Starting with polynomial:
P : t
Extension levels are: 1 2 72
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 72 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^75 - 1549585851360162397792751389413207139831779/570831318897806310999477864496173894245*t^73 + 1990860837711490739286404540172284684197659462/570831318897806310999477864496173894245*t^71 - 46045058846078898079664165526849559417533884526/16309466254223037457127938985604968407*t^69 + 26376710168596200240781127943133135637761634386707/16309466254223037457127938985604968407*t^67 - 11385762647858263452316504324268853868231151239620213/16309466254223037457127938985604968407*t^65 + 3850684607176606214828659208989201521247290687858711408/16309466254223037457127938985604968407*t^63 - 1047451047503695026766339540372690902720671255929093964304/16309466254223037457127938985604968407*t^61 + 233453349247170495357466773178804010406803448775057703221260/16309466254223037457127938985604968407*t^59 - 732418429995361316324651990935921591963483009437079966792380/276431631427509109442846423484829973*t^57 + 113730687115007785424995669619993229736204989688929583890207720/276431631427509109442846423484829973*t^55 - 14926598028372047143217879000692805408330142294679662685847464920/276431631427509109442846423484829973*t^53 + 1665032036849038633674710842208502598127638161025464989258355930660/276431631427509109442846423484829973*t^51 - 158491627702771243347240379880211250259872334761165354585935820429500/276431631427509109442846423484829973*t^49 + 12909291058178489061831650650603903254468548620965987235854916280334000/276431631427509109442846423484829973*t^47 - 901214233723963558051814216797529097837570308858373703073134183986786000/276431631427509109442846423484829973*t^45 + 53961118933540335271071950121320095757817258851758787922218801709820419750/276431631427509109442846423484829973*t^43 - 2770595603607977301475421747482273527294245524890814692882885028486410914250/276431631427509109442846423484829973*t^41 + 121856716676670361144826216120827149791275156028047717427087257124665059742500/276431631427509109442846423484829973*t^39 - 4582399045036781830341778886064345050226685954298374521624213655113017935597500/276431631427509109442846423484829973*t^37 + 146932458451457871881976666935767160911168239422646172517614408602724481423208750/276431631427509109442846423484829973*t^35 - 4002679146590409083051209414025096230077322036069433414845704237221921525078921250/276431631427509109442846423484829973*t^33 + 92214527289348283106713918356882949624117054923933406600616005536799585836006270000/276431631427509109442846423484829973*t^31 - 1786504830571519040104019435277437792294171615509703966473688080948998722069785650000/276431631427509109442846423484829973*t^29 + 28905042769560918886351714359865029256066830239438122184297650207447656382963212112500/276431631427509109442846423484829973*t^27 - 387340838660229115113650483152265771462567892723712681857912361718933504754812206387500/276431631427509109442846423484829973*t^25 + 