Starting with polynomial:
P : 8*t^3 - 12*t
Extension levels are: 3 72
-------------------------------------------------
Trying to find an order 72 Kronrod extension for:
P1 : 8*t^3 - 12*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^75 - 6198343405440649591171005557652828559327116/570831318897806310999477864496173894245*t^73 + 3981721675422981478572809080344569368395318924/570831318897806310999477864496173894245*t^71 - 46045058846078898079664165526849559417533884526/16309466254223037457127938985604968407*t^69 + 26376710168596200240781127943133135637761634386707/32618932508446074914255877971209936814*t^67 - 11385762647858263452316504324268853868231151239620213/65237865016892149828511755942419873628*t^65 + 481335575897075776853582401123650190155911335982338926/16309466254223037457127938985604968407*t^63 - 65465690468980939172896221273293181420041953495568372769/16309466254223037457127938985604968407*t^61 + 58363337311792623839366693294701002601700862193764425805315/130475730033784299657023511884839747256*t^59 - 183104607498840329081162997733980397990870752359269991698095/4422906102840145751085542775757279568*t^57 + 14216335889375973178124458702499153717025623711116197986275965/4422906102840145751085542775757279568*t^55 - 1865824753546505892902234875086600676041267786834957835730933115/8845812205680291502171085551514559136*t^53 + 416258009212259658418677710552125649531909540256366247314588982665/35383248822721166008684342206058236544*t^51 - 39622906925692810836810094970052812564968083690291338646483955107375/70766497645442332017368684412116473088*t^49 + 806830691136155566364478165662743953404284288810374202240932267520875/35383248822721166008684342206058236544*t^47 - 56325889607747722378238388549845568614848144303648356442070886499174125/70766497645442332017368684412116473088*t^45 + 26980559466770167635535975060660047878908629425879393961109400854910209875/1132263962327077312277898950593863569408*t^43 - 1385297801803988650737710873741136763647122762445407346441442514243205457125/2264527924654154624555797901187727138816*t^41 + 30464179169167590286206554030206787447818789007011929356771814281166264935625/2264527924654154624555797901187727138816*t^39 - 1145599761259195457585444721516086262556671488574593630406053413778254483899375/4529055849308309249111595802375454277632*t^37 + 73466229225728935940988333467883580455584119711323086258807204301362240711604375/18116223397233236996446383209501817110528*t^35 - 2001339573295204541525604707012548115038661018034716707422852118610960762539460625/36232446794466473992892766419003634221056*t^33 + 5763407955584267694169619897305184351507315932745837912538500346049974114750391875/9058111698616618498223191604750908555264*t^31 - 111656551910719940006501214704839862018385725969356497904605505059312420129361603125/18116223397233236996446383209501817110528*t^29 + 7226260692390229721587928589966257314016707559859530546074412551861914095740803028125/144929787177865895971571065676014536884224*t^27 - 96835209665057278778412620788066442865641973180928170464478090429733376188703051596875/289859574355731791943142131352029073768448*t^25 + 532002226205513839994600331767345959860515608969779992665796703642262375806953242378125/289859574355731791943142131352029073768448*t^23 - 4735220913348741238359263541059945785147906651552993610234014104429091438397430268696875/579719148711463583886284262704058147536896*t^21 + 67280758939353902973759081822276969196264727841392953782327886454265864774612257882203125/2318876594845854335545137050816232590147584*t^19 - 374626824638603915194279137944826294007522633121481433907099689293045041842344260569171875/4637753189691708671090274101632465180295168*t^17 + 399533064038992332038716273922389830891668396374370982039478454529635729555755418983078125/2318876594845854335545137050816232590147584*t^15 - 1268430687619178187742296777686049532269521609585858567527277820172617523466763579958546875/4637753189691708671090274101632465180295168*t^13 + 46160564691080621234268724733312303597623263510501833704170757996081640619735996632389078125/148408102070134677474888771252238885769445376*t^11 - 71420554275022155244313125228114459061225307078591972124629468342385329707113689410658046875/296816204140269354949777542504477771538890752*t^9 + 34891853328481733875506199006257394655159210279831058392986415307159489731294497641529921875/296816204140269354949777542504477771538890752*t^7 - 19183694989171043102413857852696045413801837146126878926113161365716047652940813474685703125/593632408280538709899555085008955543077781504*t^5 + 9684598878473914377513331278687585574726748957975068231352485303964667481724960202474140625/2374529633122154839598220340035822172311126016*t^3 - 706345088888966155704240304080146966451101761377629130934945303088142129786893840280234375/4749059266244309679196440680071644344622252032*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:   75 out of 75
Indefinite weights: 0 out of 75
Negative weights:   0 out of 75
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (10.78989181338727529 + 4.1666094676237594833e-1206j)  +/-  (9.53e-497, 9.53e-497j)
| (10.282174918887065219 + 1.4085493257380110476e-1206j)  +/-  (1.09e-495, 1.09e-495j)
| (-10.78989181338727529 + 6.2655618185259248041e-1202j)  +/-  (9.63e-497, 9.63e-497j)
| (-8.2926998817376995718 + 2.203422139841377105e-1206j)  +/-  (6.52e-493, 6.52e-493j)
| (-6.3627337142699650955 + 1.4649093664440051764e-1221j)  +/-  (1.46e-492, 1.46e-492j)
| (8.2926998817376995718 + 1.7710853981029235853e-1232j)  +/-  (6.47e-493, 6.47e-493j)
| (9.0211782723105601324 + 2.2625663043065326107e-1235j)  +/-  (1.2e-493, 1.2e-493j)
| (-9.0211782723105601324 + 3.7829654470841395886e-1233j)  +/-  (1.24e-493, 1.24e-493j)
| (9.8296129405477963674 - 1.2821991217988916301e-1246j)  +/-  (7.72e-495, 7.72e-495j)
| (-11.404038183907280835 + 7.4877927206809174417e-1246j)  +/-  (3.16e-498, 3.16e-498j)
| (5.1976417327112153168 + 1.3406700839151108829e-1245j)  +/-  (1.49e-493, 1.49e-493j)
| (-9.4126390120145140535 - 8.4032699707663426931e-1244j)  +/-  (3.71e-494, 3.71e-494j)
| (-3.2856899598764521428 - 8.4323793940138800257e-1257j)  +/-  (2.96e-497, 2.96e-497j)
