-  (1.68e-493, 1.68e-493j)
-------------------------------------------------
The weights are:
| (2.2762487188790489321e-53 + 2.0588239722786039173e-1482j)  +/-  (1.28e-178, 3.8e-425j)
| (1.0129676599978398454e-47 - 1.5160413785697107257e-1479j)  +/-  (4.58e-177, 1.36e-423j)
| (2.8613046012491353855e-43 + 2.7872896224763741649e-1477j)  +/-  (6.66e-176, 1.98e-422j)
| (2.8613046012491353855e-43 - 1.0861692118463336258e-1477j)  +/-  (3.11e-179, 9.23e-426j)
| (3.8237363731336350571e-36 + 1.2179977159715692629e-1473j)  +/-  (1.75e-174, 5.18e-421j)
| (1.7583071667421166102e-39 + 8.8049532244456682724e-1476j)  +/-  (4.9e-178, 1.45e-424j)
| (2.2762487188790489321e-53 - 8.9579219534371978288e-1483j)  +/-  (4.31e-183, 1.28e-429j)
| (1.7583071667421166102e-39 - 2.384292773057635256e-1475j)  +/-  (5.5e-176, 1.63e-422j)
| (6.6946015817882094603e-07 + 1.3925647387302540934e-1459j)  +/-  (4.99e-154, 1.48e-400j)
| (1.2902859558724301201e-25 - 8.8006714006119444545e-1469j)  +/-  (2.43e-173, 7.21e-420j)
| (0.0045583451023265358501 + 7.6794903151939900095e-1457j)  +/-  (1.19e-139, 3.53e-386j)
| (4.3504891667721121949e-06 - 6.3666484007488654034e-1459j)  +/-  (1.8e-152, 5.35e-399j)
| (0.0045583451023265358501 + 3.0206050374053757971e-1457j)  +/-  (5.07e-140, 1.5e-386j)
| (3.8028596470394442945e-33 + 1.3792373783652038468e-1472j)  +/-  (1.05e-176, 3.13e-423j)
| (8.5753328546285586314e-10 - 3.6328985680144480991e-1459j)  +/-  (9.79e-163, 2.9e-409j)
| (1.9775288891037391381e-13 + 1.3667679509287351408e-1462j)  +/-  (5.98e-166, 1.78e-412j)
| (0.025447921969114435733 + 7.8476356074441152862e-1457j)  +/-  (3.13e-135, 9.28e-382j)
| (1.9775288891037391381e-13 - 1.4444552301937184875e-1461j)  +/-  (1.88e-167, 5.57e-414j)
| (1.0129676599978398454e-47 + 6.2325990412278601051e-1480j)  +/-  (5.02e-182, 1.49e-428j)
| (0.025447921969114435733 + 1.4909691577740726816e-1456j)  +/-  (7.58e-138, 2.25e-384j)
| (1.7614894000539082277e-23 + 1.0600264536464315607e-1467j)  +/-  (5.73e-173, 1.7e-419j)
| (8.6881204241271429158e-08 - 1.4740786762827090692e-1458j)  +/-  (3.17e-161, 9.41e-408j)
| (3.9574899124215578496e-12 - 6.3543547655404999716e-1462j)  +/-  (1.26e-165, 3.73e-412j)
| (0.0015446190029041336638 - 5.0173588899689641164e-1457j)  +/-  (9.92e-150, 2.94e-396j)
| (6.6946015817882094603e-07 + 2.7393199635130831784e-1458j)  +/-  (7.26e-160, 2.16e-406j)
| (6.3880088486548417319e-28 + 6.0077118783096465677e-1470j)  +/-  (2.6e-175, 7.72e-422j)
| (0.00044990632660660608695 + 8.6772322432105450724e-1458j)  +/-  (1.15e-153, 3.41e-400j)
| (4.3504891667721121949e-06 - 5.2576819385931775412e-1458j)  +/-  (1.5e-159, 4.45e-406j)
| (3.8237363731336350571e-36 - 4.2395849497008369565e-1474j)  +/-  (7.42e-179, 2.2e-425j)
| (8.5753328546285586314e-10 - 1.0284063979591634217e-1460j)  +/-  (1.17e-165, 3.48e-412j)
| (2.022700864935940982e-30 - 3.2796407443529309098e-1471j)  +/-  (1.19e-176, 3.52e-423j)
| (1.6958625850857714941e-21 - 1.0725221062088509849e-1466j)  +/-  (8.35e-174, 2.48e-420j)
| (0.011591080869076673026 - 5.0474325751114411815e-1457j)  +/-  (1.86e-151, 5.52e-398j)
| (0.00044990632660660608695 + 3.0858883332943344656e-1457j)  +/-  (5.76e-159, 1.71e-405j)
