Starting with polynomial:
P : t
Extension levels are: 1 72
-------------------------------------------------
Trying to find an order 72 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^73 - 2628*t^71 + 3265290*t^69 - 2553456780*t^67 + 1411423235145*t^65 - 587152065820320*t^63 + 191117997424514160*t^61 - 49963705040980130400*t^59 + 10685987415639625389300*t^57 - 1894981768373426902369200*t^55 + 281404792603453895001826200*t^53 - 35252345837050860664774227600*t^51 + 3745561745186653945632261682500*t^49 - 338829277872269618466426133740000*t^47 + 26162460669994532683014760755210000*t^45 - 1726722404219639157078974209843860000*t^43 + 97451895688145884927644606968062848750*t^41 - 4700620850839977978862857512577149175000*t^39 + 193508891692912426796520967601092641037500*t^37 - 6782995887762088223499103390648826259525000*t^35 + 201794127660922124649098325871802581220868750*t^33 - 5073680924046041991177329336205322042124700000*t^31 + 107239164985518614813520824606157943163090250000*t^29 - 1893004390613937287577802382178266301052810500000*t^27 + 27685189212728832830825359839357144652897353562500*t^25 - 332222270552745993969904318072285735834768242750000*t^23 + 3232778248070951402860992018164934275622937131375000*t^21 - 25143830818329622022252160141282822143733955466250000*t^19 + 153556966783370191635897120862834378092089513740312500*t^17 - 720129223535805036637310635770533635190488754092500000*t^15 + 2520452282375317628230587225196867723166710639323750000*t^13 - 6341783162105637903289864631140505884096884834427500000*t^11 + 10899939809869065146279454834772744488291520809172265625*t^9 - 11890843428948071068668496183388448532681659064551562500*t^7 + 7344344470820867424765835877975218211362201186928906250*t^5 - 2098384134520247835647381679421490917532057481979687500*t^3 + 174865344543353986303948473285124243127671456831640625*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:
| (13.170189015457126477 - 2.3061803893935229413e-1209j)  +/-  (7.44e-494, 7.44e-494j)
| (-14.404441117715300586 - 2.4412716277275448667e-1224j)  +/-  (2.32e-495, 2.32e-495j)
| (-15.996283956085633293 + 1.3476391635348401463e-1226j)  +/-  (5.66e-498, 5.66e-498j)
| (-10.15742644829775617 + 1.7840513449171094989e-1219j)  +/-  (3.27e-492, 3.27e-492j)
| (-15.124927484726120041 + 1.7556188970005100056e-1233j)  +/-  (1.93e-496, 1.93e-496j)
| (11.579793415956680673 - 5.0055988227115394065e-1238j)  +/-  (1.4e-492, 1.4e-492j)
| (-13.762111157473484265 - 8.9885233298675077748e-1264j)  +/-  (1.69e-494, 1.69e-494j)
| (10.61801601647083702 + 9.3736281684855786291e-1266j)  +/-  (2.45e-492, 2.45e-492j)
| (12.614386069435147126 - 1.9108612010695366579e-1276j)  +/-  (2.25e-493, 2.25e-493j)
| (7.1778381308808543014 - 8.045287111432274504e-1287j)  +/-  (1.79e-493, 1.79e-493j)
| (-11.579793415956680673 + 6.6453738330017500043e-1300j)  +/-  (1.39e-492, 1.39e-492j)
| (-10.61801601647083702 + 8.8311101815333191941e-1300j)  +/-  (2.46e-492, 2.46e-492j)
