Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8 11 28
-------------------------------------------------
Trying to find an order 11 Kronrod extension for:
P1 : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : t^19 - 150851/1347*t^17 + 6541430/1347*t^15 - 47540390/449*t^13 + 566981260/449*t^11 - 3753992440/449*t^9 + 13180991670/449*t^7 - 21510616050/449*t^5 + 12604959675/449*t^3 - 2144332575/449*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^47 - 1194483575745888349515185867823172885300934124725225632047823528736960941417274358081537175438878857290515883617/1502776314935956282728604582436986130845347851712546655421143008199001784456031708198871184669560431884442619*t^45 + 430482409435641653794510186565753436594887241888485716659293959095910642954899710943318581917121606225202527648615/1502776314935956282728604582436986130845347851712546655421143008199001784456031708198871184669560431884442619*t^43 - 2521405736913832907768901096366818844714867478313709481676047876760859418357482596325318637041242327845714207381339295/40574960503270819633672323725798625532824391996238759696370861221373048180312856121369521986078131660879950713*t^41 + 7004419198393201410048380090859791715906241018621818183481103325742292773209525845493925427740173648008588409410991048965/770924249562145573039774150790173885123663447928536434231046363206087915425944266306020917735484501556719063547*t^39 - 244152415054285168553487567405279814931089644146027474721427907103043665082454193226281982113709097697297665126325854180125/256974749854048524346591383596724628374554482642845478077015454402029305141981422102006972578494833852239687849*t^37 + 18912657640106506215672688566424074798940129691173964704671869992478131883195584464492301930888632273396403458894494837552675/256974749854048524346591383596724628374554482642845478077015454402029305141981422102006972578494833852239687849*t^35 - 1109163450086076379467472552364002596378226034350448862252510851124950249379915134353042931929635908060072486861897054790330425/256974749854048524346591383596724628374554482642845478077015454402029305141981422102006972578494833852239687849*t^33 + 1512596881374461495206085914053469862049143567392985690107030191333164968240867954518824238134523727372690058170534666642397050/7787113631940864374139132836264382678016802504328650850818650133394827428544891578848696138742267692492111753*t^31 - 52634987244126811093775362210527403706558066405950339029177308603486487047546827272020969226251571068792192630352929752173280750/7787113631940864374139132836264382678016802504328650850818650133394827428544891578848696138742267692492111753*t^29 + 34649675850026633149291439350952620166527582300502752410802993649255278963730472586400830476433511571205772631582157781363282450/189929600779045472539978849664984943366263475715332947580942686180361644598655892167041369237616285182734433*t^27 - 9905998948762451216694177311939314877186129517408501868556223983425268957779068513002145309557094304733438263617334848146090982450/2595704543980288124713044278754794226005600834776216950272883377798275809514963859616232046247422564164037251*t^25 + 159903873397677826500585661310242697546230406713968821835011212701442496370583685946448871932649314851698942656064751104835334256250/2595704543980288124713044278754794226005600834776216950272883377798275809514963859616232046247422564164037251*t^23 - 1975694795440032130209921432661708161553608677480103940985832537969469475587152207185574407775019496396233060715948170539291080598750/2595704543980288124713044278754794226005600834776216950272883377798275809514963859616232046247422564164037251*t^21 + 971369498499402062309323352840703743379390113793183857896518523737082500457448340130365316611686831801378025400979822291789335533750/136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329*t^19 - 6742192728423615679898044424262241649999924949833958031965305288906519012459698208746960080895923529294083154054141340680499293721250/136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329*t^17 + 33942952627386772681881020463923135608030554519899484620931610739981048372912732502311045589962470830964876248976846587455934074623125/136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329*t^15 - 119868461960642203569398623164698443108682277686155351706036330971069561504620258773007573513383977701108679016065113259880527979859375/136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329*t^13 + 283278436595349206763707735515524837563051285135611119182693365852765705866162873813281051302516051373499512261074026966614551586315625/136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329*t^11 - 418667837777642410288654889155512012648845994846673089485263494108112422629560319755006306019864812756886952793610568015479001963271875/136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329*t^9 + 350159195596690367225265420925996693975950985949315077468073968833597965055899277868416508231234375428044889217282310628638676311671875/136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329*t^7 - 141868284307233351915800133795887572636183750736354986968569779470325580908903492595364025518023810261607927101875169165721120782390625/136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329*t^5 + 20654718585953766957297460447266768104540193117786730514966459393805898521156417308775379322019290060370472385866977616215356621109375/136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329*t^3 - 149581533247864174744375346975316623874146815318221828045695623595289777465459838088324379548023157448550525277180632365005767078125/136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329*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: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (6.3410934275277093073 - 7.6144781316361220952e-941j)  +/-  (1.04e-244, 1.04e-244j)
| (-5.1580652270647994111 + 1.0775643829092063775e-943j)  +/-  (1.56e-243, 1.56e-243j)
| (-10.425760863586986625 - 1.2648827026389924148e-955j)  +/-  (1.34e-246, 1.34e-246j)
| (-7.5427933361225360596 - 9.4443366518830006393e-953j)  +/-  (7.39e-245, 7.39e-245j)
| (7.5427933361225360596 - 1.6711150552454320591e-952j)  +/-  (6.71e-245, 6.71e-245j)
| (8.8651597449356411398 - 6.4557980481447931279e-963j)  +/-  (2.13e-245, 2.13e-245j)
| (5.1580652270647994111 - 3.9495560577564643287e-966j)  +/-  (1.65e-243, 1.65e-243j)
| (-11.422004882320444243 - 5.5520754687380865073e-985j)  +/-  (1.18e-247, 1.18e-247j)
| (-5.1801257915374144851 + 6.5331530958827676756e-979j)  +/-  (1.64e-243, 1.64e-243j)
| (10.425760863586986625 - 2.1162286082691328893e-982j)  +/-  (1.37e-246, 1.37e-246j)
| (11.422004882320444243 + 2.7078957433612787591e-987j)  +/-  (1.21e-247, 1.21e-247j)
| (-5.7691215455223413386 + 5.5574531672607721349e-984j)  +/-  (1.21e-244, 1.21e-244j)
| (-2.6377551349274913907 - 2.125136977815435038e-986j)  +/-  (1.54e-247, 1.54e-247j)
| (4.1445471861258943321 - 2.2305189394133437028e-981j)  +/-  (5.63e-246, 5.63e-246j)
| (-3.0950955154405111371 - 4.7357391309087924969e-990j)  +/-  (5.91e-247, 5.91e-247j)
