Starting with polynomial:
P : 429/16*t^7 - 693/16*t^5 + 315/16*t^3 - 35/16*t
Extension levels are: 7 8 16
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Trying to find an order 8 Kronrod extension for:
P1 : 429/16*t^7 - 693/16*t^5 + 315/16*t^3 - 35/16*t
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P2 : 429/16*t^15 - 27225/272*t^13 + 13131495/87856*t^11 - 1188386485/10454864*t^9 + 3595718907495/77669184656*t^7 - 107404612029/11095597808*t^5 + 9905616105/11095597808*t^3 - 264663405/11095597808*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 429/16*t^31 - 22823157060610658871115730418540993373758924538995986648144983104868352501100563436229/106850444857798423761979012169284978564855229384406912107932196628657384808757634384*t^29 + 149363049642843434127100931142364507244522960987884793099408772303173303061407185359725416279/194133902001012511172545617735069645430021344887794308436099309749691886024411526971430000*t^27 - 95766208774059187222206676236104995452509452250944047087117556909697919346900477485878481836569/57815952073708948234757011563247963663066727194176075338321279618417498352677521791750690000*t^25 + 2569374073340780228607670407064055509596652731871448434482464578409803496411574344586065611067576623/1082377064048071116618744794036490187573365245140345840494739741438763460060344099665108007545200*t^23 - 30635843759845538552927650335348303269271250199073848899950402712964531531483030506536107121475157/12834510640886218774135313763278539773597216345537697713376360570420120079766926082985470445200*t^21 + 411653767482084348982324965244242341052345674803378424434075677846579523141243915519039612093787/238033530683102804332334139970579434397542358288167827265626737396262878672369055173164113520*t^19 - 465456722765954047326139736845959706965173141039726990103029508287465026791009700389391372265783/510071851463791723569287442794098787994733624903216772712057294420563311440790832513923100400*t^17 + 2844262635109002704577804127222640738829109832954983883065074497757518904115664377664811445525213/8119143706241296493991128354122537178316171699930026982110747286482613651522235251662799468720*t^15 - 42599171104604213689655514039810080439709123677813128175594866074801059706027862540166435608071/440573689485961825255332546347734575567544200771396812982753728723862756284152300477826327760*t^13 + 354941294392592624657944338905215505607961259917449577265197024919975578700740704525862710784621/18944668647896358485979299492952586749404400633170062958258410335126098520218548920546532093680*t^11 - 797480290455978969282307156590022543423801127979542727623595367891325520595501706207769821133167/325503852222946523077280691288003535967039247242649263555530868485348420029209613271208596882320*t^9 + 917528669745036019053482493829461165453070197902870631628773074221198216058469384979764465699383/4520886836429812820517787379000049110653322878370128660493484284518728055961244628766786067810000*t^7 - 142446187302151426778149818792633403676437252971547971736275865217455700505876459437645556538819/14854342462555099267415587102428732792146632314644708455907162649132963612444089494519439937090000*t^5 + 2983734193807702394834605181171038664518854609074078506085209491534411511616888728417665206881/14005522893266236452134696410861376632595396182379296544141039069182508548875855809118329083542000*t^3 - 579354826196938765947234421232693137268688874678414260426503268116363976609958509564329287/409302251110615128133138787660857633956314588498450107750111666930624837837945247772519834786000*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:
| (-0.99868710967846672979 - 8.3134400967770384855e-413j)  +/-  (6.64e-117, 6.64e-117j)
| (-0.99145537112081263921 + 1.9853442273885260996e-412j)  +/-  (1.3e-116, 1.3e-116j)
| (-0.91220488278326287835 + 3.3415347817663383078e-413j)  +/-  (2.54e-117, 2.54e-117j)
| (0.99868710967846672979 + 8.7352765810904839094e-411j)  +/-  (6.06e-117, 6.06e-117j)
| (0.91220488278326287835 - 3.1197310192696063697e-421j)  +/-  (2.88e-117, 2.88e-117j)
| (0.94910791234275852453 + 4.8014601608365520448e-432j)  +/-  (6.68e-117, 6.68e-117j)
| (0.99145537112081263921 + 9.9276393676623509415e-444j)  +/-  (1.39e-116, 1.39e-116j)
| (-0.94910791234275852453 + 7.8346675447890736927e-453j)  +/-  (7e-117, 7e-117j)
| (-0.97538358820889336968 + 4.2273116715860534208e-456j)  +/-  (1.13e-116, 1.13e-116j)
| (0.97538358820889336968 - 5.7423149000526149398e-456j)  +/-  (1.11e-116, 1.11e-116j)