| (10.15742644829775617 - 7.3315138213558790512e-1302j)  +/-  (2.88e-492, 2.88e-492j)
| (-8.8364594266496460526 - 1.6573884211691717416e-1316j)  +/-  (2.1e-492, 2.1e-492j)
| (-5.5976505119568056858 + 6.5955616076192036097e-1321j)  +/-  (1.97e-495, 1.97e-495j)
| (15.124927484726120041 + 3.949221768124905376e-1319j)  +/-  (1.88e-496, 1.88e-496j)
| (12.086135399179619516 + 2.6533919168906310209e-1316j)  +/-  (5.97e-493, 5.97e-493j)
| (15.996283956085633293 + 8.2395641353880488143e-1333j)  +/-  (5.82e-498, 5.82e-498j)
| (-13.170189015457126477 + 5.3800261285087419652e-1334j)  +/-  (7.28e-494, 7.28e-494j)
| (-4.069350634973953896 + 6.1731111297815229096e-1343j)  +/-  (5.28e-498, 5.28e-498j)
| (13.762111157473484265 - 1.5165863275129853049e-1336j)  +/-  (1.58e-494, 1.58e-494j)
| (7.583822539796973245 + 1.7004410300089888254e-1381j)  +/-  (3.62e-493, 3.62e-493j)
| (11.091394252460198756 - 1.8180037073356949856e-1442j)  +/-  (1.77e-492, 1.77e-492j)
| (-9.2679346409463920314 + 3.8615087492386756952e-1481j)  +/-  (2.52e-492, 2.52e-492j)
| (-3.6931400789239644566 + 4.2005775076721420161e-1503j)  +/-  (6.49e-499, 6.49e-499j)
| (8.4124763186180661186 + 4.7331612507207152557e-1519j)  +/-  (1.47e-492, 1.47e-492j)
| (1.8357053272425466141 - 1.4401861743211363422e-1558j)  +/-  (1.01e-503, 1.01e-503j)
| (3.6931400789239644566 + 2.5077029134914879339e-1548j)  +/-  (6.19e-499, 6.19e-499j)
| (-6.7766771355212650242 - 3.2511557052860310333e-1547j)  +/-  (7.59e-494, 7.59e-494j)
| (-1.4675478178941488875 - 1.325039675957021204e-1579j)  +/-  (8.64e-505, 8.64e-505j)
| (8.8364594266496460526 - 4.5926307244148639073e-1565j)  +/-  (2.1e-492, 2.1e-492j)
| (-8.4124763186180661186 - 3.1786875878144598771e-1583j)  +/-  (1.51e-492, 1.51e-492j)
| (6.7766771355212650242 - 1.5676358782325416185e-1588j)  +/-  (7.57e-494, 7.57e-494j)
| (-12.086135399179619516 + 6.3889245147537268986e-1601j)  +/-  (6.57e-493, 6.57e-493j)
| (-2.2047211560212228834 - 1.1620095071889378483e-1609j)  +/-  (1.5e-502, 1.5e-502j)
| (-6.3798664816845307496 - 1.8548473239649195429e-1600j)  +/-  (2.84e-494, 2.84e-494j)
| (-7.9951651813027653918 + 2.8153966268465567521e-1598j)  +/-  (5.94e-493, 5.94e-493j)
| (5.5976505119568056858 + 9.1156225312661694527e-1605j)  +/-  (1.99e-495, 1.99e-495j)
| (9.7078703149762650461 + 7.2437631759499060253e-1621j)  +/-  (2.78e-492, 2.78e-492j)
| (-2.9460672459732909034 + 1.0986146100614756292e-1645j)  +/-  (1.37e-500, 1.37e-500j)
| (-12.614386069435147126 - 1.0655612766323947595e-1637j)  +/-  (2.38e-493, 2.38e-493j)
| (14.404441117715300586 - 6.25870759780413676e-1637j)  +/-  (2.45e-495, 2.45e-495j)
| (6.3798664816845307496 - 4.1268030325950455934e-1641j)  +/-  (2.85e-494, 2.85e-494j)
| (2.9460672459732909034 + 1.5827044144928753673e-1660j)  +/-  (1.42e-500, 1.42e-500j)
| (-4.4476492803967695902 - 5.8984248031242486792e-1656j)  +/-  (2.44e-497, 2.44e-497j)
| (-7.1778381308808543014 + 8.3915911710874872403e-1651j)  +/-  (1.78e-493, 1.78e-493j)
| (7.9951651813027653918 - 9.3067709825069442513e-1666j)  +/-  (5.73e-493, 5.73e-493j)