| (-3.8195294038802143268 - 1.242783566137232453e-1253j)  +/-  (5.89e-496, 5.89e-496j)
| (-6.0647471582927445677 + 3.8158904595998777419e-1256j)  +/-  (9.42e-493, 9.42e-493j)
| (2.240990797186609772 + 3.1056348529880896954e-1275j)  +/-  (2.21e-500, 2.21e-500j)
| (2.7597624107748923653 + 1.1450816906841586559e-1274j)  +/-  (1.08e-498, 1.08e-498j)
| (-9.8296129405477963674 - 8.3112191852463094889e-1267j)  +/-  (7.62e-495, 7.62e-495j)
| (-1.9841948172247531663 + 1.0794850816034324026e-1279j)  +/-  (2.63e-501, 2.63e-501j)
| (-1.7291572743549798166 - 7.6009624312914422317e-1281j)  +/-  (2.81e-502, 2.81e-502j)
| (4.3624750255560023644 - 1.1533202766738665107e-1273j)  +/-  (7.9e-495, 7.9e-495j)
| (1.2247448713915890491 - 1.1020662855995011118e-1282j)  +/-  (2.79e-504, 2.79e-504j)
| (5.4826545734262849067 - 2.6166495424093492461e-1270j)  +/-  (3.29e-493, 3.29e-493j)
| (6.3627337142699650955 + 1.1781957826474782106e-1269j)  +/-  (1.41e-492, 1.41e-492j)
| (-5.4826545734262849067 + 1.6444242710608211268e-1273j)  +/-  (3.08e-493, 3.08e-493j)
| (-4.916146731601613018 - 9.9749839314641138454e-1284j)  +/-  (5.85e-494, 5.85e-494j)
| (-10.282174918887065219 - 1.6909846811554828528e-1302j)  +/-  (1.08e-495, 1.08e-495j)
| (11.404038183907280835 - 3.5928357816070678279e-1323j)  +/-  (3.23e-498, 3.23e-498j)
| (-7.6157653298628376323 - 1.5058210248031438425e-1344j)  +/-  (1.58e-492, 1.58e-492j)
| (-4.3624750255560023644 + 1.6843797774212069183e-1369j)  +/-  (7.44e-495, 7.44e-495j)
| (-8.6491911214234841607 + 8.4207786240465579973e-1390j)  +/-  (3.41e-493, 3.41e-493j)
| (5.7715498046095411359 - 1.5195313547164039175e-1423j)  +/-  (5.86e-493, 5.86e-493j)
| (3.0217954323614121151 - 6.252833241505741898e-1446j)  +/-  (5.96e-498, 5.96e-498j)
| (8.6491911214234841607 - 1.8444644923532607739e-1463j)  +/-  (3.11e-493, 3.11e-493j)
| (-2.7597624107748923653 - 9.5658176498687384171e-1486j)  +/-  (1.02e-498, 1.02e-498j)
| (-1.475962987688717624 + 3.1556639853954100389e-1499j)  +/-  (2.84e-503, 2.84e-503j)
| (4.916146731601613018 - 2.7355246523994994306e-1490j)  +/-  (6e-494, 6e-494j)
| (3.2856899598764521428 - 1.0574183187074495165e-1506j)  +/-  (3.02e-497, 3.02e-497j)
| (-6.6660801516875339988 - 8.0566946974032265621e-1520j)  +/-  (1.78e-492, 1.78e-492j)
| (-5.1976417327112153168 + 4.5284990961627711656e-1554j)  +/-  (1.41e-493, 1.41e-493j)
| (7.9489104320498079176 + 3.6521595145800863951e-1589j)  +/-  (1.17e-492, 1.17e-492j)
| (-6.9754627788498218769 - 4.5164283625780351405e-1620j)  +/-  (2.01e-492, 2.01e-492j)
| (1.475962987688717624 - 1.5680197303245612593e-1648j)  +/-  (2.85e-503, 2.85e-503j)
| (0.97566331749257619681 + 3.1512172916486954003e-1651j)  +/-  (1.99e-505, 1.99e-505j)
| (4.0897730618328225626 - 3.683494090137657554e-1641j)  +/-  (2.23e-495, 2.23e-495j)
| (-2.4995101460299189001 + 7.8372739615905934827e-1645j)  +/-  (1.52e-499, 1.52e-499j)
| (9.4126390120145140535 + 2.498966091505763393e-1639j)  +/-  (3.58e-494, 3.58e-494j)
| (-3.0217954323614121151 - 4.2887903607119579875e-1643j)  +/-  (6.36e-498, 6.36e-498j)
