Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 5 28
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Trying to find an order 5 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : 35/8*t^9 - 855/88*t^7 + 45297/6292*t^5 - 24885/12584*t^3 + 1845/12584*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^37 - 257472905352985429977813406576309874567525501107174200799866831750572295/6267578758349973388506161314660174986081400567263366359640710231584424*t^35 + 770460909225556733074106451068241637234350157643017567766308939381620013727/4343432079536531558234769791059501265354410593113512887231012190488005832*t^33 - 24366285190463984139145570830384151139817239325772523944398358201636835365831/52186994531401053419396552186517947021606781823318419993548373743287706436*t^31 + 103939000036556908629580738322999968987779123445655489368237286514567728506709/124154543441639602892919216895345115898177424499023660468522340760240914505*t^29 - 4377158803736069087652511411392843016910655280185743095510472981507976742163413/4043890843527689922797940207448383774969207540825342083831870527619275501020*t^27 + 52124287332127084732723044716884117448537510769107652351753686298786299548689/50025640214580059773703713767355174904027533680925284437866144628668500350*t^25 - 3063666237206675950365479848603969415882543135175734294441594382750693323263743/4030065575686569615369571181098132890268458113335340914314496611285534388196*t^23 + 155314509641117412986162985387368975654207073927078837099314191159081985427501/366369597789688146851779198281648444569859828485030992210408782844139489836*t^21 - 1623719124273245714782174488377517036470554891457608872547536553551297897050631/8976055145847359597868590357900386891961565797883259309155015179681417500982*t^19 + 2608843690306771550066466008691344741610757112891920179023679119204195696474043/44407851774192200115770920718033493044441430789527703950556390888950170794332*t^17 - 9556360397757187387146564117869572961041354029260173943510751553212724541550613/666117776612883001736563810770502395666621461842915559258345863334252561914980*t^15 + 315086836103375312993516650708812746060927414425732283513048568338959278916/121999592786242308010359672302289816056157776894306878985045029914698271413*t^13 - 73211737246770275085588527956358738120471610974220025349660657005594576399283/220087265386381123650688848833330828165308629517329609689021233966115681629052*t^11 + 491934985380476960753874557851583958093835393036474607217474923358767224827991/16776652002407324743736599976977081765146480531843716156749482243689818095087282*t^9 - 451109435080261503366128683528932472188949332520096739773633815176454069207/272791089470037800711164227267920028701568789135670181410560686889265334879468*t^7 + 544751551570473939835725922726063769474679467955659464252890255445332605650371/10177835548127110344533537319366096270855531522651854468428019227838489644352951080*t^5 - 18284298204940617492176352506441883773738418494399129845098561198143790237483/22391238205879642757973782102605411795882169349834079830541642301244677217576492376*t^3 + 63000647237790689854367113883229719391018688436175634794327670384281717771/16929960594689485987736274272701652821276762191337962798702217349721585213289543016*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-0.99812454929748304797 - 1.2188204208118579876e-423j)  +/-  (3.81e-115, 3.81e-115j)