| (9.2679346409463920314 - 4.6470109649481823943e-1687j)  +/-  (2.49e-492, 2.49e-492j)
| (0.73310053043388036248 + 5.7542529781736871263e-1715j)  +/-  (4.64e-507, 4.64e-507j)
| (4.069350634973953896 - 3.3684775162691372132e-1706j)  +/-  (5.88e-498, 5.88e-498j)
| (5.2115217778060919206 + 7.2831753522959217065e-1704j)  +/-  (5.74e-496, 5.74e-496j)
| (-7.583822539796973245 - 1.0911428491101094665e-1701j)  +/-  (3.29e-493, 3.29e-493j)
| (-1.8357053272425466141 - 2.0557476134138973233e-1711j)  +/-  (9.94e-504, 9.94e-504j)
| (-11.091394252460198756 + 1.5364415987639048575e-1700j)  +/-  (1.64e-492, 1.64e-492j)
| (5.9869841204925936962 + 1.9382170878903840019e-1700j)  +/-  (9.13e-495, 9.13e-495j)
| (-3.318785258751954023 + 1.5596390477116672856e-1711j)  +/-  (9.29e-500, 9.29e-500j)
| (-1.1000707775327009806 - 8.1952822285202205681e-1718j)  +/-  (7.31e-506, 7.31e-506j)
| (-0.36646646866587314122 - 3.80047904105412505e-1720j)  +/-  (1.16e-508, 1.16e-508j)
| (3.318785258751954023 - 4.0353584519716579927e-1712j)  +/-  (1e-499, 1e-499j)
| (2.2047211560212228834 + 3.8025418576618385479e-1715j)  +/-  (1.48e-502, 1.48e-502j)
| (1.1000707775327009806 - 1.7580734365531894797e-1718j)  +/-  (6.88e-506, 6.88e-506j)
| (-5.2115217778060919206 - 5.7848402635777243949e-1707j)  +/-  (5.51e-496, 5.51e-496j)
| (-2.5747785124666284236 + 3.2337429685370259628e-1713j)  +/-  (1.45e-501, 1.45e-501j)
| (-4.8282841291170329356 + 2.37786428109435391e-1708j)  +/-  (1.16e-496, 1.16e-496j)
| (0.36646646866587314122 + 3.1746063335796326495e-1720j)  +/-  (1.1e-508, 1.1e-508j)
| (1.4675478178941488875 - 1.0926838097888006871e-1717j)  +/-  (8.37e-505, 8.37e-505j)
| (-5.9869841204925936962 - 1.0432048143709856817e-1705j)  +/-  (9.49e-495, 9.49e-495j)
| (-0.73310053043388036248 + 8.5683784756179156276e-1720j)  +/-  (4.8e-507, 4.8e-507j)
| (-9.7078703149762650461 - 9.1728401337534781655e-1704j)  +/-  (2.97e-492, 2.97e-492j)
| (4.4476492803967695902 - 8.512812650848704515e-1708j)  +/-  (2.41e-497, 2.41e-497j)
| (2.5747785124666284236 + 1.3949377456566727283e-1714j)  +/-  (1.36e-501, 1.36e-501j)
| (4.8282841291170329356 + 1.2321442999567969674e-1707j)  +/-  (1.16e-496, 1.16e-496j)
| (5.3962012111368239479e-1738 - 3.3308170676999427763e-1738j)  +/-  (4.63e-1736, 4.63e-1736j)
-------------------------------------------------
The weights are:
| (4.9356648255966463786e-39 + 7.4956496112144706391e-1247j)  +/-  (1.5e-174, 1.9e-420j)
| (2.3698636911068663879e-46 + 8.8721543448179688122e-1253j)  +/-  (1.17e-177, 1.48e-423j)
| (1.097045334512777968e-56 + 5.7326408393308909304e-1258j)  +/-  (2.26e-181, 2.86e-427j)
| (7.1604829638577492307e-24 + 2.5073074298053623664e-1241j)  +/-  (8.18e-169, 1.04e-414j)
| (6.5394985116746441101e-51 - 4.5527724137030483693e-1255j)  +/-  (1.95e-179, 2.47e-425j)
| (1.5117414074434629439e-30 - 1.2528333621456790313e-1243j)  +/-  (1.71e-174, 2.16e-420j)
| (1.8295476803842760544e-42 - 7.9578678175982696402e-1251j)  +/-  (2.85e-177, 3.61e-423j)