4256017809644110719956802654138767678884124871758239941326373629138099006455625939025000/276431631427509109442846423484829973*t^23 - 37881767306789929906874108328479566281183253212423948881872112835432731507179442149575000/276431631427509109442846423484829973*t^21 + 269123035757415611895036327289107876785058911365571815129311545817063459098449031528812500/276431631427509109442846423484829973*t^19 - 1498507298554415660777116551779305176030090532485925735628398757172180167369377042276687500/276431631427509109442846423484829973*t^17 + 6392529024623877312619460382758237294266694341989935712631655272474171672892086703729250000/276431631427509109442846423484829973*t^15 - 20294891001906851003876748442976792516312345753373737080436445122761880375468217279336750000/276431631427509109442846423484829973*t^13 + 46160564691080621234268724733312303597623263510501833704170757996081640619735996632389078125/276431631427509109442846423484829973*t^11 - 71420554275022155244313125228114459061225307078591972124629468342385329707113689410658046875/276431631427509109442846423484829973*t^9 + 69783706656963467751012398012514789310318420559662116785972830614318979462588995283059843750/276431631427509109442846423484829973*t^7 - 38367389978342086204827715705392090827603674292253757852226322731432095305881626949371406250/276431631427509109442846423484829973*t^5 + 9684598878473914377513331278687585574726748957975068231352485303964667481724960202474140625/276431631427509109442846423484829973*t^3 - 706345088888966155704240304080146966451101761377629130934945303088142129786893840280234375/276431631427509109442846423484829973*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:
| (-15.259211339030713086 - 5.1689893913683018489e-1193j)  +/-  (1.27e-496, 1.27e-496j)
| (15.259211339030713086 + 2.4713170845203537039e-1187j)  +/-  (1.37e-496, 1.37e-496j)
| (-13.901171933400773252 + 3.1734339590293826771e-1192j)  +/-  (1.12e-494, 1.12e-494j)
| (16.12774546550231689 + 3.2399686048801409959e-1191j)  +/-  (4.07e-498, 4.07e-498j)
| (-13.311481748513015727 + 5.361577125738756445e-1191j)  +/-  (4.84e-494, 4.84e-494j)
| (9.8647940656781354854 - 7.1172952871437235817e-1189j)  +/-  (2.91e-492, 2.91e-492j)
| (2.0873268747500979811 - 4.8700645481714770593e-1208j)  +/-  (3.83e-503, 3.83e-503j)
| (12.231803387474050429 - 3.2222576977959174362e-1196j)  +/-  (4.49e-493, 4.49e-493j)
| (-11.727648641443216128 + 4.2566174772220373278e-1206j)  +/-  (8.58e-493, 8.58e-493j)
| (2.4453976688689072766 - 1.0922142646778092829e-1215j)  +/-  (3.91e-502, 3.91e-502j)
| (-10.770318617342832917 + 2.1855474592717145324e-1205j)  +/-  (2.22e-492, 2.22e-492j)
| (13.311481748513015727 + 4.7402606384407638461e-1204j)  +/-  (5.15e-494, 5.15e-494j)
| (-16.12774546550231689 - 3.6714804532150327797e-1218j)  +/-  (4.3e-498, 4.3e-498j)
| (-9.427260958382609267 - 6.3807422238167202579e-1211j)  +/-  (2.56e-492, 2.56e-492j)
| (-10.312012520776024003 + 6.8916577516232841878e-1213j)  +/-  (2.61e-492, 2.61e-492j)
