Starting with polynomial:
P : 2*t
Extension levels are: 1 8 56
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 56 Kronrod extension for:
P2 : 2*t^9 - 36*t^7 + 189*t^5 - 315*t^3 + 945/8*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^65 - 48756443636972876374566540204142356882643669712300959510316795886366760/26329924825818023815358945523436194015742759935352760191605320169273*t^63 + 176073695858275382267364466816182275680128253425460542693435414035216864868/219416040215150198461324546028634950131189666127939668263377668077275*t^61 - 47513966295112218405083583062749136515161461355531672372041400138793124639646/219416040215150198461324546028634950131189666127939668263377668077275*t^59 + 35845507046591040784580030080798344022447089524954257877628147599453602327184913/877664160860600793845298184114539800524758664511758673053510672309100*t^57 - 1256916644071043844459322147733356786890152518526961416812731846110976132629962089/219416040215150198461324546028634950131189666127939668263377668077275*t^55 + 43585615756238156441995675591362526048472604848253235956118268872991788793074265229/70213132868848063507623854729163184041980693160940693844280853784728*t^53 - 275198189067762920449639714410169296729119732906582622354097345855654958320381557363/5162730358003534081442930494791410591322109791245639253255945131230*t^51 + 121969034495127784746588728257128928046607013925660036835129038662851006245552369894889/33041474291222618121234755166665027784461502663972091220838048839872*t^49 - 3448554105942877674156149005684403614736421980711776323459288762219915520865325518646069/16520737145611309060617377583332513892230751331986045610419024419936*t^47 + 80328587847208559373725534963499473620685138361802171733151378734881071743967641019046209/8260368572805654530308688791666256946115375665993022805209512209968*t^45 - 24817771679280220000849159193618849171593810803327788708664066059765398968337834487190581625/66082948582445236242469510333330055568923005327944182441676097679744*t^43 + 6382396315847745584151884325723171418962675191886867404014182148427193164252773377483560628825/528663588659561889939756082666640444551384042623553459533408781437952*t^41 - 21399322549084050527964715240635387111980709366561477128647004751145524625122934058096526186765/66082948582445236242469510333330055568923005327944182441676097679744*t^39 + 7670285663258705585398912117594872902174811109456719969182099581430182574486165854499129943501855/1057327177319123779879512165333280889102768085247106919066817562875904*t^37 - 71729147426426518860958324663988106587353133749669303092531823474918620859758161885238054890864805/528663588659561889939756082666640444551384042623553459533408781437952*t^35 + 2236454758776111005133269959898741595400139577406376570926910264474949791271529284965515666116543375/1057327177319123779879512165333280889102768085247106919066817562875904*t^33 - 694102673422455608542970160365987300343444781711205330084879253993782766491239583204125848258811575/25325201851955060595916459049898943451563307431068429199205211086848*t^31 + 2486516725431785113411237868375076114161129858060405402577127740496824515161421350534554103490891523525/8458617418552990239036097322666247112822144681976855352534540503007232*t^29 - 43910264608902810843465955512896137518174979121820475690866048147345727888652917977536699788384334325225/16917234837105980478072194645332494225644289363953710705069081006014464*t^27 + 