| (1.1764383603342096967 - 1.578008915166122509e-993j)  +/-  (2.12e-251, 2.12e-251j)
| (2.6377551349274913907 - 2.6921963603764814817e-990j)  +/-  (1.58e-247, 1.58e-247j)
| (-2.8024858612875416991 + 7.9951798847642799731e-990j)  +/-  (4.13e-247, 4.13e-247j)
| (-1.6365190424351079992 + 6.8342192473282084109e-994j)  +/-  (2.26e-250, 2.26e-250j)
| (8.1843656382449753275 + 1.1139022543157519649e-986j)  +/-  (5.11e-245, 5.11e-245j)
| (6.9305727747017500842 + 1.937815578895626431e-995j)  +/-  (8.44e-245, 8.44e-245j)
| (0.79867251029900488539 - 1.6626352580893228866e-1013j)  +/-  (3.39e-252, 3.39e-252j)
| (5.7691215455223413386 - 2.5520782740245525558e-1004j)  +/-  (1.14e-244, 1.14e-244j)
| (4.6793300988208990782 - 4.2750044436065734893e-1017j)  +/-  (3.77e-245, 3.77e-245j)
| (-6.9305727747017500842 - 3.8387856898849004729e-1027j)  +/-  (8.61e-245, 8.61e-245j)
| (-8.8651597449356411398 - 9.5495815607282276684e-1028j)  +/-  (2.05e-245, 2.05e-245j)
| (0.087377958629245133054 + 7.9799885361671591155e-1036j)  +/-  (9.73e-255, 9.73e-255j)
| (-4.1445471861258943321 - 1.6043166069770304734e-1027j)  +/-  (5.61e-246, 5.61e-246j)
| (3.6198756563604648783 - 3.3247879689715273224e-1026j)  +/-  (1.38e-246, 1.38e-246j)
| (2.1217757315011551974 + 2.5138239871983292388e-1035j)  +/-  (3.48e-249, 3.48e-249j)
| (9.6016164690693789197 - 9.8292734531322479856e-1032j)  +/-  (7.35e-246, 7.35e-246j)
| (-4.6793300988208990782 - 1.3465939843480261458e-1033j)  +/-  (3.56e-245, 3.56e-245j)
| (1.6365190424351079992 + 2.6826914445303193016e-1043j)  +/-  (2.22e-250, 2.22e-250j)
| (-9.6016164690693789197 + 1.0489143124636036606e-1039j)  +/-  (6.84e-246, 6.84e-246j)
| (2.8024858612875416991 + 4.7103317515334702193e-1040j)  +/-  (4.16e-247, 4.16e-247j)
| (-2.1217757315011551974 - 3.845652953787695983e-1042j)  +/-  (3.59e-249, 3.59e-249j)
| (1.3777303149738884739e-1048 + 6.5916682684921731898e-1049j)  +/-  (7.18e-1047, 7.18e-1047j)
| (-3.6198756563604648783 - 5.2887704471942856465e-1039j)  +/-  (1.4e-246, 1.4e-246j)
| (-8.1843656382449753275 + 1.8135658918749294954e-1039j)  +/-  (4.55e-245, 4.55e-245j)
| (-6.3410934275277093073 - 3.6591799992017590866e-1045j)  +/-  (1.05e-244, 1.05e-244j)
| (-0.53907981135137510807 + 2.5975007897721682199e-1055j)  +/-  (4.41e-253, 4.41e-253j)
| (5.1801257915374144851 + 1.0839630478175653676e-1055j)  +/-  (1.76e-243, 1.76e-243j)
| (3.0950955154405111371 + 1.4488679065790291119e-1074j)  +/-  (5.5e-247, 5.5e-247j)
| (0.53907981135137510807 - 6.9772204139526864485e-1081j)  +/-  (3.81e-253, 3.81e-253j)
| (-0.087377958629245133054 + 2.4820211180074958553e-1083j)  +/-  (9.73e-255, 9.73e-255j)
| (-0.79867251029900488539 - 6.5957597677535348684e-1080j)  +/-  (3.62e-252, 3.62e-252j)
| (-1.1764383603342096967 + 2.6740801265566985581e-1079j)  +/-  (2.11e-251, 2.11e-251j)
-------------------------------------------------
The weights are:
| (4.2939727667245704861e-10 + 1.6559828841452857477e-949j)  +/-  (8.45e-79, 1.71e-199j)
| (-6.3809254761420043116e-07 - 1.7399279715455400815e-947j)  +/-  (4.62e-75, 9.38e-196j)
| (8.8271669402251592391e-25 + 8.4981831871657994307e-961j)  +/-  (2.28e-89, 4.63e-210j)
| (1.1037866870001781057e-13 + 5.9602676977911671688e-954j)  +/-  (7.66e-83, 1.55e-203j)
| (1.1037866870001781057e-13 - 6.8979151105120475068e-953j)  +/-  (1.27e-83, 2.58e-204j)
| (2.4171511201100099611e-18 - 3.5287183329454032849e-956j)  +/-  (3.78e-87, 7.68e-208j)
| (-6.3809254761420043116e-07 - 1.9632428146580993869e-946j)  +/-  (1.59e-77, 3.23e-198j)