| (11.727648641443216128 + 1.9305251421409035188e-1215j)  +/-  (8.88e-493, 8.88e-493j)
| (-12.757872661287080163 + 4.0007884506061417219e-1231j)  +/-  (1.59e-493, 1.59e-493j)
| (-4.273464083162579613 - 5.5289240248241413558e-1236j)  +/-  (8.66e-498, 8.66e-498j)
| (13.901171933400773252 - 2.1267385164966316062e-1229j)  +/-  (1.04e-494, 1.04e-494j)
| (-9.8647940656781354854 + 4.5563276384475687177e-1235j)  +/-  (2.79e-492, 2.79e-492j)
| (14.541191220982566133 + 6.7501858921372849164e-1237j)  +/-  (1.54e-495, 1.54e-495j)
| (1.3797962959079282449 - 1.1302110251521563313e-1252j)  +/-  (3.07e-505, 3.07e-505j)
| (-6.5589117948044728859 + 5.7983490970516360457e-1239j)  +/-  (3.28e-494, 3.28e-494j)
| (-5.0226583583027636125 + 1.5962381881519760239e-1245j)  +/-  (2e-496, 2e-496j)
| (4.6466673030103891207 + 7.7967629086225773813e-1242j)  +/-  (4.44e-497, 4.44e-497j)
| (-1.7320508075688772935 + 1.1648943574352119287e-1253j)  +/-  (3.98e-504, 3.98e-504j)
| (3.1692395785345975552 - 1.5607372560901868325e-1249j)  +/-  (3.24e-500, 3.24e-500j)
| (-12.231803387474050429 + 7.0369624697678737805e-1242j)  +/-  (4.03e-493, 4.03e-493j)
| (-11.241456939093816942 + 1.8161517797002020995e-1250j)  +/-  (1.62e-492, 1.62e-492j)
| (-2.0873268747500979811 - 1.3683165150314090217e-1275j)  +/-  (3.85e-503, 3.85e-503j)
| (-4.6466673030103891207 + 4.8673751005951949255e-1265j)  +/-  (4.25e-497, 4.25e-497j)
| (-3.9028934302453214034 + 6.2542726645724570694e-1269j)  +/-  (1.58e-498, 1.58e-498j)
| (4.273464083162579613 - 7.2744893087484365229e-1264j)  +/-  (8.1e-498, 8.1e-498j)
| (10.770318617342832917 + 6.8808263874864164906e-1303j)  +/-  (2.27e-492, 2.27e-492j)
| (5.0226583583027636125 + 8.2220922304730352916e-1373j)  +/-  (2.06e-496, 2.06e-496j)
| (7.7536444555463281979 - 1.5158147532079981505e-1450j)  +/-  (4.51e-493, 4.51e-493j)
| (8.162204009590599845 - 6.4525623557562374336e-1490j)  +/-  (8.64e-493, 8.64e-493j)
| (-14.541191220982566133 - 4.8938662724716577272e-1514j)  +/-  (1.46e-495, 1.46e-495j)
| (12.757872661287080163 - 1.0398128415910488916e-1508j)  +/-  (1.65e-493, 1.65e-493j)
| (6.1694713466552129668 + 7.8560913762890565873e-1517j)  +/-  (1.03e-494, 1.03e-494j)
| (-8.5768476836212872708 + 2.011134873456206069e-1523j)  +/-  (1.33e-492, 1.33e-492j)
| (-2.8060752209096503921 - 1.0828786162657060918e-1539j)  +/-  (3.83e-501, 3.83e-501j)
| (1.0307437262888798825 + 6.7322071762940310214e-1545j)  +/-  (2.21e-506, 2.21e-506j)
| (-6.1694713466552129668 - 8.3305021924611256922e-1530j)  +/-  (1.12e-494, 1.12e-494j)
| (9.427260958382609267 + 1.4029522739838057104e-1533j)  +/-  (2.43e-492, 2.43e-492j)
| (-7.3505754307565941264 + 7.0428841479779373387e-1544j)  +/-  (2.12e-493, 2.12e-493j)
| (-5.7838125310721163249 - 2.7895342533417223974e-1546j)  +/-  (3.21e-495, 3.21e-495j)
| (6.5589117948044728859 + 1.3783495029179030266e-1542j)  +/-  (3.29e-494, 3.29e-494j)
| (0.6848560323508248877 + 3.8504011361084111765e-1563j)  +/-  (1.41e-507, 1.41e-507j)
| (5.4016302848502220338 + 3.7298713021215937286e-1550j)  +/-  (9.33e-496, 9.33e-496j)