15183195171249769798341311792876621002299758102299987445932256946235136848298128680135651656995860089925/810406459262561939069326689596766190450025837794189734374566754779136*t^25 - 3707648392907208704371098616944039864915210950784050228698819545343938812248261212873060859314945101690625/33834469674211960956144389290664988451288578727907421410138162012028928*t^23 + 139045326437661190283017354440714961641046897686819042751264510533240278370317894902067495722719138744466875/270675757393695687649155114325319907610308629823259371281105296096231424*t^21 - 64413879143523058522557824730701790932431670313090055720359098368403019403331755693559561515850117195218125/33834469674211960956144389290664988451288578727907421410138162012028928*t^19 + 11872960188970214470488119500503339813092488348054255055502910026734769349531445330903947808992976368049229375/2165406059149565501193240914602559260882469038586074970248842368769851392*t^17 - 13000233832134552115763916206398404106223572083503524327394913632317457618558584198800483659721415670494291875/1082703029574782750596620457301279630441234519293037485124421184384925696*t^15 + 21047251402042403062595053380443104805699544298144399797210627292310369871431081170201062388855428981050296875/1082703029574782750596620457301279630441234519293037485124421184384925696*t^13 - 97106493597757717297999007144767861832053368301455313886304415800660531770160435650573566380252063443362194375/4330812118299131002386481829205118521764938077172149940497684737539702784*t^11 + 607083255393716640074179231373552519203031289255620974681780251118995723899294460398008299695034225792357106875/34646496946393048019091854633640948174119504617377199523981477900317622272*t^9 - 18703170972795345256786027890357288945886951677771238756262060139223453709515623713878993571630723428032073125/2165406059149565501193240914602559260882469038586074970248842368769851392*t^7 + 166793765802262727840634957397092415195132095196089546752599201968219302846323268899923817588111497235611095625/69292993892786096038183709267281896348239009234754399047962955800635244544*t^5 - 10848165662890142607042534440263925107422133563844438039421072258237071234011103893993661066169143012928015625/34646496946393048019091854633640948174119504617377199523981477900317622272*t^3 + 13556758378337454458626117896759264645633286272527541101598186980644171057071585514880117385709841584287628125/1108687902284577536610939348276510341571824147756070384767407292810163912704*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: 0
  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:
| (-7.3995774508728235761 + 1.6829774482412174126e-728j)  +/-  (1.63e-240, 1.63e-240j)
| (-9.0977351437550055904 + 1.149603160308805634e-735j)  +/-  (1.85e-242, 1.85e-242j)
| (7.0276951162574104426 + 1.9881273095802220052e-734j)  +/-  (2.75e-240, 2.75e-240j)
| (8.194539055665773259 - 3.3565830137528758202e-743j)  +/-  (3.44e-241, 3.44e-241j)
| (-7.787159550266447353 + 2.9267140875924657802e-746j)  +/-  (8.11e-241, 8.11e-241j)
| (9.6240934615480360945 - 1.193304731660869893e-757j)  +/-  (1.98e-243, 1.98e-243j)
| (-6.6686342547986555474 + 1.0978176561382368302e-754j)  +/-  (3.39e-240, 3.39e-240j)
| (-1.7402568832330897309 + 7.3665041582030943584e-774j)  +/-  (3.46e-247, 3.46e-247j)
| (7.787159550266447353 - 8.1774337422483726226e-765j)  +/-  (8.55e-241, 8.55e-241j)
| (4.69286801223924306 + 8.6563473345063189442e-775j)  +/-  (5.46e-241, 5.46e-241j)
| (1.7402568832330897309 - 1.4163868159736942346e-784j)  +/-  (3.56e-247, 3.56e-247j)
