Starting with polynomial:
P : t
Extension levels are: 1 68
-------------------------------------------------
Trying to find an order 68 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^69 - 2346*t^67 + 2593503*t^65 - 1798162080*t^63 + 877952635560*t^61 - 321330664614960*t^59 + 91632794526032760*t^57 - 20892277151935469280*t^55 + 3878128946328021485100*t^53 - 593784632004445956274200*t^51 + 75707540580566859424960500*t^49 - 8093824338431511516704868000*t^47 + 729118675820371995796496859000*t^45 - 55525191466320636602963991570000*t^43 + 3581374849577681060891177456265000*t^41 - 195781825110246564662051034275820000*t^39 + 9067145775418294025911238524898913750*t^37 - 355218769789916695368052050446039797500*t^35 + 11741953779166690763555053889744093306250*t^33 - 326302715547369090692477287041309540300000*t^31 + 7586538136476331358600096923710446811975000*t^29 - 146673070638542406266268540525068638364850000*t^27 + 2340102172460381118157284442013595093911925000*t^25 - 30523071814700623280312405765394718616242500000*t^23 + 321764048713302403746626610776869325412889687500*t^21 - 2702818009191740191471663530525702333468273375000*t^19 + 17776226137376445105448248604611349962425951812500*t^17 - 89539509432710982753368955934338651662589979500000*t^15 + 335773160372666185325133584753769943734712423125000*t^13 - 903114017554067670874497227958415710734743758750000*t^11 + 1655709032182457396603244917923762136347030224375000*t^9 - 1922758876082853750894090872427594738983648002500000*t^7 + 1261810512429372774024247135030609047458019001640625*t^5 - 382366821948294780007347616675942135593339091406250*t^3 + 33738248995437774706530672059641953140588743359375*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:   69 out of 69
Indefinite weights: 0 out of 69
Negative weights:   0 out of 69
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (15.512107936324507297 - 1.8233190775840290327e-1172j)  +/-  (1.62e-498, 1.62e-498j)
| (13.903844420124942933 - 9.6049855951790073389e-1170j)  +/-  (5.43e-496, 5.43e-496j)
| (13.254498211160966243 - 9.0345644683931641324e-1169j)  +/-  (3.21e-495, 3.21e-495j)
| (-3.8015501900992123014 - 3.769638012929937102e-1172j)  +/-  (4.04e-499, 4.04e-499j)
| (11.559034970749135348 - 1.5287799153525213388e-1167j)  +/-  (1.08e-493, 1.08e-493j)
| (9.6054994954763983523 - 1.388985148245775852e-1167j)  +/-  (3.49e-493, 3.49e-493j)
| (4.9736302805707340039 + 9.4051892106790104677e-1171j)  +/-  (5.92e-497, 5.92e-497j)
| (-4.9736302805707340039 - 5.9531697934017470849e-1171j)  +/-  (6.1e-497, 6.1e-497j)
| (12.655895455537154637 - 1.7893488596320359613e-1168j)  +/-  (1.28e-494, 1.28e-494j)
| (-4.5802977916187171745 - 2.2986865578215023502e-1171j)  +/-  (1.44e-497, 1.44e-497j)
| (10.551836990333653851 + 2.2406015905423666967e-1167j)  +/-  (2.13e-493, 2.13e-493j)