| (-8.162204009590599845 + 1.7310175398395312604e-1548j)  +/-  (8.18e-493, 8.18e-493j)
| (-0.6848560323508248877 + 1.8598774810187218463e-1601j)  +/-  (1.29e-507, 1.29e-507j)
| (-7.7536444555463281979 + 8.0054033481385361511e-1549j)  +/-  (4.72e-493, 4.72e-493j)
| (6.9524813824471651159 + 7.4734540174370467702e-1547j)  +/-  (8.8e-494, 8.8e-494j)
| (-2.0270930850495340744e-1611 - 3.156190353522514578e-1611j)  +/-  (2.81e-1609, 2.81e-1609j)
| (-8.998264312489122013 + 2.4653377448308334604e-1555j)  +/-  (1.93e-492, 1.93e-492j)
| (-2.4453976688689072766 - 1.3685231100850047506e-1576j)  +/-  (3.91e-502, 3.91e-502j)
| (-3.5348411478046666261 + 1.7793380793013697496e-1574j)  +/-  (2.26e-499, 2.26e-499j)
| (1.7320508075688772935 + 2.4600938904813095586e-1578j)  +/-  (3.88e-504, 3.88e-504j)
| (11.241456939093816942 + 2.5807771067949023306e-1565j)  +/-  (1.49e-492, 1.49e-492j)
| (8.5768476836212872708 + 5.7882094176870999568e-1593j)  +/-  (1.34e-492, 1.34e-492j)
| (-3.1692395785345975552 - 4.2349478781935283757e-1625j)  +/-  (3.38e-500, 3.38e-500j)
| (3.9028934302453214034 - 1.5985953231829246439e-1623j)  +/-  (1.47e-498, 1.47e-498j)
| (-0.34164232062632571072 + 1.3325286821570857876e-1633j)  +/-  (8.67e-509, 8.67e-509j)
| (-1.3797962959079282449 - 2.0357962342049321908e-1630j)  +/-  (2.83e-505, 2.83e-505j)
| (0.34164232062632571072 - 1.4251710125525255328e-1633j)  +/-  (8.67e-509, 8.67e-509j)
| (8.998264312489122013 + 6.2020486936895546171e-1616j)  +/-  (1.99e-492, 1.99e-492j)
| (-1.0307437262888798825 - 3.2549613853488578059e-1645j)  +/-  (2.46e-506, 2.46e-506j)
| (3.5348411478046666261 + 3.5545821178370193307e-1638j)  +/-  (2.17e-499, 2.17e-499j)
| (5.7838125310721163249 - 1.4719238130473788648e-1630j)  +/-  (3.41e-495, 3.41e-495j)
| (2.8060752209096503921 + 3.5096244659081056478e-1646j)  +/-  (3.89e-501, 3.89e-501j)
| (7.3505754307565941264 + 1.5637034436540619558e-1636j)  +/-  (2.16e-493, 2.16e-493j)
| (-5.4016302848502220338 + 4.7087318647165808941e-1652j)  +/-  (8.85e-496, 8.85e-496j)
| (-6.9524813824471651159 - 2.7511764126161028581e-1649j)  +/-  (9.24e-494, 9.24e-494j)
| (10.312012520776024003 + 5.8952492000290984004e-1662j)  +/-  (2.65e-492, 2.65e-492j)
-------------------------------------------------
The weights are:
| (8.4744336105401324782e-52 + 6.144861592633436197e-1227j)  +/-  (4.74e-171, 2.01e-416j)
| (8.4744336105401324782e-52 - 2.8619131216769832768e-1226j)  +/-  (6.72e-172, 2.85e-417j)
| (2.6631864891879796735e-43 + 1.2622686021518013078e-1222j)  +/-  (2.31e-168, 9.82e-414j)
| (1.3238165155181092233e-57 + 2.9171356361805958304e-1229j)  +/-  (7.1e-174, 3.01e-419j)
| (7.5713554180997844047e-40 - 7.2018704035671732343e-1221j)  +/-  (2.98e-167, 1.26e-412j)
| (1.3031464724257011834e-22 + 4.6656799272588268254e-1210j)  +/-  (6.46e-160, 2.74e-405j)
| (0.016111235460848837966 + 4.8083762485460854906e-1201j)  +/-  (1e-114, 4.26e-360j)
| (6.6564089255984143849e-34 + 7.1833796290424985955e-1217j)  +/-  (4.21e-166, 1.78e-411j)