| (1.9841948172247531663 - 3.2569260050207968178e-1648j)  +/-  (3.03e-501, 3.03e-501j)
| (-5.7715498046095411359 - 7.4015655178683045856e-1637j)  +/-  (5.99e-493, 5.99e-493j)
| (-4.0897730618328225626 + 1.0710365566548333355e-1643j)  +/-  (2.34e-495, 2.34e-495j)
| (-0.72884587852435762022 + 1.2585531690268045202e-1654j)  +/-  (1.73e-506, 1.73e-506j)
| (4.6378510073106721048 - 2.1414047546316123231e-1642j)  +/-  (2.17e-494, 2.17e-494j)
| (7.2916939811213103622 - 4.8279692903348075544e-1640j)  +/-  (1.87e-492, 1.87e-492j)
| (2.4995101460299189001 + 2.914262926629762538e-1653j)  +/-  (1.56e-499, 1.56e-499j)
| (6.9754627788498218769 + 2.5556614206957605226e-1645j)  +/-  (2.02e-492, 2.02e-492j)
| (-4.6378510073106721048 - 2.2068275852972972306e-1652j)  +/-  (2.1e-494, 2.1e-494j)
| (-1.2247448713915890491 - 1.5320094353241495463e-1661j)  +/-  (2.69e-504, 2.69e-504j)
| (6.6660801516875339988 + 1.8074390820123256341e-1649j)  +/-  (1.78e-492, 1.78e-492j)
| (0.72884587852435762022 - 2.0644706010726051326e-1669j)  +/-  (1.58e-506, 1.58e-506j)
| (1.7291572743549798166 + 5.4182555868625703967e-1665j)  +/-  (3.08e-502, 3.08e-502j)
| (6.0647471582927445677 - 1.9425224876935633042e-1654j)  +/-  (1.02e-492, 1.02e-492j)
| (-0.48426634461178184644 + 2.299007749092536988e-1680j)  +/-  (1.07e-507, 1.07e-507j)
| (-1.8899577543004765745e-1709 - 5.4937223779418407375e-1710j)  +/-  (1.48e-1707, 1.48e-1707j)
| (0.24157760165518360631 - 5.6100359634666543061e-1682j)  +/-  (5e-509, 5e-509j)
| (3.5515557847391762841 + 2.8298933855627367725e-1669j)  +/-  (1.4e-496, 1.4e-496j)
| (-7.2916939811213103622 + 4.8968285661695176841e-1664j)  +/-  (1.9e-492, 1.9e-492j)
| (-0.24157760165518360631 + 4.1927042131419774059e-1696j)  +/-  (5e-509, 5e-509j)
| (-3.5515557847391762841 - 1.3218142908220449037e-1683j)  +/-  (1.38e-496, 1.38e-496j)
| (3.8195294038802143268 + 3.237210057536643178e-1682j)  +/-  (6.22e-496, 6.22e-496j)
| (7.6157653298628376323 - 4.2454879488438644381e-1678j)  +/-  (1.62e-492, 1.62e-492j)
| (0.48426634461178184644 + 4.068614557044457723e-1698j)  +/-  (9.06e-508, 9.06e-508j)
| (-0.97566331749257619681 - 1.0637488710000166907e-1695j)  +/-  (2.01e-505, 2.01e-505j)
| (-2.240990797186609772 - 2.7189237461756567821e-1690j)  +/-  (2.24e-500, 2.24e-500j)
| (-7.9489104320498079176 - 1.8165449964914772563e-1680j)  +/-  (1.09e-492, 1.09e-492j)
-------------------------------------------------
The weights are:
| (8.4744336105401324782e-52 + 1.3455589621439350393e-1248j)  +/-  (1.87e-185, 3.34e-431j)
| (3.2633028753568838014e-47 - 2.8445542356692972083e-1246j)  +/-  (6.37e-184, 1.14e-429j)
| (8.4744336105401324782e-52 - 1.0281657290087270074e-1247j)  +/-  (2.25e-187, 4.01e-433j)
| (2.6868122787222415868e-31 + 4.9791499777277490293e-1236j)  +/-  (3.08e-179, 5.5e-425j)
| (4.4383161000403741145e-19 + 5.0969299914708300297e-1231j)  +/-  (2.41e-171, 4.29e-417j)
| (2.6868122787222415868e-31 + 3.5695206709875086854e-1238j)  +/-  (1.54e-179, 2.74e-425j)
| (9.7423732215148729208e-37 + 5.9962052795763981541e-1241j)  +/-  (7.45e-182, 1.33e-427j)
