Starting with polynomial:
P : t
Extension levels are: 1 2 6 10 22
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P3 : t^9 - 117/4*t^7 + 945/4*t^5 - 2205/4*t^3 + 945/4*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P4 : t^19 - 23713751/205892*t^17 + 2134183615/411784*t^15 - 48885080515/411784*t^13 + 623352876985/411784*t^11 - 4536269518165/411784*t^9 + 18427952550645/411784*t^7 - 38805894891225/411784*t^5 + 36681698574675/411784*t^3 - 11110847880825/411784*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 20186539540935324640978282625139084335195484869011510131338502173541414255442317992772533506348506636102216085049401123/35568538848339947881892718663924101777326132051654956865080221854355911613679822055724775480400251645497948138311656*t^39 + 61457071084921257944284584872696717826580934225725094864849136586358864585974318600885044373988102516723884506285205669445/426822466180079374582712623967089221327913584619859482380962662252270939364157864668697305764803019745975377659739872*t^37 - 18487552757429280625816423834062605802076016180584700259163439391457622438551328341373269747102369196181135660146048657766745/853644932360158749165425247934178442655827169239718964761925324504541878728315729337394611529606039491950755319479744*t^35 + 167798323492690130816951591743965070837969602064556627223831116317059006336700007047476504027751426916621111802267674577979359115/77681688844774446174053697562010238281680272400814425793335204529913310964276731369702909649194149593767518734072656704*t^33 - 11763693076467864608998679296514406421219184392774871603681437457182530766148281397003884748285240400542198967384343505186654694265/77681688844774446174053697562010238281680272400814425793335204529913310964276731369702909649194149593767518734072656704*t^31 + 599701890586492249692535509787331610459558790209026555904578641996068174967574154262346903234608306991742752799447699908137881321145/77681688844774446174053697562010238281680272400814425793335204529913310964276731369702909649194149593767518734072656704*t^29 - 22693876053375036804967850909729346781486029321940125904089475051166266613832166924107905525598829181482011273835513145557222240823575/77681688844774446174053697562010238281680272400814425793335204529913310964276731369702909649194149593767518734072656704*t^27 + 71697600618933697626660896379140027088453895188450537791352932285374362319256872595850889809119705296796363656570290476779500411136275/8631298760530494019339299729112248697964474711201602865926133836657034551586303485522545516577127732640835414896961856*t^25 - 220182475063239394219325463029839739000555898122769857666425036426845996407436225769577416026080386513228060195675064475921741176878875/1233042680075784859905614247016035528280639244457371837989447690951004935940900497931792216653875390377262202128137408*t^23 + 25081710485328395120529642174508576691168490077431470094384903180604316943219219874128944521896378882037913223536069960014381101682510625/8631298760530494019339299729112248697964474711201602865926133836657034551586303485522545516577127732640835414896961856*t^21 - 43999159754913915487886307126286776516169800342106311230379180921411236896397177506418365381392996747625368944389049960715146260812744375/1233042680075784859905614247016035528280639244457371837989447690951004935940900497931792216653875390377262202128137408*t^19 + 404452642781559611691738853356016815346504172698534865671314545641260047270282385140080571977012353045014757997583902956220673037187336875/1233042680075784859905614247016035528280639244457371837989447690951004935940900497931792216653875390377262202128137408*t^17 - 2745029705461398886433219965935493642500582284294554267410933754783005276631343977351373625092613446393150718221561660531585687853099253125/1233042680075784859905614247016035528280639244457371837989447690951004935940900497931792216653875390377262202128137408*t^15 + 1035614304144575148167224169247816186386991481060479229770600294330102073514309589231229270386734900196990555623277694754430543522516965625/94849436928906527685047249770464271406203018804413218306880591611615764303146192148599401281067337721327861702164416*t^13 - 3552099288309566580729636197736803072171467482349013342317115338309517957646787788334861695321460530673408206262965457164036923371122189375/94849436928906527685047249770464271406203018804413218306880591611615764303146192148599401281067337721327861702164416*t^11 + 8101876581853806660258038286023112882171865959664665798986874285638751269443555905420313498663487350108451519638495105479127531249472911875/94849436928906527685047249770464271406203018804413218306880591611615764303146192148599401281067337721327861702164416*t^9 - 11337722413269233446562257779943935413427430703928736165666265206813755759397534595182427126925938458959168443262465113893739518655116603125/94849436928906527685047249770464271406203018804413218306880591611615764303146192148599401281067337721327861702164416*t^7 + 8476031761029077938691521051001017422352381274279059999395025259644244667897860109167065937479156241944124335162150643909265223463120784375/94849436928906527685047249770464271406203018804413218306880591611615764303146192148599401281067337721327861702164416*t^5 - 161102343691748229530571037999598820120692789976317882154864645712345227371100242822308239052147072512398159160975502793653234930557103125/5928089808056657980315453110654016962887688675275826144180036975725985268946637009287462580066708607582991356385276*t^3 + 38026167010563526543677975214044988387315392887450023149815680688205957366806520148838216411108332424150121600144024875656568536155328125/23712359232226631921261812442616067851550754701103304576720147902903941075786548037149850320266834430331965425541104*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:
| (-4.6614099650992373673 + 1.131802052771501459e-740j)  +/-  (3.76e-246, 3.76e-246j)
| (7.6897061445989755852 - 1.0487020444620997511e-740j)  +/-  (1.96e-246, 1.96e-246j)
| (10.255584009566288654 - 6.258662614824634057e-746j)  +/-  (1.73e-248, 1.73e-248j)
| (-6.3633944943363699876 - 1.1288226888994120652e-743j)  +/-  (4.63e-246, 4.63e-246j)
| (-9.2589739380116354184 + 1.269351390071031132e-744j)  +/-  (1.77e-247, 1.77e-247j)
| (-10.255584009566288654 + 6.7950284189149272033e-746j)  +/-  (1.85e-248, 1.85e-248j)
| (-3.2053337944991945187 - 8.8245766835395664531e-743j)  +/-  (1.76e-246, 1.76e-246j)
| (-8.4307790591415064708 - 8.9858659100394367558e-744j)  +/-  (7.75e-247, 7.75e-247j)