| (8.2658001354364515612 + 4.7843459370645995363e-1167j)  +/-  (1.96e-493, 1.96e-493j)
| (6.5813148568342871013 - 1.3868243298831614857e-1168j)  +/-  (1.02e-494, 1.02e-494j)
| (10.072274608029020661 + 1.925826504096526795e-1168j)  +/-  (2.62e-493, 2.62e-493j)
| (6.9938934686800743694 + 6.7638891038360740794e-1168j)  +/-  (2.31e-494, 2.31e-494j)
| (4.5802977916187171745 + 1.3142209661070679024e-1171j)  +/-  (1.35e-497, 1.35e-497j)
| (1.1313753186338882076 - 2.6278827175199868467e-1180j)  +/-  (6.1e-506, 6.1e-506j)
| (11.046440674284101652 - 3.9620476669804545658e-1167j)  +/-  (1.31e-493, 1.31e-493j)
| (9.1497384492103963528 + 4.1243730458052506035e-1167j)  +/-  (2.86e-493, 2.86e-493j)
| (3.4155580932782206499 - 2.7514215274416991585e-1173j)  +/-  (7.93e-500, 7.93e-500j)
| (12.093621895515055215 + 8.1758412576325178219e-1168j)  +/-  (4.08e-494, 4.08e-494j)
| (14.631927339885941312 - 1.4350563472597623383e-1170j)  +/-  (5.01e-497, 5.01e-497j)
| (-2.2680262970856078247 - 1.2158414752084585485e-1176j)  +/-  (1.23e-502, 1.23e-502j)
| (1.5094061326512441487 - 4.5567969675326161487e-1178j)  +/-  (7.64e-505, 7.64e-505j)
| (3.0314678725601418344 + 5.645564864151506761e-1175j)  +/-  (1.12e-500, 1.12e-500j)
| (3.8015501900992123014 - 1.9883364707672183955e-1173j)  +/-  (4.06e-499, 4.06e-499j)
| (-4.1897041278863394644 + 1.1334072933575116003e-1171j)  +/-  (3.15e-498, 3.15e-498j)
| (-1.1313753186338882076 + 1.7676105148347074984e-1179j)  +/-  (6.6e-506, 6.6e-506j)
| (4.1897041278863394644 + 1.7194898738999890122e-1172j)  +/-  (3.18e-498, 3.18e-498j)
| (7.8354688718752383288 + 3.5799653663593820374e-1169j)  +/-  (8.13e-494, 8.13e-494j)
| (-1.8882211142899334971 + 3.6700597809049997586e-1177j)  +/-  (8.54e-504, 8.54e-504j)
| (-1.5094061326512441487 + 6.1448853938831613404e-1178j)  +/-  (7.54e-505, 7.54e-505j)
| (-3.0314678725601418344 + 5.8225408792966645332e-1174j)  +/-  (1.11e-500, 1.11e-500j)
| (6.1734574475698226414 - 3.9761642461094356869e-1169j)  +/-  (3.67e-495, 3.67e-495j)
| (5.3700258093308856696 - 3.7714521881215285414e-1170j)  +/-  (2.57e-496, 2.57e-496j)
| (5.7698383806205389684 - 2.0402327661140816024e-1169j)  +/-  (1.22e-495, 1.22e-495j)
| (2.6490346690755143632 + 1.6987594307021114536e-1175j)  +/-  (1.1e-501, 1.1e-501j)
| (0.75392804038522584484 + 6.1274993796393873191e-1181j)  +/-  (3.79e-507, 3.79e-507j)
| (-5.3700258093308856696 + 1.4279597180883971471e-1169j)  +/-  (2.64e-496, 2.64e-496j)
| (-2.6490346690755143632 - 1.2326585889242268722e-1175j)  +/-  (1.1e-501, 1.1e-501j)
| (7.4117380015669706489 + 1.6278066081700065081e-1167j)  +/-  (4.78e-494, 4.78e-494j)
| (0.37686762579250028748 + 1.7480535617219869033e-1181j)  +/-  (1.03e-508, 1.03e-508j)
| (8.7035631560878051043 - 1.9614813192379092553e-1167j)  +/-  (2.6e-493, 2.6e-493j)
| (-0.75392804038522584484 + 1.0244925454132957448e-1180j)  +/-  (3.79e-507, 3.79e-507j)
