Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 69
-------------------------------------------------
Trying to find an order 69 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^71 - 85266651010580523429007702201744820622010371893/35236959593376964507038384782516353459077539*t^69 + 97323173567289427238063346370812517899603918642183/35236959593376964507038384782516353459077539*t^67 - 1040914220490846905432907238648761973305486381592647/525924770050402455328931116156960499389217*t^65 + 525862236505585257848501186953664849851971422223066120/525924770050402455328931116156960499389217*t^63 - 199381410005826306774960472191775638782336125102613535480/525924770050402455328931116156960499389217*t^61 + 58975114281934158609460396131632185099810124868893720568840/525924770050402455328931116156960499389217*t^59 - 13966379336312600491360925478115180204970604105132846461236440/525924770050402455328931116156960499389217*t^57 + 2696752369901631252700587239003110843668680013903706795074710220/525924770050402455328931116156960499389217*t^55 - 430189990264468286716820524445170134013544543957512768986903858900/525924770050402455328931116156960499389217*t^53 + 57244302682434070026502484483875157681638098838561937733177017240700/525924770050402455328931116156960499389217*t^51 - 6399158318244647539351777581044316853878858489792521388404301861304500/525924770050402455328931116156960499389217*t^49 + 603991792178665731366449729861031471331103495828578363058109682613367000/525924770050402455328931116156960499389217*t^47 - 48301247751697987706955054044529015550125172868442022314373707940555641000/525924770050402455328931116156960499389217*t^45 + 3279605170642966618274517883001096648112023623257754813246268357988477855000/525924770050402455328931116156960499389217*t^43 - 189246050866434847171744288045772017235804783339275990522561835598867370005000/525924770050402455328931116156960499389217*t^41 + 9279318361083359076072333226162498333082369408619800990994538697399954123373750/525924770050402455328931116156960499389217*t^39 - 386182027759358340343131989545563115298637650605080307857145143552073238275736250/525924770050402455328931116156960499389217*t^37 + 13612112906791196256646169575683598955739226022650702559658313124817270091196358750/525924770050402455328931116156960499389217*t^35 - 405085106208381562250257423432521619685798478362289108869386435959666266730701756250/525924770050402455328931116156960499389217*t^33 + 10134858368861698550003169236456195603791645848907957800560825788953027378511978875000/525924770050402455328931116156960499389217*t^31 - 212028262820347028253275583802220309917303262814711412097189528375497731982383123525000/525924770050402455328931116156960499389217*t^29 + 3684298757911596226233240118711895144307425146539232999812548781737111010766927555275000/525924770050402455328931116156960499389217*t^27 - 