| (-4.3842571050737804815 + 2.3883056577838396695e-776j)  +/-  (2.3e-241, 2.3e-241j)
| (-10.259865297592656384 - 4.9615722369061173415e-785j)  +/-  (9.6e-245, 9.6e-245j)
| (7.3995774508728235761 + 9.619310521597944729e-783j)  +/-  (1.79e-240, 1.79e-240j)
| (-7.0276951162574104426 - 3.9506860400275161039e-788j)  +/-  (2.72e-240, 2.72e-240j)
| (-9.6240934615480360945 + 1.9474289325090525486e-794j)  +/-  (1.98e-243, 1.98e-243j)
| (-8.194539055665773259 - 2.0943030571582077647e-791j)  +/-  (3.16e-241, 3.16e-241j)
| (9.0977351437550055904 + 1.0456619056329398755e-791j)  +/-  (1.7e-242, 1.7e-242j)
| (-0.95368252163373860128 + 2.073716060857399058e-802j)  +/-  (2.84e-250, 2.84e-250j)
| (10.259865297592656384 - 2.190176923622012628e-796j)  +/-  (9.89e-245, 9.89e-245j)
| (3.4832703689786113884 - 3.2969706618739963971e-796j)  +/-  (1.06e-242, 1.06e-242j)
| (1.2038037004294363572 - 7.7715901978482342554e-802j)  +/-  (3.3e-249, 3.3e-249j)
| (8.6279377543943093516 - 1.200134390064166707e-792j)  +/-  (8.65e-242, 8.65e-242j)
| (-2.2665805845318431118 - 9.1015386351503195164e-804j)  +/-  (5.17e-245, 5.17e-245j)
| (-1.4685532892166679317 + 3.4517644085800080458e-807j)  +/-  (3.47e-248, 3.47e-248j)
| (5.9810038079251622642 + 1.4613924970021723542e-798j)  +/-  (3.43e-240, 3.43e-240j)
| (0.72355101875283757332 - 1.058126626095273617e-814j)  +/-  (2.67e-251, 2.67e-251j)
| (3.1909932017815276072 + 9.6151876493360602337e-807j)  +/-  (3.22e-243, 3.22e-243j)
| (-3.1909932017815276072 + 1.4387272506705660151e-803j)  +/-  (3.08e-243, 3.08e-243j)
| (-2.9043144539356750964 - 1.1783739488461730836e-806j)  +/-  (1.06e-243, 1.06e-243j)
| (-5.3249017598831021692 - 5.7428721541083771006e-805j)  +/-  (1.79e-240, 1.79e-240j)
| (4.0799638330464117979 - 6.6025921072144803606e-810j)  +/-  (9e-242, 9e-242j)
| (5.00623264620481984 - 7.3172528413210933332e-810j)  +/-  (1.04e-240, 1.04e-240j)
| (2.4293327417654644929 + 2.4519069104860616483e-815j)  +/-  (1.71e-244, 1.71e-244j)
| (-1.2038037004294363572 - 3.7264536622377793268e-820j)  +/-  (3.13e-249, 3.13e-249j)
| (-5.9810038079251622642 - 7.4868557480114632141e-810j)  +/-  (3.74e-240, 3.74e-240j)
| (-8.6279377543943093516 - 1.8875980161756923078e-815j)  +/-  (8.84e-242, 8.84e-242j)
| (0.95368252163373860128 - 1.1763959285677882746e-824j)  +/-  (3.15e-250, 3.15e-250j)
| (4.3842571050737804815 + 1.6010984629306502299e-816j)  +/-  (2.18e-241, 2.18e-241j)
| (-3.4832703689786113884 - 3.1057127433899633924e-815j)  +/-  (1.01e-242, 1.01e-242j)
| (-0.72355101875283757332 + 1.1360976235605848601e-825j)  +/-  (2.57e-251, 2.57e-251j)
| (-4.0799638330464117979 - 4.7433014417278169638e-814j)  +/-  (9.05e-242, 9.05e-242j)
| (2.2665805845318431118 + 5.8689937723124857837e-820j)  +/-  (5.01e-245, 5.01e-245j)
| (1.4685532892166679317 + 1.1106868439754059022e-823j)  +/-  (3.2e-248, 3.2e-248j)
| (-6.320275933857202619 + 3.8055180908354097586e-814j)  +/-  (3.61e-240, 3.61e-240j)
| (-5.6495506238354577792 + 1.3275972876037108338e-815j)  +/-  (2.75e-240, 2.75e-240j)
| (-4.69286801223924306 + 4.9386183287625192338e-823j)  +/-  (5.46e-241, 5.46e-241j)
| (5.3249017598831021692 - 1.6974112779201279951e-845j)  +/-  (1.78e-240, 1.78e-240j)
| (9.3659967656446315478e-917 + 9.5692498482607022928e-917j)  +/-  (8.7e-915, 8.7e-915j)
| (6.320275933857202619 + 3.2837415556135074013e-874j)  +/-  (3.79e-240, 3.79e-240j)
| (-5.00623264620481984 - 2.8229223260571950304e-894j)  +/-  (1.06e-240, 1.06e-240j)