| (0.86486442335976907279 - 3.3172240661112091387e-464j)  +/-  (8.93e-118, 8.93e-118j)
| (0.49863678655283200429 + 1.5271292164103440867e-475j)  +/-  (7.68e-122, 7.68e-122j)
| (-0.86486442335976907279 + 3.213745386745093093e-470j)  +/-  (9.23e-118, 9.23e-118j)
| (-0.80768893917243750909 + 4.8395030537949605373e-472j)  +/-  (2.29e-118, 2.29e-118j)
| (1.3044054840530130393e-481 + 4.2613187951704036014e-481j)  +/-  (1.38e-479, 1.38e-479j)
| (0.74153118559939443986 + 1.7490842285655896659e-471j)  +/-  (4.37e-119, 4.37e-119j)
| (0.80768893917243750909 + 3.9006707941525631803e-477j)  +/-  (1.98e-118, 1.98e-118j)
| (-0.3085792479105877789 + 8.3748086576851044865e-483j)  +/-  (3.49e-124, 3.49e-124j)
| (-0.74153118559939443986 + 4.361539774402802389e-479j)  +/-  (4.07e-119, 4.07e-119j)
| (-0.40584515137739716691 - 1.7923340414017587554e-484j)  +/-  (5.61e-123, 5.61e-123j)
| (0.40584515137739716691 + 3.834656818059765477e-483j)  +/-  (5.9e-123, 5.9e-123j)
| (0.66734809810430017543 - 1.6692118638497672174e-479j)  +/-  (6.42e-120, 6.42e-120j)
| (0.1045282738107807134 - 4.4664469055795155043e-487j)  +/-  (9.25e-127, 9.25e-127j)
| (-0.49863678655283200429 + 3.8372293154573765783e-482j)  +/-  (7.75e-122, 7.75e-122j)
| (-0.58608723546769113029 - 1.1621171964347198705e-481j)  +/-  (7.57e-121, 7.57e-121j)
| (0.2077849550078984676 - 5.336584128688683517e-486j)  +/-  (2.04e-125, 2.04e-125j)
| (0.58608723546769113029 - 2.700920827041277485e-482j)  +/-  (8.13e-121, 8.13e-121j)
| (0.3085792479105877789 + 2.2970997469981290878e-486j)  +/-  (3.65e-124, 3.65e-124j)
| (-0.1045282738107807134 + 2.2294097376344764538e-489j)  +/-  (7.84e-127, 7.84e-127j)
| (-0.66734809810430017543 + 3.0915453844890679864e-483j)  +/-  (6.54e-120, 6.54e-120j)
| (-0.2077849550078984676 + 1.5150389028795366642e-487j)  +/-  (1.96e-125, 1.96e-125j)
-------------------------------------------------
The weights are:
| (0.0036349311950498838561 + 2.7627071059230051625e-413j)  +/-  (1.2e-23, 2.1e-78j)
| (0.011319468444683435107 + 1.6008947885020918774e-412j)  +/-  (9.78e-24, 1.7e-78j)
| (0.042193500584546594485 - 1.0122648312178807546e-412j)  +/-  (1.91e-24, 3.32e-79j)
| (0.0036349311950498838561 - 8.0274626298934721926e-411j)  +/-  (1.2e-25, 2.1e-80j)
| (0.042193500584546594485 - 1.1182700052909992545e-411j)  +/-  (5.03e-26, 8.76e-81j)
| (0.031577706217045857274 + 2.0048414123877869998e-411j)  +/-  (5.26e-26, 9.16e-81j)
| (0.011319468444683435107 + 1.0892183261932886463e-410j)  +/-  (6.73e-26, 1.17e-80j)
| (0.031577706217045857274 + 1.7628905387376871488e-412j)  +/-  (1.4e-26, 2.44e-81j)
| (0.021039446258726795607 - 2.8395080248655213841e-412j)  +/-  (3.01e-26, 5.24e-81j)
| (0.021039446258726795607 - 4.1722131334223731672e-411j)  +/-  (1.24e-26, 2.16e-81j)
| (0.052384370820982692472 + 7.0189090870303918755e-412j)  +/-  (3.31e-28, 5.76e-83j)
| (0.09026180214655860231 - 1.9042390561466469982e-412j)  +/-  (7.42e-31, 1.29e-85j)
| (0.052384370820982692472 + 4.9217434597730235893e-413j)  +/-  (9.87e-29, 1.72e-83j)
| (0.061821985645449856431 - 5.7105791252237296289e-413j)  +/-  (1.71e-29, 2.97e-84j)
| (0.10474321356480584473 + 9.5480411854924883732e-413j)  +/-  (9.05e-32, 1.57e-86j)
| (0.070332046410400650935 + 3.5925615868384103819e-412j)  +/-  (2.25e-30, 3.92e-85j)
| (0.061821985645449856431 - 4.8413714653651088487e-412j)  +/-  (9.97e-30, 1.74e-84j)
| (0.09919685766743291249 - 7.5245139762382979868e-413j)  +/-  (7.2e-33, 1.25e-87j)
| (0.070332046410400650935 + 5.8955975515236502624e-413j)  +/-  (8.68e-32, 1.51e-86j)
| (0.095178029931830680121 + 7.0861137898135904683e-413j)  +/-  (5.39e-33, 9.38e-88j)
| (0.095178029931830680121 + 1.6133788714924117811e-412j)  +/-  (2.62e-33, 4.56e-88j)
| (0.077875347115245996421 - 2.8129642755238411573e-412j)  +/-  (1.15e-32, 2e-87j)
| (0.10409995547269735501 - 1.0643520172242098745e-412j)  +/-  (6.89e-34, 1.2e-88j)
| (0.09026180214655860231 - 6.7051334377983859643e-413j)  +/-  (5.21e-34, 9.08e-89j)
| (0.084498765301243021195 + 6.3732201050207024406e-413j)  +/-  (3.77e-34, 6.56e-89j)
| (0.10221418000570274392 + 1.205555908865258749e-412j)  +/-  (1.09e-34, 1.9e-89j)
| (0.084498765301243021195 + 2.2859769765875541708e-412j)  +/-  (3.57e-34, 6.21e-89j)
| (0.09919685766743291249 - 1.3854882861858891603e-412j)  +/-  (8.2e-35, 1.43e-89j)
| (0.10409995547269735501 - 8.7040529161132077867e-413j)  +/-  (1.16e-35, 2.02e-90j)
| (0.077875347115245996421 - 6.0994741005840077373e-413j)  +/-  (7.23e-36, 1.33e-90j)
| (0.10221418000570274392 + 8.0486417717812058698e-413j)  +/-  (7.25e-36, 1.25e-90j)