52737174695079680849179585075231820402388646625451877384946467301322653471152054866825000/525924770050402455328931116156960499389217*t^25 + 615609332579725567203474799887385077640201912138867161289854822538650051572718995637187500/525924770050402455328931116156960499389217*t^23 - 5788680292486065852777112437703848690535522903571008855310933494564961379731097531043312500/525924770050402455328931116156960499389217*t^21 + 43190491124835187797906253042882526270152404454703970309899715340697872687873790519616937500/525924770050402455328931116156960499389217*t^19 - 250966293132279010150649992050379226662485118153835863249875565555067978339643921596393812500/525924770050402455328931116156960499389217*t^17 + 1109336501540066035870721852979773822315643372649702442037114250625859134520042444285323625000/525924770050402455328931116156960499389217*t^15 - 3619581235377640426069658385519279209945437861999352502426119110287784458482431492612314375000/525924770050402455328931116156960499389217*t^13 + 8378758116362418912365428230097553495434530650211503127231950738294425952247554544691160625000/525924770050402455328931116156960499389217*t^11 - 13034299230350435465555998586499159918567766363140578585438049949717215393040106337821506875000/525924770050402455328931116156960499389217*t^9 + 12603442350548974307094194505517105864196455478942535494736355872929295737717096116460791640625/525924770050402455328931116156960499389217*t^7 - 6709371497152360091642294018959872521820837872314858233271303533362460827986228020009701484375/525924770050402455328931116156960499389217*t^5 + 1587756055708799515146286280173728728093134888725377878845299107579386846301533252005023828125/525924770050402455328931116156960499389217*t^3 - 103042933151280922975271916459365113341491076580278437215379757937244614962962977150196484375/525924770050402455328931116156960499389217*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:
| (-12.791550955201324293 + 5.7310542571330102539e-1101j)  +/-  (8.32e-495, 8.32e-495j)
| (-14.761371731102116942 + 1.1224075519409569213e-1103j)  +/-  (2.99e-497, 2.99e-497j)
| (-11.698504445062152335 - 7.9865421052594836395e-1099j)  +/-  (6.96e-494, 6.96e-494j)
| (-14.035487946837654921 + 5.3164147991356599895e-1102j)  +/-  (3.23e-496, 3.23e-496j)
| (-10.217427422732912398 - 5.7775858480214633916e-1099j)  +/-  (2.5e-493, 2.5e-493j)
| (-10.695084947337073047 + 3.0874209646250121407e-1100j)  +/-  (2.05e-493, 2.05e-493j)
| (-7.1534406098306227999 - 5.8467541816910066978e-1100j)  +/-  (2.36e-494, 2.36e-494j)
| (2.0961107513677165933 + 9.3911734505024552372e-1110j)  +/-  (2.58e-503, 2.58e-503j)
| (-8.8545944375847974747 + 1.7754889923955642894e-1098j)  +/-  (2.07e-493, 2.07e-493j)
| (-1.7262090762181637647 + 8.2725234087783420256e-1111j)  +/-  (2.33e-504, 2.33e-504j)
| (-3.22160818956516283 - 1.1170367337962042308e-1106j)  +/-  (1.56e-500, 1.56e-500j)
| (-12.231196160636618444 - 1.1654265720381588158e-1100j)  +/-  (2.74e-494, 2.74e-494j)