| (2.6868122787222415868e-31 + 1.6485221597306398265e-1216j)  +/-  (6.62e-165, 2.81e-410j)
| (0.0072103182939620270522 - 3.0627037837204012968e-1201j)  +/-  (3.59e-121, 1.52e-366j)
| (1.1988673769093930406e-26 + 3.9591143894882554365e-1214j)  +/-  (4.99e-163, 2.12e-408j)
| (7.5713554180997844047e-40 + 4.8426939369619402242e-1220j)  +/-  (6.81e-170, 2.89e-415j)
| (1.3238165155181092233e-57 - 7.0288933106962772114e-1230j)  +/-  (2.02e-175, 8.57e-421j)
| (8.6877733882216968051e-21 - 4.1012444421243894844e-1211j)  +/-  (9.2e-161, 3.9e-406j)
| (1.4642497727725145956e-24 - 4.6678347335672761389e-1213j)  +/-  (1.79e-162, 7.59e-408j)
| (2.6868122787222415868e-31 - 1.9108104706691130631e-1215j)  +/-  (2.43e-168, 1.03e-413j)
| (9.7423732215148729208e-37 + 2.7592290070338246021e-1219j)  +/-  (3.8e-168, 1.61e-413j)
| (1.6056250458034892296e-05 + 4.9746858195844834608e-1203j)  +/-  (1.27e-144, 5.39e-390j)
| (2.6631864891879796735e-43 - 7.4321665678781163804e-1222j)  +/-  (2.62e-173, 1.11e-418j)
| (1.3031464724257011834e-22 + 4.7009994262541610494e-1212j)  +/-  (3.36e-162, 1.42e-407j)
| (3.2633028753568838014e-47 + 6.7934242975291820026e-1224j)  +/-  (7.86e-175, 3.33e-420j)
| (0.054000647167912209283 + 9.7896333978540134804e-1201j)  +/-  (6.6e-121, 2.8e-366j)
| (7.1129778903438950837e-11 + 6.1493600277469505855e-1206j)  +/-  (6.12e-156, 2.6e-401j)
| (5.0092267983739764652e-07 + 7.2545471719635664924e-1204j)  +/-  (3.51e-150, 1.49e-395j)
| (3.0612756005489065781e-06 - 5.4776183227798052272e-1203j)  +/-  (9.4e-151, 3.99e-396j)
| (0.031494177803173118352 - 4.9709755189472051428e-1201j)  +/-  (1.93e-129, 8.17e-375j)
| (0.00095813609216566379593 - 1.0315950774551788064e-1201j)  +/-  (1.69e-141, 7.17e-387j)
| (6.6564089255984143849e-34 - 7.6949071349703958736e-1218j)  +/-  (8.51e-168, 3.61e-413j)
| (6.9117480896692453839e-29 - 2.8190367488113874493e-1215j)  +/-  (1.81e-165, 7.69e-411j)
| (0.016111235460848837966 + 3.1288997695652656402e-1201j)  +/-  (2.68e-135, 1.14e-380j)
| (3.0612756005489065781e-06 - 1.9696780402584096951e-1203j)  +/-  (4.8e-150, 2.04e-395j)
| (7.2539186951099774085e-05 - 1.1712683240375898351e-1202j)  +/-  (3.14e-147, 1.33e-392j)
| (1.6056250458034892296e-05 + 1.2579009373117069668e-1202j)  +/-  (3.48e-152, 1.47e-397j)
| (1.1988673769093930406e-26 - 9.0220382641607382095e-1213j)  +/-  (3.05e-172, 1.29e-417j)
| (5.0092267983739764652e-07 + 2.2304564003612612842e-1203j)  +/-  (2.09e-156, 8.86e-402j)
| (1.4271299361361902468e-14 - 5.7909772075755354397e-1207j)  +/-  (7.72e-167, 3.27e-412j)
| (5.6051082738283578188e-16 + 1.3552618020515547687e-1207j)  +/-  (7.11e-168, 3.02e-413j)
| (3.2633028753568838014e-47 - 1.3016786541917962563e-1224j)  +/-  (6.47e-179, 2.75e-424j)
| (9.7423732215148729208e-37 - 2.1576018843728094406e-1218j)  +/-  (1.86e-176, 7.89e-422j)
| (8.3953060498234818821e-10 - 9.9362613094041825858e-1205j)  +/-  (4.27e-163, 1.81e-408j)
| (1.7706595396830259102e-17 - 2.1210768684003573658e-1209j)  +/-  (1.48e-167, 6.26e-413j)
| (0.0028165051566834837114 + 1.0213839736195941495e-1201j)  +/-  (6.41e-151, 2.72e-396j)