| (2.1538337430281983207e-29 - 2.0175323777955908572e-963j)  +/-  (1.35e-92, 2.73e-213j)
| (8.8711958789488457461e-07 + 1.5425497262298512298e-947j)  +/-  (9.42e-77, 1.91e-197j)
| (8.8271669402251592391e-25 - 3.4913767513141886517e-960j)  +/-  (3.47e-91, 7.05e-212j)
| (2.1538337430281983207e-29 + 7.0586714101607573625e-963j)  +/-  (2.7e-93, 5.47e-214j)
| (1.33626864605407302e-08 - 5.4161805403216714813e-950j)  +/-  (9.17e-81, 1.86e-201j)
| (0.0073075514041899694337 - 1.1667289308564594138e-944j)  +/-  (1.26e-70, 2.56e-191j)
| (3.9279603909867421369e-05 - 1.2357410832787395983e-946j)  +/-  (7.06e-78, 1.43e-198j)
| (0.0018027887629870198136 - 1.9000044576019725508e-945j)  +/-  (3.4e-73, 6.9e-194j)
| (0.087432104453201267014 + 1.8660538872431348787e-943j)  +/-  (7.88e-62, 1.6e-182j)
| (0.0073075514041899694337 - 2.8261843190767345176e-944j)  +/-  (1.37e-72, 2.78e-193j)
| (-0.0011680644275554887203 + 9.6408597493963090576e-945j)  +/-  (9.35e-72, 1.9e-192j)
| (0.049713063102060696497 - 3.1602064930512882295e-944j)  +/-  (9.97e-67, 2.02e-187j)
| (7.4909527353012788437e-16 + 1.7254802823127155135e-954j)  +/-  (7.4e-88, 1.5e-208j)
| (8.8880777223109961287e-12 + 2.9549814801643291128e-951j)  +/-  (2.71e-85, 5.5e-206j)
| (0.083837004417334615383 - 7.0243500998447029757e-943j)  +/-  (4.44e-67, 9.01e-188j)
| (1.33626864605407302e-08 - 1.1535401229014071325e-948j)  +/-  (3.83e-83, 7.77e-204j)
| (3.8105842635308505672e-06 + 4.4028909309750754634e-947j)  +/-  (5.55e-81, 1.13e-201j)
| (8.8880777223109961287e-12 - 1.3096052309390750807e-952j)  +/-  (6.82e-89, 1.38e-209j)
| (2.4171511201100099611e-18 + 5.8504726638906158222e-957j)  +/-  (8.52e-94, 1.73e-214j)
| (0.56586922339106684806 - 1.3719632259437238886e-941j)  +/-  (3.53e-72, 7.16e-193j)
| (3.9279603909867421369e-05 - 2.5963945349528057708e-947j)  +/-  (1.81e-82, 3.67e-203j)
| (0.00029701714159395521347 + 5.7368705548819579052e-946j)  +/-  (4.1e-81, 8.32e-202j)
| (0.020774555887641572227 + 2.3039697333324725427e-944j)  +/-  (2.13e-77, 4.33e-198j)
| (2.950791910379294885e-21 + 4.8760294151020953729e-958j)  +/-  (1.56e-93, 3.17e-214j)
| (3.8105842635308505672e-06 + 6.6840060865758492017e-948j)  +/-  (4.89e-84, 9.93e-205j)
| (0.049713063102060696497 - 5.3563124233764759261e-944j)  +/-  (5.02e-77, 1.02e-197j)
| (2.950791910379294885e-21 - 9.9622698255500995786e-959j)  +/-  (8.14e-96, 1.65e-216j)
| (-0.0011680644275554887203 + 2.4886163452099345429e-944j)  +/-  (2.37e-80, 4.81e-201j)
| (0.020774555887641572227 + 1.1494367483738563037e-944j)  +/-  (7.24e-80, 1.47e-200j)
| (-0.84468639754808449775 + 2.562096026273357194e-941j)  +/-  (7.03e-77, 1.43e-197j)
| (0.00029701714159395521347 + 1.5701051060651077979e-946j)  +/-  (6.51e-83, 1.32e-203j)
| (7.4909527353012788437e-16 - 2.1866023312345249886e-955j)  +/-  (5.66e-93, 1.15e-213j)
| (4.2939727667245704861e-10 + 2.5699504584714709339e-951j)  +/-  (7.66e-89, 1.55e-209j)
| (0.10643460162522516989 + 1.1170357769569682461e-942j)  +/-  (1.97e-80, 4e-201j)
| (8.8711958789488457461e-07 + 1.8108309115902556967e-946j)  +/-  (1.55e-85, 3.15e-206j)
| (0.0018027887629870198136 - 5.5165284611943781534e-945j)  +/-  (1.77e-83, 3.6e-204j)
| (0.10643460162522516989 + 1.3244243578793784283e-942j)  +/-  (1.01e-80, 2.05e-201j)
| (0.56586922339106684806 - 1.334696691903404514e-941j)  +/-  (1.03e-79, 2.09e-200j)
| (0.083837004417334615383 - 5.45396807815962072e-943j)  +/-  (5.87e-82, 1.23e-202j)
| (0.087432104453201267014 + 1.2824135585748718141e-943j)  +/-  (1.31e-82, 2.54e-203j)