| (-2.5960831150492021594 - 4.3465259322165946476e-748j)  +/-  (3.29e-247, 3.29e-247j)
| (8.4307790591415064708 + 3.2850339395951924802e-748j)  +/-  (7.48e-247, 7.48e-247j)
| (1.2304236340273060078 + 3.6221447368188430219e-756j)  +/-  (1.4e-251, 1.4e-251j)
| (-4.1849560176727318607 - 5.5868098636698709138e-754j)  +/-  (2.63e-246, 2.63e-246j)
| (2.8612795760570581173 + 1.2541624285277802261e-762j)  +/-  (9.82e-246, 9.82e-246j)
| (5.7571492399661859082 + 1.1102847997437900819e-779j)  +/-  (4.9e-246, 4.9e-246j)
| (2.2427631215161635324 - 3.4610413918642186902e-782j)  +/-  (1.82e-248, 1.82e-248j)
| (-7.0054120179709303476 + 1.2586574730623049535e-782j)  +/-  (3.38e-246, 3.38e-246j)
| (5.187016039913656066 + 1.9952772531532131415e-781j)  +/-  (4.51e-246, 4.51e-246j)
| (-5.187016039913656066 + 5.5588542245197478833e-785j)  +/-  (4.76e-246, 4.76e-246j)
| (-3.7199689020743816627 - 1.2308745118668731662e-783j)  +/-  (1.85e-246, 1.85e-246j)
| (-2.2427631215161635324 + 3.1075078550414117547e-786j)  +/-  (1.56e-248, 1.56e-248j)
| (9.2589739380116354184 + 1.9514370594375731441e-785j)  +/-  (1.74e-247, 1.74e-247j)
| (2.5960831150492021594 + 1.0973685134123548952e-781j)  +/-  (3.49e-247, 3.49e-247j)
| (6.3633944943363699876 - 3.3741108910808733554e-792j)  +/-  (4.75e-246, 4.75e-246j)
| (-5.7571492399661859082 + 1.9354217516127534082e-795j)  +/-  (5.31e-246, 5.31e-246j)
| (-1.7320508075688772935 + 2.0160184365680153211e-808j)  +/-  (4.16e-250, 4.16e-250j)
| (4.6614099650992373673 + 6.9038069910185864396e-811j)  +/-  (3.43e-246, 3.43e-246j)
| (2.89041882896369058 - 9.2076609231812001191e-834j)  +/-  (1.17e-245, 1.17e-245j)
| (3.2053337944991945187 - 1.1879110663378905691e-849j)  +/-  (1.78e-246, 1.78e-246j)
| (-7.6897061445989755852 + 5.8653058914126056249e-854j)  +/-  (2.01e-246, 2.01e-246j)
| (-0.74109534999454084186 + 3.5202740243721876703e-860j)  +/-  (7.05e-253, 7.05e-253j)
| (-2.89041882896369058 - 6.8793722479585377568e-852j)  +/-  (1.14e-245, 1.14e-245j)
| (3.7199689020743816627 - 8.692496594329911522e-855j)  +/-  (1.73e-246, 1.73e-246j)
| (1.7320508075688772935 - 2.5882375313505007768e-863j)  +/-  (3.59e-250, 3.59e-250j)
| (4.1849560176727318607 - 1.7222395033656636203e-859j)  +/-  (2.73e-246, 2.73e-246j)
| (-0.27623095918843283934 + 1.6373345580248685793e-867j)  +/-  (4.85e-254, 4.85e-254j)
| (7.0054120179709303476 - 5.5785519543646818598e-865j)  +/-  (3.23e-246, 3.23e-246j)
| (0.27623095918843283934 - 5.4157097192277608134e-871j)  +/-  (4.85e-254, 4.85e-254j)
| (0.74109534999454084186 + 1.212450529975885541e-870j)  +/-  (7.05e-253, 7.05e-253j)
| (1.608808312612980236e-882 - 1.3399423925991923138e-882j)  +/-  (8.58e-881, 8.58e-881j)
| (-2.8612795760570581173 + 6.7084510628686397879e-868j)  +/-  (1.06e-245, 1.06e-245j)
| (-1.2304236340273060078 - 3.5269595352855487927e-877j)  +/-  (1.36e-251, 1.36e-251j)
-------------------------------------------------
The weights are:
| (3.8118279174917750559e-06 + 2.0582484717706654654e-745j)  +/-  (5.09e-79, 2.01e-201j)
| (4.0882016120250598284e-14 + 4.0961965201386715003e-754j)  +/-  (4.16e-88, 1.64e-210j)
| (6.6419589381275780148e-24 + 1.3994531553160068768e-759j)  +/-  (4.06e-93, 1.6e-215j)
| (4.0078414160483475891e-10 + 8.3825490082982373128e-750j)  +/-  (2.18e-85, 8.6e-208j)