| (1.8882211142899334971 + 1.1157571412087593295e-1177j)  +/-  (8.45e-504, 8.45e-504j)
| (2.2680262970856078247 - 2.1539947626448207332e-1177j)  +/-  (1.3e-502, 1.3e-502j)
| (-1.3192794112897761969e-1214 - 1.6828806081139618617e-1213j)  +/-  (1.16e-1211, 1.16e-1211j)
| (-0.37686762579250028748 - 1.8454340652024668213e-1181j)  +/-  (1.03e-508, 1.03e-508j)
| (-3.4155580932782206499 - 1.0986573641817734778e-1173j)  +/-  (7.08e-500, 7.08e-500j)
| (-13.903844420124942933 + 4.2600000622262558545e-1166j)  +/-  (5.51e-496, 5.51e-496j)
| (-7.8354688718752383288 + 4.9760877248401072228e-1169j)  +/-  (8.06e-494, 8.06e-494j)
| (-13.254498211160966243 - 5.0760404789924803092e-1177j)  +/-  (3.18e-495, 3.18e-495j)
| (-8.7035631560878051043 + 4.2332772100567678417e-1206j)  +/-  (2.45e-493, 2.45e-493j)
| (-12.093621895515055215 + 1.0581194995700020638e-1256j)  +/-  (4.23e-494, 4.23e-494j)
| (-11.559034970749135348 - 2.2039780125463513817e-1308j)  +/-  (1.07e-493, 1.07e-493j)
| (-14.631927339885941312 + 1.4775276736457090018e-1345j)  +/-  (4.88e-497, 4.88e-497j)
| (-5.7698383806205389684 - 6.6631986623291571195e-1381j)  +/-  (1.23e-495, 1.23e-495j)
| (-10.072274608029020661 - 1.5069537603233269982e-1413j)  +/-  (3.04e-493, 3.04e-493j)
| (-15.512107936324507297 - 1.5031483399935830715e-1445j)  +/-  (1.63e-498, 1.63e-498j)
| (-6.9938934686800743694 - 1.5936389005508342433e-1474j)  +/-  (2.33e-494, 2.33e-494j)
| (-10.551836990333653851 + 1.1378773079094495117e-1491j)  +/-  (2.14e-493, 2.14e-493j)
| (-8.2658001354364515612 + 8.2458822788104070424e-1512j)  +/-  (1.98e-493, 1.98e-493j)
| (-7.4117380015669706489 + 2.6765026382598871813e-1552j)  +/-  (4.84e-494, 4.84e-494j)
| (-12.655895455537154637 - 1.7393839630717282599e-1600j)  +/-  (1.26e-494, 1.26e-494j)
| (-11.046440674284101652 + 4.6912396106477714822e-1637j)  +/-  (1.35e-493, 1.35e-493j)
| (-9.6054994954763983523 + 4.2635576362594646175e-1653j)  +/-  (3.05e-493, 3.05e-493j)
| (-6.5813148568342871013 + 1.2188508411777155032e-1660j)  +/-  (9.59e-495, 9.59e-495j)
| (-6.1734574475698226414 + 5.5236610458948524945e-1661j)  +/-  (3.58e-495, 3.58e-495j)
| (-9.1497384492103963528 + 4.0762786733939627285e-1658j)  +/-  (2.75e-493, 2.75e-493j)
-------------------------------------------------
The weights are:
| (2.2762487188790489321e-53 + 1.2143037649655568444e-1200j)  +/-  (3.58e-153, 7.88e-399j)
| (2.8613046012491353855e-43 + 1.5513980279484328755e-1195j)  +/-  (3.77e-150, 8.31e-396j)
| (1.7583071667421166102e-39 - 1.2919906149000754163e-1193j)  +/-  (5.15e-149, 1.13e-394j)
| (0.00011232794041524786581 + 1.431893645806954155e-1176j)  +/-  (4.47e-117, 9.84e-363j)
| (2.022700864935940982e-30 + 5.2920031255955610925e-1189j)  +/-  (3.4e-146, 7.49e-392j)
| (1.6958625850857714941e-21 + 2.0538155928812693226e-1184j)  +/-  (3.49e-142, 7.68e-388j)