| (-3.9835133571449832751 - 2.9260604187464839571e-1105j)  +/-  (7.87e-499, 7.87e-499j)
| (15.639018527535982579 - 5.59806741112597432e-1104j)  +/-  (1.21e-498, 1.21e-498j)
| (-9.2987752056930632091 - 5.3838112768762056669e-1099j)  +/-  (2.7e-493, 2.7e-493j)
| (-8.4188712224713214959 + 1.604069798472329464e-1099j)  +/-  (1.5e-493, 1.5e-493j)
| (-5.9366234838228236454 - 2.1381981744985148337e-1104j)  +/-  (1.23e-495, 1.23e-495j)
| (-5.5394625058961226975 - 2.0606005053667802485e-1103j)  +/-  (3.49e-496, 3.49e-496j)
| (-15.639018527535982579 - 1.2601332569999083622e-1105j)  +/-  (1.2e-498, 1.2e-498j)
| (1.7262090762181637647 + 2.2015855479868918881e-1112j)  +/-  (2.25e-504, 2.25e-504j)
| (2.4688903926109961191 - 1.1050882171701788967e-1110j)  +/-  (2.13e-502, 2.13e-502j)
| (-6.3377227578192276661 + 3.6696756624878097121e-1102j)  +/-  (3.45e-495, 3.45e-495j)
| (-9.7525792983428296438 - 7.4003842146147189673e-1100j)  +/-  (2.73e-493, 2.73e-493j)
| (-2.8441099330469854394 + 1.9415033094713166225e-1109j)  +/-  (1.87e-501, 1.87e-501j)
| (-4.7555365413752956495 + 2.6333212450497051995e-1106j)  +/-  (1.95e-497, 1.95e-497j)
| (3.22160818956516283 - 7.1540780170627789998e-1109j)  +/-  (1.7e-500, 1.7e-500j)
| (-13.388188907136384116 - 9.6474749214073469739e-1105j)  +/-  (2.1e-495, 2.1e-495j)
| (2.8441099330469854394 - 2.0241301548501999248e-1109j)  +/-  (1.97e-501, 1.97e-501j)
| (-6.7431727956076118503 + 4.5116987707966143602e-1103j)  +/-  (9.92e-495, 9.92e-495j)
| (1.3601561504938735675 - 3.8552692277216511676e-1114j)  +/-  (1.75e-505, 1.75e-505j)
| (-11.187797422838583079 - 1.5333441518724598575e-1102j)  +/-  (1.23e-493, 1.23e-493j)
| (-1 + 6.8877910152734915868e-1115j)  +/-  (1.48e-506, 1.48e-506j)
| (-5.1458745681080915823 - 2.5521891376908365645e-1105j)  +/-  (8.85e-497, 8.85e-497j)
| (-4.3681645188438657971 - 2.3827420371021869848e-1106j)  +/-  (4.5e-498, 4.5e-498j)
| (-1.3601561504938735675 - 9.50469640443671356e-1115j)  +/-  (1.91e-505, 1.91e-505j)
| (-2.0961107513677165933 + 2.0834202891828481338e-1112j)  +/-  (2.59e-503, 2.59e-503j)
| (-7.9906331557519273143 - 1.8021112677614509836e-1101j)  +/-  (9.11e-494, 9.11e-494j)
| (1 + 2.7054905701982145093e-1114j)  +/-  (1.43e-506, 1.43e-506j)
| (-6.4965403606857997081e-1143 + 1.3091794389851337885e-1144j)  +/-  (4.61e-1141, 4.61e-1141j)
| (-3.6013794254002150685 - 5.7397710564612579052e-1108j)  +/-  (1.16e-499, 1.16e-499j)
| (-7.5690576868306004164 - 1.2577864443568376386e-1102j)  +/-  (4.85e-494, 4.85e-494j)
| (0.6498615617278924183 + 2.3151012502259954625e-1116j)  +/-  (1.25e-507, 1.25e-507j)
| (-2.4688903926109961191 + 1.6319971816155313785e-1110j)  +/-  (2.47e-502, 2.47e-502j)
| (-0.6498615617278924183 - 7.3020416604183623537e-1132j)  +/-  (1.05e-507, 1.05e-507j)
| (-0.31617492508319598021 + 1.3941721364936586358e-1116j)  +/-  (7.09e-509, 7.09e-509j)