| (7.9355575673709728697e-15 + 2.1562283102123034987e-1462j)  +/-  (8.22e-176, 2.44e-422j)
| (2.5237598417092487026e-16 + 4.5533521013204297778e-1464j)  +/-  (4.59e-172, 1.36e-418j)
| (7.9355575673709728697e-15 - 2.641619001476480957e-1463j)  +/-  (6.75e-171, 2e-417j)
| (0.048319294470221085559 - 1.8866719698926313072e-1456j)  +/-  (5.51e-151, 1.63e-397j)
| (3.9574899124215578496e-12 + 9.7509081717905760406e-1461j)  +/-  (5.25e-174, 1.56e-420j)
| (0.0015446190029041336638 - 1.6798944868749640876e-1457j)  +/-  (2.16e-159, 6.41e-406j)
| (2.3960892641704577176e-05 + 1.908404143501236878e-1458j)  +/-  (7.67e-164, 2.27e-410j)
| (6.432546916617666986e-11 - 7.9063696344884733825e-1460j)  +/-  (6.94e-173, 2.06e-419j)
| (0.15033562847355904515 - 2.5072594468440365735e-1456j)  +/-  (2.02e-154, 5.98e-401j)
| (0.048319294470221085559 - 1.1367002222634829807e-1456j)  +/-  (1.04e-154, 3.09e-401j)
| (0.011591080869076673026 - 1.104554592479080371e-1456j)  +/-  (7.79e-159, 2.31e-405j)
| (9.4558133943281638298e-09 + 9.6824603615540577903e-1459j)  +/-  (1.82e-170, 5.39e-417j)
| (0.1132604252487336219 - 2.4828437549062373254e-1456j)  +/-  (5.34e-156, 1.58e-402j)
| (6.432546916617666986e-11 + 2.6745008397870579208e-1461j)  +/-  (4.34e-170, 1.29e-416j)
| (0.079453542822606192849 + 1.5353419542446003847e-1456j)  +/-  (4.69e-157, 1.39e-403j)
| (0.00011232794041524786581 - 4.1678196325704503251e-1458j)  +/-  (8.49e-164, 2.52e-410j)
| (0.1132604252487336219 - 1.9354463625487661145e-1456j)  +/-  (1.4e-157, 4.14e-404j)
| (0.079453542822606192849 + 2.2366509757092660527e-1456j)  +/-  (2.23e-158, 6.6e-405j)
| (9.4558133943281638298e-09 + 3.6747457331840157905e-1460j)  +/-  (5.67e-169, 1.68e-415j)
| (1.1906357269809230056e-19 + 9.2712809209798089047e-1466j)  +/-  (2.52e-176, 7.48e-423j)
| (6.2630657395788268887e-18 - 6.9418215612752772393e-1465j)  +/-  (2.19e-175, 6.51e-422j)
| (8.6881204241271429158e-08 - 1.3032900391032899387e-1459j)  +/-  (4.75e-169, 1.41e-415j)
| (2.3960892641704577176e-05 + 9.906640841253806588e-1458j)  +/-  (9.3e-172, 2.76e-418j)
| (0.00011232794041524786581 - 1.7934085481165936164e-1457j)  +/-  (7.63e-171, 2.26e-417j)
| (0.14006564390620946203 + 2.278708328672342016e-1456j)  +/-  (9.25e-164, 2.74e-410j)
| (0.14006564390620946203 + 2.579580615180523213e-1456j)  +/-  (3.5e-164, 1.04e-410j)
| (1.1906357269809230056e-19 - 4.6663214433844821385e-1465j)  +/-  (7.51e-188, 2.23e-434j)
| (6.3880088486548417319e-28 - 2.0890097236493475608e-1469j)  +/-  (5.95e-193, 1.77e-439j)
| (1.6958625850857714941e-21 + 4.8302753832935371822e-1466j)  +/-  (1.31e-189, 3.89e-436j)
| (3.8028596470394442945e-33 - 4.1982376312823913986e-1472j)  +/-  (3.08e-195, 9.14e-442j)
| (2.5237598417092487026e-16 - 3.0549668816299360552e-1463j)  +/-  (1.39e-186, 4.11e-433j)
| (1.2902859558724301201e-25 + 3.3037102216978801905e-1468j)  +/-  (1.76e-192, 5.22e-439j)
| (1.7614894000539082277e-23 - 4.3341770008077332478e-1467j)  +/-  (1.84e-191, 5.44e-438j)
| (2.022700864935940982e-30 + 1.0638680374322357527e-1470j)  +/-  (5.45e-195, 1.62e-441j)
| (6.2630657395788268887e-18 + 3.9805487418441000437e-1464j)  +/-  (1.26e-188, 3.71e-435j)