| (-0.99025663947855333836 + 5.0519242784292041651e-425j)  +/-  (1.09e-114, 1.09e-114j)
| (-0.93206082263122601427 - 3.2303360611095975814e-426j)  +/-  (7.29e-115, 7.29e-115j)
| (0.99025663947855333836 + 1.8118193617930959486e-423j)  +/-  (1.08e-114, 1.08e-114j)
| (0.93206082263122601427 - 4.1341275037696887324e-432j)  +/-  (7.92e-115, 7.92e-115j)
| (0.95730358585642100833 - 7.6544062963740890354e-440j)  +/-  (1.17e-114, 1.17e-114j)
| (-0.17239333441660060633 + 6.8668676778857610243e-460j)  +/-  (1.82e-125, 1.82e-125j)
| (-0.90010899849718324067 - 1.3886365430120304621e-448j)  +/-  (3.37e-115, 3.37e-115j)
| (-0.97656025073757311153 - 1.2675316055406717985e-446j)  +/-  (1.6e-114, 1.6e-114j)
| (0.99812454929748304797 - 7.788330218845349826e-447j)  +/-  (3.68e-115, 3.68e-115j)
| (0.90010899849718324067 + 9.1049567812054243054e-455j)  +/-  (3.08e-115, 3.08e-115j)
| (-0.95730358585642100833 - 2.8106742219441153064e-463j)  +/-  (1.17e-114, 1.17e-114j)
| (-0.42039427900056715239 + 6.1012222982651949591e-470j)  +/-  (1e-121, 1e-121j)
| (-0.86113631159405257522 - 2.9700667513194038878e-462j)  +/-  (1.08e-115, 1.08e-115j)
| (0.57119047011350816116 - 2.4554528020387846513e-466j)  +/-  (1.38e-119, 1.38e-119j)
| (0.86113631159405257522 - 7.7712972180296351719e-461j)  +/-  (9.56e-116, 9.56e-116j)
| (0.17239333441660060633 + 1.2149545440058896163e-482j)  +/-  (1.86e-125, 1.86e-125j)
| (0.3399810435848562648 - 4.2310512478850322403e-478j)  +/-  (6.54e-123, 6.54e-123j)
| (-0.76286487069422558089 + 2.1242113071228187551e-476j)  +/-  (5.63e-117, 5.63e-117j)
| (-0.3399810435848562648 + 4.7313886545946572943e-485j)  +/-  (6.51e-123, 6.51e-123j)
| (0.97656025073757311153 - 1.8475918626655432989e-475j)  +/-  (1.34e-114, 1.34e-114j)
| (0.76286487069422558089 + 5.9091539841051724319e-483j)  +/-  (5.74e-117, 5.74e-117j)
| (0.49768166320740860683 + 1.4650553950472854143e-488j)  +/-  (1.19e-120, 1.19e-120j)
| (-0.81527197354663227634 - 7.667472735621241191e-486j)  +/-  (2.82e-116, 2.82e-116j)
| (-0.70436525926518706251 - 3.0118775243004407645e-487j)  +/-  (9.22e-118, 9.22e-118j)
| (-0.086492135729479269146 - 9.1222975585191060293e-496j)  +/-  (9.43e-127, 9.43e-127j)
| (0.70436525926518706251 - 3.7800266425243166967e-484j)  +/-  (9.53e-118, 9.53e-118j)
| (0.81527197354663227634 - 1.1437230402263143919e-487j)  +/-  (2.95e-116, 2.95e-116j)
| (-0.2570985460827512626 - 1.8091797334782274676e-499j)  +/-  (3.56e-124, 3.56e-124j)
| (-0.6402862174963099824 - 3.0920477292851581043e-493j)  +/-  (1.27e-118, 1.27e-118j)
| (2.4422364030709601604e-515 + 1.6661033263953314031e-514j)  +/-  (6.23e-513, 6.23e-513j)
| (0.42039427900056715239 - 1.4096762097237616311e-494j)  +/-  (1.02e-121, 1.02e-121j)
| (0.6402862174963099824 - 5.0626562321549402557e-495j)  +/-  (1.29e-118, 1.29e-118j)
| (0.086492135729479269146 + 7.2895707544541649004e-505j)  +/-  (9.43e-127, 9.43e-127j)
| (-0.57119047011350816116 - 1.9955879963219844027e-498j)  +/-  (1.47e-119, 1.47e-119j)
| (-0.49768166320740860683 + 1.8553845940566492035e-499j)  +/-  (1.28e-120, 1.28e-120j)
| (0.2570985460827512626 + 1.42481252204655083e-501j)  +/-  (3.88e-124, 3.88e-124j)