| (9.7423732215148729208e-37 - 1.4251250351723100871e-1239j)  +/-  (9.06e-183, 1.62e-428j)
| (2.6631864891879796735e-43 + 2.7531700435185094733e-1244j)  +/-  (1.64e-184, 2.93e-430j)
| (1.3238165155181092233e-57 + 9.7663311555586239366e-1251j)  +/-  (6.31e-191, 1.13e-436j)
| (2.9569256330041032578e-13 + 7.2159397140979284223e-1229j)  +/-  (1.26e-169, 2.25e-415j)
| (7.5713554180997844047e-40 + 2.4787474059793998338e-1241j)  +/-  (2.23e-184, 3.98e-430j)
| (3.0612756005489065781e-06 - 9.4943887464474602034e-1225j)  +/-  (3.28e-158, 5.86e-404j)
| (7.0059681130929679058e-08 - 1.4074539119440188091e-1225j)  +/-  (3.3e-162, 5.89e-408j)
| (1.7706595396830259102e-17 - 2.9200407471222460249e-1230j)  +/-  (1.1e-173, 1.96e-419j)
| (0.00095813609216566379593 - 1.0905722638435217519e-1223j)  +/-  (8.45e-151, 1.51e-396j)
| (7.2539186951099774085e-05 - 2.426596473861177741e-1224j)  +/-  (3.52e-156, 6.27e-402j)
| (2.6631864891879796735e-43 - 3.2463473049395284484e-1243j)  +/-  (1.74e-186, 3.1e-432j)
| (0.0028165051566834837114 + 3.4119928093273265182e-1223j)  +/-  (2.65e-148, 4.73e-394j)
| (0.0072103182939620270522 - 5.7580361067516769056e-1223j)  +/-  (3.33e-145, 5.94e-391j)
| (8.3953060498234818821e-10 - 4.8255458990584142064e-1227j)  +/-  (7.65e-169, 1.37e-414j)
| (0.031494177803173118352 - 1.0073961597798021111e-1222j)  +/-  (8.49e-140, 1.52e-385j)
| (1.4271299361361902468e-14 - 1.4760712578743277173e-1229j)  +/-  (2.16e-174, 3.86e-420j)
| (4.4383161000403741145e-19 + 6.71212565706427478e-1232j)  +/-  (8.6e-179, 1.53e-424j)
| (1.4271299361361902468e-14 - 7.2359655355837858183e-1229j)  +/-  (1.55e-174, 2.77e-420j)
| (5.0361437680198709555e-12 - 1.2536823186198901797e-1227j)  +/-  (2.13e-172, 3.8e-418j)
| (3.2633028753568838014e-47 + 2.6558074338166186146e-1245j)  +/-  (1.7e-190, 3.04e-436j)
| (1.3238165155181092233e-57 - 1.5426967180048409859e-1251j)  +/-  (1.59e-197, 2.85e-443j)
| (1.1988673769093930406e-26 + 2.007228765768444805e-1234j)  +/-  (2.54e-183, 4.54e-429j)
| (8.3953060498234818821e-10 - 1.5538067263758677439e-1226j)  +/-  (1.58e-171, 2.81e-417j)
| (6.6564089255984143849e-34 + 7.9326490911896447644e-1238j)  +/-  (1.73e-185, 3.08e-431j)
| (5.6051082738283578188e-16 + 2.728701094878167723e-1230j)  +/-  (5.13e-180, 9.15e-426j)
| (1.6056250458034892296e-05 + 1.0338691763932101013e-1224j)  +/-  (6.21e-168, 1.11e-413j)
| (6.6564089255984143849e-34 - 1.6691916108475003823e-1239j)  +/-  (5.31e-190, 9.47e-436j)
| (7.2539186951099774085e-05 - 4.8473092108908044002e-1224j)  +/-  (3.93e-166, 7.01e-412j)
| (0.016111235460848837966 + 9.1242930642073002654e-1223j)  +/-  (4.08e-156, 7.27e-402j)
| (5.0361437680198709555e-12 - 3.2047668611359889716e-1228j)  +/-  (4.74e-177, 8.46e-423j)
| (3.0612756005489065781e-06 - 4.1057966685340070892e-1225j)  +/-  (2.36e-170, 4.22e-416j)
| (8.6877733882216968051e-21 - 8.0899703871999648306e-1232j)  +/-  (6.7e-182, 1.2e-427j)
| (2.9569256330041032578e-13 + 3.1451890958326561001e-1228j)  +/-  (3.67e-177, 6.55e-423j)
| (6.9117480896692453839e-29 - 6.0928715491365628065e-1237j)  +/-  (1.61e-189, 2.87e-435j)