| (-2.0127021820851302343 + 3.8944501981323184635e-908j)  +/-  (4.22e-246, 4.22e-246j)
| (-2.631504328248421401 + 1.4081247702348323286e-902j)  +/-  (4.25e-244, 4.25e-244j)
| (0.49689185942775325436 - 6.8487449288586877476e-925j)  +/-  (2.07e-252, 2.07e-252j)
| (5.6495506238354577792 - 2.9824736160095156055e-910j)  +/-  (2.79e-240, 2.79e-240j)
| (3.7796777588876455555 - 5.9673922785069785294e-923j)  +/-  (3.08e-242, 3.08e-242j)
| (-0.49689185942775325436 + 1.1318619193468636894e-940j)  +/-  (2.07e-252, 2.07e-252j)
| (-3.7796777588876455555 - 3.4650443805544471873e-934j)  +/-  (3.22e-242, 3.22e-242j)
| (0.25413938922587106587 - 1.3380813666522701239e-957j)  +/-  (1.26e-253, 1.26e-253j)
| (-0.25413938922587106587 + 1.7709121064082177377e-957j)  +/-  (1.26e-253, 1.26e-253j)
| (2.0127021820851302343 + 1.2957483984621979062e-950j)  +/-  (4.22e-246, 4.22e-246j)
| (-2.4293327417654644929 + 6.8184894592825884028e-946j)  +/-  (1.63e-244, 1.63e-244j)
| (2.631504328248421401 + 1.7725228029618824062e-949j)  +/-  (4.07e-244, 4.07e-244j)
| (6.6686342547986555474 - 8.9657764834875774667e-957j)  +/-  (3.52e-240, 3.52e-240j)
| (2.9043144539356750964 - 9.7456954160711586044e-971j)  +/-  (1e-243, 1e-243j)
-------------------------------------------------
The weights are:
| (3.5563979256819212137e-25 + 4.7724425801805981398e-752j)  +/-  (2.55e-60, 6.52e-179j)
| (3.1517838179797919434e-37 - 1.3936014603380105738e-759j)  +/-  (3.8e-66, 9.71e-185j)
| (7.3222430838196722748e-23 - 7.4270126327047118179e-753j)  +/-  (2.4e-60, 6.12e-179j)
| (1.624307051370149312e-30 + 5.3308568131148963876e-757j)  +/-  (7.78e-65, 1.99e-183j)
| (1.0334560762126076827e-27 + 6.7064748111700788001e-754j)  +/-  (8.29e-63, 2.12e-181j)
| (1.9014068816142411976e-41 - 8.5496684935286123803e-763j)  +/-  (5.25e-70, 1.34e-188j)
| (9.6900325159925764687e-21 + 2.1091887923146484298e-750j)  +/-  (1.46e-59, 3.74e-178j)
| (0.0074602538731044178888 - 5.3082207713572303313e-740j)  +/-  (8.39e-28, 2.14e-146j)
| (1.0334560762126076827e-27 - 1.7111004754189079982e-755j)  +/-  (1.29e-63, 3.29e-182j)
| (4.7816942267319857127e-11 + 4.3362077938447049913e-746j)  +/-  (8.77e-53, 2.24e-171j)
| (0.0074602538731044178888 - 3.286861076005836991e-740j)  +/-  (9.07e-30, 2.32e-148j)
| (7.7591750499379179554e-10 - 9.7142770249639778733e-745j)  +/-  (1.82e-51, 4.65e-170j)
| (7.9706297181307967589e-47 - 7.9997850502884936477e-765j)  +/-  (1.77e-72, 4.53e-191j)
| (3.5563979256819212137e-25 + 4.042188006045623864e-754j)  +/-  (4.36e-63, 1.11e-181j)
| (7.3222430838196722748e-23 - 2.8770173085029290123e-751j)  +/-  (2.12e-61, 5.41e-180j)
| (1.9014068816142411976e-41 + 6.5434217246868443053e-762j)  +/-  (1.84e-70, 4.71e-189j)
| (1.624307051370149312e-30 - 1.0459003518788241586e-755j)  +/-  (1.43e-65, 3.65e-184j)
| (3.1517838179797919434e-37 + 1.4343559274348074411e-760j)  +/-  (5.22e-71, 1.33e-189j)
| (0.054497179525566154982 + 2.4622963010417076718e-739j)  +/-  (1.16e-33, 2.96e-152j)
| (7.9706297181307967589e-47 + 1.2956262981829221428e-765j)  +/-  (1.9e-75, 4.86e-194j)
| (8.9340147951387903991e-07 + 3.0784730691267162356e-743j)  +/-  (1.75e-53, 4.46e-172j)
| (0.034302615644956640395 - 1.0592393219798664294e-739j)  +/-  (1.16e-33, 2.96e-152j)
| (1.1872907940552507403e-33 - 1.1301664416662817453e-758j)  +/-  (1.75e-69, 4.48e-188j)
| (0.00073347825397032011378 - 3.4623800989577601853e-740j)  +/-  (2.64e-46, 6.74e-165j)
| (0.017577136904215197921 + 8.5831619610069059667e-740j)  +/-  (2.58e-38, 6.59e-157j)