| (0.31617492508319598021 - 1.4648397091169931572e-1116j)  +/-  (7.09e-509, 7.09e-509j)
| (12.791550955201324293 + 7.8376545007156584763e-1101j)  +/-  (8.59e-495, 8.59e-495j)
| (5.5394625058961226975 + 1.1189757172652885e-1115j)  +/-  (3.37e-496, 3.37e-496j)
| (14.035487946837654921 + 3.1785290325088384692e-1111j)  +/-  (3.26e-496, 3.26e-496j)
| (14.761371731102116942 - 8.3884091041841909771e-1134j)  +/-  (3.13e-497, 3.13e-497j)
| (10.695084947337073047 - 1.1250385809700965161e-1193j)  +/-  (1.94e-493, 1.94e-493j)
| (11.698504445062152335 + 1.4914062259439742394e-1271j)  +/-  (6.26e-494, 6.26e-494j)
| (5.1458745681080915823 - 1.873168867871592368e-1335j)  +/-  (8.63e-497, 8.63e-497j)
| (9.7525792983428296438 + 8.9781094104401837792e-1407j)  +/-  (2.82e-493, 2.82e-493j)
| (8.8545944375847974747 + 1.8828791025184653673e-1452j)  +/-  (2.07e-493, 2.07e-493j)
| (13.388188907136384116 + 2.1023409475560387538e-1465j)  +/-  (2.03e-495, 2.03e-495j)
| (5.9366234838228236454 - 3.9625078162221355811e-1474j)  +/-  (1.16e-495, 1.16e-495j)
| (12.231196160636618444 - 1.4461277919274606862e-1478j)  +/-  (2.66e-494, 2.66e-494j)
| (3.6013794254002150685 - 7.5691365062598549901e-1496j)  +/-  (1.14e-499, 1.14e-499j)
| (7.5690576868306004164 + 9.3224208631930545515e-1491j)  +/-  (4.99e-494, 4.99e-494j)
| (3.9835133571449832751 - 9.222795352020981351e-1512j)  +/-  (7.15e-499, 7.15e-499j)
| (9.2987752056930632091 + 1.8185169305655420164e-1504j)  +/-  (2.71e-493, 2.71e-493j)
| (4.7555365413752956495 + 1.1894674786026154746e-1521j)  +/-  (1.92e-497, 1.92e-497j)
| (7.1534406098306227999 - 5.8694001507665773382e-1517j)  +/-  (2.38e-494, 2.38e-494j)
| (8.4188712224713214959 - 5.1416384235404598397e-1527j)  +/-  (1.58e-493, 1.58e-493j)
| (4.3681645188438657971 - 1.4131871511505343837e-1552j)  +/-  (4.51e-498, 4.51e-498j)
| (11.187797422838583079 + 1.2564035552727182401e-1546j)  +/-  (1.29e-493, 1.29e-493j)
| (6.3377227578192276661 - 1.7699890326168539557e-1562j)  +/-  (3.68e-495, 3.68e-495j)
| (10.217427422732912398 - 9.3070761162422741885e-1572j)  +/-  (2.56e-493, 2.56e-493j)
| (7.9906331557519273143 + 4.7504666614894635464e-1587j)  +/-  (9.34e-494, 9.34e-494j)
| (6.7431727956076118503 + 2.913061867978269901e-1594j)  +/-  (9.71e-495, 9.71e-495j)
-------------------------------------------------
The weights are:
| (6.7829810550940176274e-37 + 5.0812483313939996689e-1125j)  +/-  (2.4e-143, 4.37e-388j)
| (1.5069865151741890644e-48 - 4.892099367461615523e-1131j)  +/-  (4.42e-148, 8.07e-393j)
| (3.9810301994665695113e-31 + 5.2465547638617871466e-1122j)  +/-  (2.13e-141, 3.89e-386j)
| (4.5346745059333287366e-44 + 9.8500204413911725133e-1129j)  +/-  (1.36e-146, 2.49e-391j)
| (4.0234259961152633488e-24 - 2.7630930959530872505e-1118j)  +/-  (1.37e-138, 2.5e-383j)
| (2.8059865747664269326e-26 + 1.9307811810504879508e-1119j)  +/-  (1.23e-139, 2.25e-384j)
| (1.2732214426029378169e-12 - 2.8104811723695973014e-1111j)  +/-  (2.71e-131, 4.94e-376j)