| (6.1409610836416112298e-26 - 1.5737340464943032681e-1241j)  +/-  (1.98e-172, 2.51e-418j)
| (6.0389806802044886257e-36 - 7.1640451237633284065e-1246j)  +/-  (5.43e-177, 6.88e-423j)
| (1.0447699212823432865e-12 - 2.7664404214268421277e-1235j)  +/-  (6.96e-163, 8.81e-409j)
| (1.5117414074434629439e-30 - 7.6361057093520977772e-1245j)  +/-  (1.35e-174, 1.71e-420j)
| (6.1409610836416112298e-26 - 1.4309545206680777905e-1242j)  +/-  (3.15e-172, 3.98e-418j)
| (7.1604829638577492307e-24 + 1.4396671438728092998e-1240j)  +/-  (2.31e-172, 2.92e-418j)
| (1.8898071651522673076e-18 - 1.0617757860865334113e-1238j)  +/-  (5.97e-169, 7.55e-415j)
| (2.4285943169750093268e-08 - 1.3616474529594039921e-1233j)  +/-  (5.32e-159, 6.73e-405j)
| (6.5394985116746441101e-51 + 6.7011712557414059409e-1254j)  +/-  (1.44e-185, 1.82e-431j)
| (3.9290605843798225558e-33 + 9.3696218974653553467e-1245j)  +/-  (2.86e-177, 3.62e-423j)
| (1.097045334512777968e-56 - 6.0027926953568644055e-1257j)  +/-  (4.99e-188, 6.32e-434j)
| (4.9356648255966463786e-39 + 4.2100016157064333905e-1249j)  +/-  (6.17e-181, 7.81e-427j)
| (3.8161373053170931952e-05 - 5.8541119035180733095e-1232j)  +/-  (3.55e-156, 4.5e-402j)
| (1.8295476803842760544e-42 + 3.7020451966746751531e-1249j)  +/-  (4.43e-182, 5.61e-428j)
| (5.2855421926486843273e-14 + 6.6739693597267714697e-1236j)  +/-  (5.8e-170, 7.34e-416j)
| (3.7096451329002690245e-28 + 1.5015709131413596425e-1242j)  +/-  (5.36e-176, 6.78e-422j)
| (3.8739124051695607342e-20 + 1.5268334807684514427e-1239j)  +/-  (1.35e-174, 1.71e-420j)
| (0.00016349043374974860492 + 1.2379253375190583112e-1231j)  +/-  (4.27e-157, 5.4e-403j)
| (7.1984692749157402393e-17 + 2.8914501109497563396e-1237j)  +/-  (1.53e-172, 1.93e-418j)
| (0.027268952858838580359 - 2.3670438377566012555e-1230j)  +/-  (1.39e-145, 1.75e-391j)
| (0.00016349043374974860492 + 2.1903517598531407211e-1231j)  +/-  (3e-159, 3.8e-405j)
| (1.6969040056110007269e-11 + 3.404124135761465158e-1235j)  +/-  (1.96e-170, 2.49e-416j)
| (0.049984847265092552608 + 2.4869185799592568315e-1230j)  +/-  (3.1e-143, 3.93e-389j)
| (1.8898071651522673076e-18 - 5.1428625492498743101e-1238j)  +/-  (9.77e-174, 1.24e-419j)
| (7.1984692749157402393e-17 + 6.6012661597345712926e-1238j)  +/-  (5.67e-174, 7.18e-420j)
| (1.6969040056110007269e-11 + 1.0450525712096008086e-1234j)  +/-  (1.92e-170, 2.42e-416j)
| (3.9290605843798225558e-33 + 3.8659062687283520204e-1246j)  +/-  (3.55e-182, 4.49e-428j)
| (0.01297247152510639489 + 1.2070682610591887516e-1230j)  +/-  (3.88e-154, 4.92e-400j)
| (2.2844778933329723269e-10 - 1.2716988409795108946e-1234j)  +/-  (2.35e-170, 2.98e-416j)
| (2.1752466349821180222e-15 - 3.6731919601617502236e-1237j)  +/-  (1.16e-173, 1.47e-419j)
| (2.4285943169750093268e-08 - 3.3390023656654736479e-1233j)  +/-  (1.05e-170, 1.33e-416j)
| (6.085029311574782796e-22 - 1.154923919338855447e-1239j)  +/-  (1.96e-177, 2.48e-423j)
| (0.0019352133975236287801 + 4.4516073363616576987e-1231j)  +/-  (1.85e-161, 2.34e-407j)