| (8.6042717251220723632e-20 + 1.2001549971099491481e-756j)  +/-  (2.68e-92, 1.05e-214j)
| (6.6419589381275780148e-24 - 3.3699834239474160887e-759j)  +/-  (2.18e-94, 8.58e-217j)
| (0.0014069742406524682538 - 4.357978738692320102e-743j)  +/-  (3.66e-77, 1.44e-199j)
| (1.1407007853085089957e-16 - 1.2826187981237935814e-754j)  +/-  (5.87e-91, 2.31e-213j)
| (0.00070547111012296261215 + 2.3261136614667431983e-742j)  +/-  (8.09e-75, 3.19e-197j)
| (1.1407007853085089957e-16 + 4.9467744981836873275e-755j)  +/-  (3.11e-93, 1.23e-215j)
| (0.092833822851011184454 - 2.9503784292746776011e-743j)  +/-  (1.58e-67, 6.22e-190j)
| (2.8897678027447868876e-05 - 7.9997984272317495584e-745j)  +/-  (4.89e-81, 1.93e-203j)
| (0.017885254303369973179 - 3.6464811223711755534e-742j)  +/-  (2.27e-79, 8.93e-202j)
| (1.4915821041783140767e-08 + 2.1515296463178257432e-749j)  +/-  (9.23e-89, 3.64e-211j)
| (0.01654455267058607719 - 3.11569394537591164e-743j)  +/-  (8.38e-77, 3.3e-199j)
| (5.8180339317032041896e-12 - 2.7889656107195557714e-751j)  +/-  (1.6e-89, 6.29e-212j)
| (3.1537226585226487074e-07 - 3.4299823384059929001e-748j)  +/-  (1.11e-87, 4.38e-210j)
| (3.1537226585226487074e-07 + 6.9520262195322436841e-747j)  +/-  (1.96e-85, 7.73e-208j)
| (0.00018901090980509788652 + 3.2509055302906943015e-744j)  +/-  (1.18e-81, 4.64e-204j)
| (0.01654455267058607719 - 9.0983158297725377878e-743j)  +/-  (4.83e-78, 1.91e-200j)
| (8.6042717251220723632e-20 - 4.6284278954895567422e-757j)  +/-  (1.62e-96, 6.37e-219j)
| (0.00070547111012296261215 + 6.4337688413347983957e-743j)  +/-  (1.98e-81, 7.79e-204j)
| (4.0078414160483475891e-10 - 1.0858389136235639752e-750j)  +/-  (2.8e-91, 1.11e-213j)
| (1.4915821041783140767e-08 - 2.2848578354041363939e-748j)  +/-  (4.58e-88, 1.81e-210j)
| (0.045109010335859128034 + 4.9322961589432910721e-743j)  +/-  (1.96e-79, 7.72e-202j)
| (3.8118279174917750559e-06 + 4.3608250078487483467e-747j)  +/-  (3.08e-88, 1.22e-210j)
| (-0.014452842220698823713 + 3.2822890969961312892e-742j)  +/-  (9.24e-83, 3.64e-205j)
| (0.0014069742406524682538 - 7.6488357324159031312e-744j)  +/-  (4.86e-85, 1.91e-207j)
| (4.0882016120250598284e-14 + 7.2727350938448073732e-753j)  +/-  (2.49e-94, 9.83e-217j)
| (0.1459662938959264287 + 7.3704195482007759575e-743j)  +/-  (2.45e-82, 9.67e-205j)
| (-0.014452842220698823713 + 1.4517587762756691627e-741j)  +/-  (2.62e-84, 1.03e-206j)
| (0.00018901090980509788652 + 3.5286088621532547726e-745j)  +/-  (2.28e-87, 8.99e-210j)
| (0.045109010335859128034 + 2.2230607172312061301e-743j)  +/-  (9.01e-85, 3.55e-207j)
| (2.8897678027447868876e-05 - 4.1140183807238439656e-746j)  +/-  (1.6e-88, 6.31e-211j)
| (0.16563974040052955412 - 1.6097340837270968931e-742j)  +/-  (1.13e-84, 4.46e-207j)
| (5.8180339317032041896e-12 + 3.726373007332811672e-752j)  +/-  (1.05e-94, 4.15e-217j)
| (0.16563974040052955412 - 1.4261486036688108903e-742j)  +/-  (3.4e-85, 1.34e-207j)
| (0.1459662938959264287 + 5.3131324124602147609e-743j)  +/-  (1.19e-85, 4.69e-208j)
| (0.056279342604321887748 + 2.2283041309491114158e-742j)  +/-  (3.78e-85, 1.49e-207j)
| (0.017885254303369973179 - 1.5787898486876856083e-741j)  +/-  (1.07e-85, 4.37e-208j)
| (0.092833822851011184454 - 5.1236748352946995475e-743j)  +/-  (9.78e-87, 3.63e-209j)