| (0.016471397250010959814 + 2.9159448972628788852e-1107j)  +/-  (2.72e-101, 4.96e-346j)
| (1.6556288748527794925e-18 + 5.6739903346212116744e-1115j)  +/-  (2.92e-136, 5.34e-381j)
| (0.033108801409974194843 - 8.5875467484486886894e-1107j)  +/-  (1.13e-96, 2.07e-341j)
| (0.00084217429877639366942 - 1.129003077259855197e-1107j)  +/-  (6.18e-113, 1.13e-357j)
| (7.1108302499220327328e-34 - 1.9051645786541753334e-1123j)  +/-  (4.2e-144, 7.67e-389j)
| (5.4795497065206225671e-05 - 2.9483167869705492597e-1108j)  +/-  (7.65e-119, 1.4e-363j)
| (3.1443286200839398177e-54 - 2.269782270076653948e-1134j)  +/-  (1.36e-161, 2.48e-406j)
| (2.997951315286949436e-20 - 3.4616039080379539775e-1116j)  +/-  (1.41e-137, 2.58e-382j)
| (7.0047865430741006217e-17 - 3.6122811129844694643e-1114j)  +/-  (9.14e-136, 1.67e-380j)
| (3.5393689451121150051e-09 + 2.2654948518989887591e-1110j)  +/-  (8.93e-130, 1.63e-374j)
| (3.4241492661774809613e-08 - 9.899965320732938715e-1110j)  +/-  (1.45e-128, 2.64e-373j)
| (3.1443286200839398177e-54 + 5.9895809265474462503e-1134j)  +/-  (5.02e-156, 9.17e-401j)
| (0.033108801409974194843 - 5.1269769040998709507e-1107j)  +/-  (1.72e-108, 3.14e-353j)
| (0.0070831941629188521408 - 1.5793275837083650085e-1107j)  +/-  (4.07e-117, 7.43e-362j)
| (3.0502667612791860293e-10 - 1.1461043698940462462e-1110j)  +/-  (1.5e-131, 2.73e-376j)
| (4.0672488125935718671e-22 + 3.3292079802308659655e-1117j)  +/-  (7.5e-140, 1.37e-384j)
| (0.0026304470162099877663 + 2.0164210985959039227e-1107j)  +/-  (1.34e-118, 2.44e-363j)
| (1.9047408677629432244e-06 - 5.283931093770004215e-1109j)  +/-  (1.66e-127, 3.03e-372j)
| (0.00084217429877639366942 - 3.9162870093607269778e-1108j)  +/-  (1.51e-127, 2.75e-372j)
| (2.9528572468549260524e-40 - 9.1805701176562843945e-1127j)  +/-  (5.43e-150, 9.92e-395j)
| (0.0026304470162099877663 + 8.0982271945820934609e-1108j)  +/-  (4.37e-125, 7.98e-370j)
| (2.1755266579386946739e-11 + 8.5260852437407154022e-1111j)  +/-  (1.63e-133, 2.98e-378j)
| (0.057514834602646305786 + 8.6299844700230851914e-1107j)  +/-  (1.27e-111, 2.31e-356j)
| (1.322050009444030383e-28 - 1.1206781418828611997e-1120j)  +/-  (5.2e-144, 9.5e-389j)
| (0.08615781283651643238 - 1.8697820438081053539e-1106j)  +/-  (5.93e-110, 1.08e-354j)
| (2.7799356776987904069e-07 + 2.4862893852999438904e-1109j)  +/-  (1.26e-129, 2.31e-374j)
| (1.1069086485711632904e-05 + 1.055260354006413065e-1108j)  +/-  (1.02e-127, 1.86e-372j)
| (0.057514834602646305786 + 1.289886461071180605e-1106j)  +/-  (6.42e-114, 1.17e-358j)
| (0.016471397250010959814 + 5.5070124641532789383e-1107j)  +/-  (1.14e-119, 2.07e-364j)
| (2.3130011216165801898e-15 + 3.2816301811938545667e-1113j)  +/-  (9.92e-138, 1.81e-382j)
| (0.08615781283651643238 - 1.3946765240371438503e-1106j)  +/-  (7.94e-114, 1.45e-358j)
| (0.12444814290588640902 + 3.5045850683697639959e-1106j)  +/-  (3.74e-115, 6.83e-360j)