| (6.6946015817882094603e-07 - 2.515835795197100993e-1176j)  +/-  (3.17e-126, 6.98e-372j)
| (6.6946015817882094603e-07 - 1.1461177351667698918e-1175j)  +/-  (9e-128, 1.98e-373j)
| (3.8237363731336350571e-36 + 6.4032562694264132788e-1192j)  +/-  (1.25e-148, 2.75e-394j)
| (4.3504891667721121949e-06 + 1.5234361762380432965e-1175j)  +/-  (8.25e-126, 1.82e-371j)
| (1.2902859558724301201e-25 + 1.5393047960045476887e-1186j)  +/-  (1.2e-144, 2.63e-390j)
| (2.5237598417092487026e-16 - 1.7822659103423455599e-1181j)  +/-  (3.86e-140, 8.49e-386j)
| (6.432546916617666986e-11 + 5.9601155289349258903e-1178j)  +/-  (1.23e-135, 2.7e-381j)
| (1.7614894000539082277e-23 - 1.9404153224831318348e-1185j)  +/-  (5.95e-144, 1.31e-389j)
| (3.9574899124215578496e-12 - 1.4520543145095489451e-1179j)  +/-  (3.32e-137, 7.32e-383j)
| (4.3504891667721121949e-06 + 2.2699272974331822138e-1176j)  +/-  (2.76e-129, 6.07e-375j)
| (0.079453542822606192849 - 1.0083666815514359267e-1174j)  +/-  (1.67e-101, 3.68e-347j)
| (6.3880088486548417319e-28 - 1.0072937778280122479e-1187j)  +/-  (1.65e-146, 3.64e-392j)
| (1.1906357269809230056e-19 - 1.8655903519231917447e-1183j)  +/-  (9.58e-143, 2.11e-388j)
| (0.00044990632660660608695 - 6.3836410217203081013e-1176j)  +/-  (2.57e-126, 5.66e-372j)
| (3.8028596470394442945e-33 - 2.1497327699338354743e-1190j)  +/-  (2.02e-149, 4.45e-395j)
| (1.0129676599978398454e-47 - 8.6748336933313485752e-1198j)  +/-  (6.65e-157, 1.46e-402j)
| (0.011591080869076673026 + 8.1155948698460245487e-1175j)  +/-  (1e-123, 2.21e-369j)
| (0.048319294470221085559 + 7.255825155874754525e-1175j)  +/-  (2.3e-113, 5.05e-359j)
| (0.0015446190029041336638 + 7.1184980731348114461e-1176j)  +/-  (1.54e-125, 3.39e-371j)
| (0.00011232794041524786581 + 6.8350245161237427232e-1176j)  +/-  (2.98e-129, 6.57e-375j)
| (2.3960892641704577176e-05 - 1.326529507771228511e-1175j)  +/-  (2.03e-137, 4.46e-383j)
| (0.079453542822606192849 - 1.6470633925126913068e-1174j)  +/-  (7.52e-113, 1.66e-358j)
| (2.3960892641704577176e-05 - 1.8591274813294978551e-1176j)  +/-  (6.48e-131, 1.43e-376j)
| (7.9355575673709728697e-15 + 7.1258003003170188124e-1181j)  +/-  (4.82e-142, 1.06e-387j)
| (0.025447921969114435733 - 1.1052792866963235262e-1174j)  +/-  (1.19e-123, 2.62e-369j)
| (0.048319294470221085559 + 1.3985803014196705389e-1174j)  +/-  (5.39e-120, 1.19e-365j)
| (0.0015446190029041336638 + 2.9986509578083800036e-1175j)  +/-  (8.07e-133, 1.78e-378j)
| (8.5753328546285586314e-10 + 9.2431462999483083466e-1178j)  +/-  (1.3e-138, 2.86e-384j)
| (8.6881204241271429158e-08 - 9.5714694008317382795e-1177j)  +/-  (8.12e-137, 1.79e-382j)
| (9.4558133943281638298e-09 + 7.8834148606080829582e-1177j)  +/-  (5.84e-138, 1.28e-383j)
| (0.0045583451023265358501 - 1.6602868332850264012e-1175j)  +/-  (8.18e-130, 1.8e-375j)