| (5.5072901512181557734e-17 + 1.3955086812555368941e-749j)  +/-  (1.29e-63, 3.29e-182j)
| (0.074711952840857609801 - 2.875549523823244099e-739j)  +/-  (2.62e-36, 6.68e-155j)
| (6.1877243346395051138e-06 - 1.4313961886436079261e-742j)  +/-  (1.61e-52, 4.11e-171j)
| (6.1877243346395051138e-06 - 3.6018806292170010193e-742j)  +/-  (1.12e-53, 2.86e-172j)
| (3.4605238759697318283e-05 + 1.5813749194279625535e-741j)  +/-  (5.86e-52, 1.5e-170j)
| (8.798655685083024386e-14 + 6.0416500496109415196e-747j)  +/-  (2.4e-63, 6.13e-182j)
| (1.0057265220192404064e-08 + 1.3147842830869345721e-744j)  +/-  (1.82e-58, 4.66e-177j)
| (2.3256735664045648739e-12 - 6.8897644908050983018e-747j)  +/-  (7.22e-62, 1.85e-180j)
| (0.00021648589642809890955 + 1.2398536835590693087e-740j)  +/-  (2.04e-51, 5.2e-170j)
| (0.034302615644956640395 - 1.4708332072605586365e-739j)  +/-  (6.46e-42, 1.65e-160j)
| (5.5072901512181557734e-17 + 1.3160753234426220847e-748j)  +/-  (4.54e-66, 1.16e-184j)
| (1.1872907940552507403e-33 + 1.474828619212399288e-757j)  +/-  (3.62e-73, 9.24e-192j)
| (0.054497179525566154982 + 1.9000756440684670533e-739j)  +/-  (4.74e-44, 1.21e-162j)
| (7.7591750499379179554e-10 - 2.485891019259683011e-745j)  +/-  (1.88e-60, 4.81e-179j)
| (8.9340147951387903991e-07 + 8.5543149421907522316e-743j)  +/-  (3.13e-58, 8e-177j)
| (0.074711952840857609801 - 3.4988361193384733773e-739j)  +/-  (1.19e-45, 3.05e-164j)
| (1.0057265220192404064e-08 + 4.5464273419453248553e-744j)  +/-  (9.14e-61, 2.33e-179j)
| (0.00073347825397032011378 - 1.8386564263058305492e-740j)  +/-  (5.21e-54, 1.33e-172j)
| (0.017577136904215197921 + 5.7405065263484539716e-740j)  +/-  (1.2e-49, 3.07e-168j)
| (8.693063026527338956e-19 - 1.706972774837124797e-749j)  +/-  (2.91e-67, 7.43e-186j)
| (2.5445169767885466138e-15 - 9.3350854506563502675e-748j)  +/-  (7.12e-66, 1.82e-184j)
| (4.7816942267319857127e-11 + 1.9371058246705147544e-745j)  +/-  (7.61e-64, 1.95e-182j)
| (8.798655685083024386e-14 + 9.8516490074573739755e-748j)  +/-  (6.07e-68, 1.55e-186j)
| (0.14442941804906974131 + 3.6250012538456469113e-739j)  +/-  (4.3e-53, 1.1e-171j)
| (8.693063026527338956e-19 - 1.3431793984286526999e-750j)  +/-  (2.76e-71, 7.06e-190j)
| (2.3256735664045648739e-12 - 3.5709942155759308625e-746j)  +/-  (3.12e-65, 7.97e-184j)
| (0.0026467338445152123427 + 3.766020318933772281e-740j)  +/-  (6.74e-58, 1.72e-176j)
| (0.00014186995428910288273 - 7.8512929521428640078e-741j)  +/-  (6.48e-60, 1.66e-178j)
| (0.10303789684790312076 + 3.4430316026342150551e-739j)  +/-  (8.9e-56, 2.27e-174j)
| (2.5445169767885466138e-15 - 1.2520931581899453018e-748j)  +/-  (1.44e-69, 3.68e-188j)
| (1.051550615873793613e-07 - 6.511128401982724974e-744j)  +/-  (6.31e-65, 1.61e-183j)
| (0.10303789684790312076 + 3.9387112590339254298e-739j)  +/-  (8.44e-57, 2.15e-175j)
| (1.051550615873793613e-07 - 2.0107322124157894336e-743j)  +/-  (1.97e-63, 5.02e-182j)
| (0.13241788498660788722 - 3.55917406071552418e-739j)  +/-  (3.88e-57, 9.89e-176j)
| (0.13241788498660788722 - 3.8123422393696042293e-739j)  +/-  (2.7e-57, 6.88e-176j)
| (0.0026467338445152123427 + 2.1554220755020242736e-740j)  +/-  (3.89e-61, 9.92e-180j)
| (0.00021648589642809890955 + 2.4518195688339226538e-740j)  +/-  (2.05e-60, 5.24e-179j)
| (0.00014186995428910288273 - 3.7320451099659550583e-741j)  +/-  (4.7e-63, 1.2e-181j)
| (9.6900325159925764687e-21 + 1.0964563178913645169e-751j)  +/-  (6.52e-74, 1.73e-192j)
| (3.4605238759697318283e-05 + 6.8992320064221399322e-742j)  +/-  (5.94e-64, 1.51e-182j)