| (0.0002319378604696116469 + 6.1153848554261489978e-1108j)  +/-  (8.13e-127, 1.48e-371j)
| (6.0546547776178553386e-14 - 3.637996494652413155e-1112j)  +/-  (9.53e-137, 1.74e-381j)
| (0.11080352098205949731 + 2.1443757035249362018e-1106j)  +/-  (2.92e-115, 5.32e-360j)
| (0.0070831941629188521408 - 3.3931993344535192529e-1107j)  +/-  (2.47e-123, 4.5e-368j)
| (0.11080352098205949731 + 2.5918760317540883974e-1106j)  +/-  (6.44e-116, 1.18e-360j)
| (0.12286372270050840713 - 3.2865855635449305027e-1106j)  +/-  (1.24e-115, 2.26e-360j)
| (0.12286372270050840713 - 2.9978495332132157361e-1106j)  +/-  (2.83e-116, 5.17e-361j)
| (6.7829810550940176274e-37 - 1.4735346509765781781e-1125j)  +/-  (1.05e-169, 1.92e-414j)
| (3.4241492661774809613e-08 - 1.1998230872550876973e-1110j)  +/-  (2e-150, 3.65e-395j)
| (4.5346745059333287366e-44 - 3.2678524373060355104e-1129j)  +/-  (4e-172, 7.3e-417j)
| (1.5069865151741890644e-48 + 1.7316825623188510858e-1131j)  +/-  (1.89e-173, 3.44e-418j)
| (2.8059865747664269326e-26 - 4.0066647476197672042e-1120j)  +/-  (3.93e-167, 7.18e-412j)
| (3.9810301994665695113e-31 - 1.3061270529917756601e-1122j)  +/-  (6.93e-169, 1.26e-413j)
| (2.7799356776987904069e-07 + 3.7954263866796002236e-1110j)  +/-  (5.94e-153, 1.09e-397j)
| (4.0672488125935718671e-22 - 5.5853475066313588048e-1118j)  +/-  (5.96e-166, 1.09e-410j)
| (1.6556288748527794925e-18 - 4.1451726543045750704e-1116j)  +/-  (1.33e-164, 2.43e-409j)
| (2.9528572468549260524e-40 + 2.8518912343528106501e-1127j)  +/-  (1.71e-172, 3.13e-417j)
| (3.5393689451121150051e-09 + 3.4919155578520000312e-1111j)  +/-  (5.16e-158, 9.43e-403j)
| (7.1108302499220327328e-34 + 5.1342368061179192691e-1124j)  +/-  (2.25e-170, 4.11e-415j)
| (0.0002319378604696116469 + 1.780914389337453485e-1108j)  +/-  (5.71e-151, 1.04e-395j)
| (6.0546547776178553386e-14 + 1.0081323217376173901e-1113j)  +/-  (3.01e-163, 5.49e-408j)
| (5.4795497065206225671e-05 - 7.5737351614246418822e-1109j)  +/-  (2.98e-153, 5.43e-398j)
| (2.997951315286949436e-20 + 5.1680944269269194888e-1117j)  +/-  (3.6e-166, 6.57e-411j)
| (1.9047408677629432244e-06 - 1.109281981004904373e-1109j)  +/-  (3.01e-156, 5.49e-401j)
| (1.2732214426029378169e-12 - 5.0330371576382840432e-1113j)  +/-  (8.42e-163, 1.54e-407j)
| (7.0047865430741006217e-17 + 2.9150626339173795116e-1115j)  +/-  (2.87e-165, 5.23e-410j)
| (1.1069086485711632904e-05 + 3.0055296475377298267e-1109j)  +/-  (1.43e-156, 2.61e-401j)
| (1.322050009444030383e-28 + 2.558310129504081973e-1121j)  +/-  (6.15e-171, 1.12e-415j)
| (3.0502667612791860293e-10 - 9.320212016721567691e-1112j)  +/-  (7.47e-162, 1.36e-406j)
| (4.0234259961152633488e-24 + 5.1603767413818419128e-1119j)  +/-  (3.41e-169, 6.23e-414j)
| (2.3130011216165801898e-15 - 1.814673827017988684e-1114j)  +/-  (3.97e-165, 7.27e-410j)
| (2.1755266579386946739e-11 + 2.271767598693228367e-1112j)  +/-  (5.36e-163, 9.76e-408j)