-------------------------------------------------
The weights are:
| (0.0047965200821197702381 - 1.5556842501660859846e-423j)  +/-  (7.94e-23, 3.15e-76j)
| (0.010863602706163376116 + 2.613882818333062297e-423j)  +/-  (5.94e-23, 2.36e-76j)
| (0.028498650515742088918 - 9.6158389393132925223e-424j)  +/-  (6.52e-24, 2.59e-77j)
| (0.010863602706163376116 - 1.0222117485955373891e-423j)  +/-  (1.46e-24, 5.77e-78j)
| (0.028498650515742088918 + 1.0210487722292767137e-423j)  +/-  (6.9e-25, 2.74e-78j)
| (0.022122673963160032528 - 1.5659303059667902128e-423j)  +/-  (6.32e-25, 2.51e-78j)
| (0.085405755062967585101 - 2.3609348064817543496e-425j)  +/-  (8.41e-26, 3.34e-79j)
| (0.035455108504146279199 + 6.6368823431436066896e-424j)  +/-  (2.03e-24, 8.06e-78j)
| (0.01647088719749859382 - 1.8415472225143271314e-423j)  +/-  (6.02e-24, 2.39e-77j)
| (0.0047965200821197702381 - 7.1917143174819630479e-424j)  +/-  (9.13e-26, 3.62e-79j)
| (0.035455108504146279199 - 6.7122666649558843397e-424j)  +/-  (5.07e-26, 2.01e-79j)
| (0.022122673963160032528 + 1.3499172026476699458e-423j)  +/-  (2.36e-24, 9.36e-78j)
| (0.078959912738712318569 + 6.1093631146203945821e-425j)  +/-  (1.18e-27, 4.69e-81j)
| (0.04246437573805452861 - 4.5486728099237334544e-424j)  +/-  (3.15e-26, 1.25e-79j)
| (0.071405832258134120134 - 9.2232709693311735761e-425j)  +/-  (2.42e-28, 9.61e-82j)
| (0.04246437573805452861 + 4.4861353994814771644e-424j)  +/-  (4.07e-27, 1.61e-80j)
| (0.085405755062967585101 + 1.6977798212871225242e-425j)  +/-  (7.67e-29, 3.04e-82j)
| (0.081756885689074066253 + 3.9878636185960995908e-425j)  +/-  (7.88e-29, 3.12e-82j)
| (0.055534257810806009338 - 2.3042315856530914934e-424j)  +/-  (3.88e-28, 1.54e-81j)
| (0.081756885689074066253 - 4.6870561752411698317e-425j)  +/-  (8.21e-29, 3.26e-82j)
| (0.01647088719749859382 + 2.6903658594239392687e-423j)  +/-  (6.78e-27, 2.69e-80j)
| (0.055534257810806009338 + 2.2001111014530542857e-424j)  +/-  (3.54e-29, 1.4e-82j)
| (0.075505822945831750161 + 7.0675421936416473305e-425j)  +/-  (1.4e-29, 5.57e-83j)
| (0.049204391404989337495 + 3.1902522241422167875e-424j)  +/-  (1.19e-28, 4.74e-82j)
| (0.061379272346230126081 + 1.7114789517681851504e-424j)  +/-  (8.11e-30, 3.22e-83j)
| (0.086295933787930783884 + 1.3278080166053302263e-425j)  +/-  (2.2e-31, 8.74e-85j)
| (0.061379272346230126081 - 1.6132365049147513977e-424j)  +/-  (2.04e-30, 8.08e-84j)
| (0.049204391404989337495 - 3.0901443624441600628e-424j)  +/-  (1.12e-29, 4.45e-83j)
| (0.083900178192613648962 + 3.4631358321712479674e-425j)  +/-  (2.88e-31, 1.14e-84j)
| (0.066684888701375558267 - 1.3009960052270962256e-424j)  +/-  (1.44e-31, 5.71e-85j)
| (0.086590100708900052651 - 3.2650944512544890586e-426j)  +/-  (4.58e-32, 1.81e-85j)
| (0.078959912738712318569 - 5.3781593252955245284e-425j)  +/-  (2.92e-32, 1.16e-85j)
| (0.066684888701375558267 + 1.2105382872494749077e-424j)  +/-  (8.46e-32, 3.36e-85j)
| (0.086295933787930783884 - 6.7234917338474259243e-426j)  +/-  (1.02e-32, 4.06e-86j)
| (0.071405832258134120134 + 1.0056545803662617107e-424j)  +/-  (1.86e-33, 7.43e-87j)
| (0.075505822945831750161 - 7.8428911072357286022e-425j)  +/-  (1.68e-33, 6.73e-87j)
| (0.083900178192613648962 - 2.7859511108500920737e-425j)  +/-  (1.63e-33, 6.17e-87j)