| (0.1132604252487336219 + 1.3043570506442020145e-1174j)  +/-  (1.58e-121, 3.48e-367j)
| (8.6881204241271429158e-08 + 3.3372669548368111518e-1176j)  +/-  (8.01e-149, 1.76e-394j)
| (0.0045583451023265358501 - 5.5152526428659730422e-1175j)  +/-  (4.29e-134, 9.45e-380j)
| (1.9775288891037391381e-13 - 3.1421600688602234288e-1179j)  +/-  (1.56e-142, 3.44e-388j)
| (0.14006564390620946203 - 1.5718787470705412971e-1174j)  +/-  (2.82e-123, 6.2e-369j)
| (6.2630657395788268887e-18 + 1.4121891683815335501e-1182j)  +/-  (1.35e-145, 2.97e-391j)
| (0.1132604252487336219 + 1.8074692119204494121e-1174j)  +/-  (6.27e-125, 1.38e-370j)
| (0.025447921969114435733 - 4.8522517418037653995e-1175j)  +/-  (4.26e-129, 9.37e-375j)
| (0.011591080869076673026 + 3.0076304985276211963e-1175j)  +/-  (1.28e-130, 2.81e-376j)
| (0.15033562847355904515 + 1.76577956388659009e-1174j)  +/-  (3.24e-125, 7.14e-371j)
| (0.14006564390620946203 - 1.8498089654040101068e-1174j)  +/-  (1.55e-125, 3.41e-371j)
| (0.00044990632660660608695 - 4.4725761724149731346e-1176j)  +/-  (1.12e-140, 2.46e-386j)
| (2.8613046012491353855e-43 - 2.3684492499777932886e-1195j)  +/-  (2.48e-177, 5.46e-423j)
| (7.9355575673709728697e-15 - 1.3577773170537320832e-1180j)  +/-  (8.08e-163, 1.78e-408j)
| (1.7583071667421166102e-39 + 2.0066583440868886096e-1193j)  +/-  (3.05e-176, 6.72e-422j)
| (6.2630657395788268887e-18 - 2.8428988877973169973e-1182j)  +/-  (3.78e-166, 8.32e-412j)
| (3.8028596470394442945e-33 + 3.453140371640932102e-1190j)  +/-  (1.54e-174, 3.38e-420j)
| (2.022700864935940982e-30 - 8.6457792120924907234e-1189j)  +/-  (1.17e-173, 2.57e-419j)
| (1.0129676599978398454e-47 + 1.3006862533411006331e-1197j)  +/-  (1.98e-180, 4.36e-426j)
| (9.4558133943281638298e-09 + 9.9755851667920400303e-1177j)  +/-  (3.6e-159, 7.92e-405j)
| (1.7614894000539082277e-23 + 3.358339576115807344e-1185j)  +/-  (1.48e-171, 3.26e-417j)
| (2.2762487188790489321e-53 - 1.7844231802677187094e-1200j)  +/-  (3.17e-183, 6.97e-429j)
| (3.9574899124215578496e-12 - 4.7227127406386155867e-1179j)  +/-  (9.68e-165, 2.13e-410j)
| (1.2902859558724301201e-25 - 2.6070521036575900255e-1186j)  +/-  (9.6e-173, 2.11e-418j)
| (2.5237598417092487026e-16 + 2.0913997558199420344e-1181j)  +/-  (6.69e-168, 1.47e-413j)
| (1.9775288891037391381e-13 + 8.2880505590692610463e-1180j)  +/-  (3.91e-166, 8.6e-412j)
| (3.8237363731336350571e-36 - 1.0114390814862794471e-1191j)  +/-  (1.32e-177, 2.9e-423j)
| (6.3880088486548417319e-28 + 1.6745608540009930376e-1187j)  +/-  (3.41e-174, 7.51e-420j)
| (1.6958625850857714941e-21 - 3.6623191777616709001e-1184j)  +/-  (7.67e-172, 1.68e-417j)
| (6.432546916617666986e-11 + 2.5904647990981174534e-1178j)  +/-  (9.19e-167, 2e-412j)
| (8.5753328546285586314e-10 - 1.4546694527177371859e-1177j)  +/-  (3.62e-166, 7.84e-412j)
| (1.1906357269809230056e-19 + 3.4454454756289214772e-1183j)  +/-  (2.67e-171, 5.94e-417j)