| (6.0389806802044886257e-36 - 1.4963957416903515736e-1247j)  +/-  (3.39e-184, 4.3e-430j)
| (2.3698636911068663879e-46 - 2.0205034840389742666e-1251j)  +/-  (1.18e-188, 1.5e-434j)
| (2.2844778933329723269e-10 - 3.6107240863256683337e-1234j)  +/-  (1.27e-172, 1.61e-418j)
| (0.0019352133975236287801 + 6.9871786522652343466e-1231j)  +/-  (4.21e-165, 5.33e-411j)
| (7.6651100775855474195e-06 + 2.5692320089405480504e-1232j)  +/-  (1.06e-168, 1.34e-414j)
| (1.0447699212823432865e-12 - 8.3024522105159168454e-1236j)  +/-  (2.22e-174, 2.81e-420j)
| (2.1752466349821180222e-15 - 1.4614119794651676925e-1236j)  +/-  (4.49e-175, 5.68e-421j)
| (3.8739124051695607342e-20 + 8.1767819353219325233e-1239j)  +/-  (2.95e-177, 3.73e-423j)
| (0.11184219617973975744 + 4.3712853941779376232e-1230j)  +/-  (5.52e-161, 6.99e-407j)
| (3.8161373053170931952e-05 - 1.1018298354685410205e-1231j)  +/-  (8.61e-171, 1.09e-416j)
| (1.941988135065754176e-07 + 8.9848576804987735526e-1233j)  +/-  (9.63e-173, 1.22e-418j)
| (5.2855421926486843273e-14 + 1.8374164071323415579e-1236j)  +/-  (7.07e-177, 8.94e-423j)
| (0.027268952858838580359 - 1.7924203343838615297e-1230j)  +/-  (4.54e-165, 5.74e-411j)
| (3.7096451329002690245e-28 + 1.1877644190861484786e-1243j)  +/-  (5.47e-184, 6.93e-430j)
| (2.5687327038815620165e-09 + 1.1446594613608082324e-1233j)  +/-  (7.38e-174, 9.34e-420j)
| (0.00060460144591195243957 - 2.4332213055436482376e-1231j)  +/-  (4.15e-170, 5.26e-416j)
| (0.079987999875462535935 - 3.2259538359367234369e-1230j)  +/-  (9.71e-165, 1.23e-410j)
| (0.1367250465995920329 - 4.4436965947240639245e-1230j)  +/-  (1.33e-164, 1.68e-410j)
| (0.00060460144591195243957 - 4.0526307399134402994e-1231j)  +/-  (5.83e-171, 7.38e-417j)
| (0.01297247152510639489 + 1.6872673774638877456e-1230j)  +/-  (2.57e-169, 3.25e-415j)
| (0.079987999875462535935 - 3.8083501773157787067e-1230j)  +/-  (1.62e-166, 2.05e-412j)
| (1.941988135065754176e-07 + 3.9267527371371425696e-1233j)  +/-  (1.5e-174, 1.9e-420j)
| (0.0053738931282384631566 - 7.5895829438232473961e-1231j)  +/-  (3.4e-170, 4.31e-416j)
| (1.3202034653564462983e-06 - 1.0446033509748804317e-1232j)  +/-  (5.5e-174, 6.96e-420j)
| (0.1367250465995920329 - 4.6957826972158687289e-1230j)  +/-  (3.76e-169, 4.76e-415j)
| (0.049984847265092552608 + 3.1044717233665704183e-1230j)  +/-  (2.24e-170, 2.83e-416j)
| (2.5687327038815620165e-09 + 4.344431305324298637e-1234j)  +/-  (6.56e-176, 8.3e-422j)
| (0.11184219617973975744 + 3.9141289027701448596e-1230j)  +/-  (2.63e-170, 3.33e-416j)
| (6.085029311574782796e-22 - 2.0088956222536750556e-1240j)  +/-  (1.1e-182, 1.39e-428j)
| (7.6651100775855474195e-06 + 5.1516449651638267941e-1232j)  +/-  (2.44e-176, 3.08e-422j)
| (0.0053738931282384631566 - 1.1237156553315452789e-1230j)  +/-  (1.45e-174, 1.71e-420j)
| (1.3202034653564462983e-06 - 2.2352857888995638125e-1232j)  +/-  (8.84e-177, 1.13e-422j)
| (0.14618783860828431171 + 4.7215629236280384236e-1230j)  +/-  (4.97e-173, 4.71e-419j)