| (1.3031464724257011834e-22 + 1.171070497131820133e-1232j)  +/-  (2.79e-183, 4.98e-429j)
| (0.016111235460848837966 + 6.367085707594454097e-1223j)  +/-  (1.5e-162, 2.68e-408j)
| (0.054000647167912209283 + 1.4905765871688147968e-1222j)  +/-  (2.93e-160, 5.23e-406j)
| (8.3364722529036631932e-09 + 1.6487069020244898177e-1226j)  +/-  (2.91e-176, 5.2e-422j)
| (0.00028319528204497379176 + 9.9086475764000200519e-1224j)  +/-  (9.74e-169, 1.74e-414j)
| (7.5713554180997844047e-40 - 1.5679205122147651924e-1242j)  +/-  (1.16e-193, 2.07e-439j)
| (1.6056250458034892296e-05 + 2.2192973801234122826e-1224j)  +/-  (3.64e-171, 6.5e-417j)
| (0.0028165051566834837114 + 2.0944632206747543875e-1223j)  +/-  (2.27e-168, 4.05e-414j)
| (5.6051082738283578188e-16 + 1.5222062917107564026e-1229j)  +/-  (8.05e-180, 1.44e-425j)
| (8.3364722529036631932e-09 + 4.8573435945307044657e-1226j)  +/-  (1.67e-175, 2.97e-421j)
| (0.08148514007265452268 - 2.4507563057013757983e-1222j)  +/-  (1.15e-165, 2.06e-411j)
| (7.1129778903438950837e-11 + 1.2990422626559654106e-1227j)  +/-  (8.39e-179, 1.5e-424j)
| (1.4642497727725145956e-24 - 1.0051184576136588451e-1234j)  +/-  (5.54e-189, 9.89e-435j)
| (0.00028319528204497379176 + 5.3189003165416931654e-1224j)  +/-  (2.4e-173, 4.28e-419j)
| (1.3031464724257011834e-22 + 1.0103240623121292313e-1233j)  +/-  (3.04e-188, 5.42e-434j)
| (7.1129778903438950837e-11 + 4.5959009250787335464e-1227j)  +/-  (4.32e-180, 7.71e-426j)
| (0.031494177803173118352 - 1.3565219629688266036e-1222j)  +/-  (2.79e-171, 4.98e-417j)
| (8.6877733882216968051e-21 - 8.7970533133924492056e-1233j)  +/-  (2.15e-187, 3.83e-433j)
| (0.08148514007265452268 - 2.0547658494970233948e-1222j)  +/-  (2.06e-172, 3.69e-418j)
| (0.0072103182939620270522 - 3.7710696611512651096e-1223j)  +/-  (3.67e-174, 6.56e-420j)
| (1.7706595396830259102e-17 - 4.531249872493296204e-1231j)  +/-  (1.36e-185, 2.43e-431j)
| (0.10868005942315588907 + 2.9499335352868085805e-1222j)  +/-  (5.59e-173, 1e-418j)
| (0.13618355949111000727 + 3.3233410574235293266e-1222j)  +/-  (1.93e-173, 3.47e-419j)
| (0.12877656855399429567 - 3.0860210401908559798e-1222j)  +/-  (2e-173, 3.59e-419j)
| (5.0092267983739764652e-07 + 1.5165688750663845526e-1225j)  +/-  (6.17e-180, 1.11e-425j)
| (1.4642497727725145956e-24 - 1.5648401819871575205e-1233j)  +/-  (9.91e-191, 1.81e-436j)
| (0.12877656855399429567 - 3.2712159096452746555e-1222j)  +/-  (2.59e-175, 4.55e-421j)
| (5.0092267983739764652e-07 + 3.7886684237463571319e-1225j)  +/-  (1.01e-180, 1.78e-426j)
| (7.0059681130929679058e-08 - 5.1978737026038946229e-1226j)  +/-  (5.66e-181, 9.94e-427j)
| (1.1988673769093930406e-26 + 8.5411407510872697301e-1236j)  +/-  (3.1e-191, 5.43e-437j)
| (0.10868005942315588907 + 2.6244103463207105946e-1222j)  +/-  (5.61e-177, 9.73e-423j)
| (0.054000647167912209283 + 1.8880873177494363932e-1222j)  +/-  (1.21e-177, 2.09e-423j)
| (0.00095813609216566379593 - 1.8982651451937810257e-1223j)  +/-  (1.53e-179, 2.52e-425j)
| (6.9117480896692453839e-29 - 2.8784445506852347208e-1235j)  +/-  (2.93e-193, 5.56e-439j)