| (0.08148514007265452268 - 1.2616655690912937515e-1200j)  +/-  (3.42e-139, 1.45e-384j)
| (8.3953060498234818821e-10 - 2.2899516276339401847e-1205j)  +/-  (1.68e-162, 7.14e-408j)
| (8.6877733882216968051e-21 - 1.8083530618831216157e-1209j)  +/-  (2.4e-172, 1.02e-417j)
| (2.9569256330041032578e-13 + 3.399853935845044546e-1207j)  +/-  (4.97e-166, 2.11e-411j)
| (8.3364722529036631932e-09 + 7.8439704375779814849e-1205j)  +/-  (7.45e-162, 3.16e-407j)
| (7.1129778903438950837e-11 + 3.055017450723875842e-1205j)  +/-  (5.02e-167, 2.13e-412j)
| (0.10868005942315588907 + 1.5086804012415223792e-1200j)  +/-  (1.63e-145, 6.92e-391j)
| (7.0059681130929679058e-08 - 8.4814042264790488538e-1204j)  +/-  (1.21e-163, 5.13e-409j)
| (5.6051082738283578188e-16 + 1.2799997308087080853e-1208j)  +/-  (4.14e-168, 1.75e-413j)
| (0.10868005942315588907 + 1.3128011316752320557e-1200j)  +/-  (1.48e-149, 6.28e-395j)
| (1.4271299361361902468e-14 - 6.9391048837626028996e-1208j)  +/-  (1.77e-167, 7.53e-413j)
| (5.0361437680198709555e-12 - 8.7394500354720574037e-1206j)  +/-  (1.01e-169, 4.27e-415j)
| (0.13618355949111000727 + 1.6797462362077633787e-1200j)  +/-  (9.08e-151, 3.85e-396j)
| (4.4383161000403741145e-19 + 3.1355042376625302505e-1210j)  +/-  (1.14e-169, 4.85e-415j)
| (0.0072103182939620270522 - 1.8459024862324267259e-1201j)  +/-  (1.65e-157, 6.99e-403j)
| (0.00028319528204497379176 + 2.5757283712408624482e-1202j)  +/-  (2.09e-160, 8.88e-406j)
| (0.031494177803173118352 - 7.0883378920455269944e-1201j)  +/-  (3.47e-156, 1.47e-401j)
| (6.9117480896692453839e-29 + 4.3219947568878629366e-1214j)  +/-  (4.45e-179, 1.89e-424j)
| (1.7706595396830259102e-17 - 3.0370938000638813752e-1208j)  +/-  (2.74e-174, 1.16e-419j)
| (0.00095813609216566379593 - 5.2992812898339591465e-1202j)  +/-  (9.69e-162, 4.11e-407j)
| (7.2539186951099774085e-05 - 2.7047844683853895085e-1202j)  +/-  (6.81e-166, 2.89e-411j)
| (0.12877656855399429567 - 1.5515020121540487065e-1200j)  +/-  (8.44e-158, 3.58e-403j)
| (0.054000647167912209283 + 7.3871092430551667291e-1201j)  +/-  (1.08e-159, 4.58e-405j)
| (0.12877656855399429567 - 1.6628220381660975006e-1200j)  +/-  (4.59e-158, 1.95e-403j)
| (4.4383161000403741145e-19 + 6.8255243684269633466e-1209j)  +/-  (2.97e-175, 1.26e-420j)
| (0.08148514007265452268 - 1.0229524554161981511e-1200j)  +/-  (5.35e-160, 2.27e-405j)
| (0.00028319528204497379176 + 5.4524608608228056013e-1202j)  +/-  (9.49e-166, 4.03e-411j)
| (8.3364722529036631932e-09 + 3.0077863969552223811e-1204j)  +/-  (1.74e-169, 7.38e-415j)
| (0.0028165051566834837114 + 1.8334520856125766033e-1201j)  +/-  (3.57e-165, 1.52e-410j)
| (2.9569256330041032578e-13 + 2.3279495626274687003e-1206j)  +/-  (2.2e-172, 9.35e-418j)
| (7.0059681130929679058e-08 - 2.4795522062243278524e-1204j)  +/-  (6.9e-170, 2.94e-415j)
| (5.0361437680198709555e-12 - 1.5134443907314409056e-1206j)  +/-  (2.76e-172, 1.18e-417j)
| (1.4642497727725145956e-24 + 2.105950626757690744e-1211j)  +/-  (5.91e-179, 2.49e-424j)
