Starting with polynomial:
P : 1/479001600*t^12 - 1/3326400*t^11 + 11/604800*t^10 - 11/18144*t^9 + 11/896*t^8 - 11/70*t^7 + 77/60*t^6 - 33/5*t^5 + 165/8*t^4 - 110/3*t^3 + 33*t^2 - 12*t + 1
Extension levels are: 12 21
-------------------------------------------------
Trying to find an order 21 Kronrod extension for:
P1 : 1/479001600*t^12 - 1/3326400*t^11 + 11/604800*t^10 - 11/18144*t^9 + 11/896*t^8 - 11/70*t^7 + 77/60*t^6 - 33/5*t^5 + 165/8*t^4 - 110/3*t^3 + 33*t^2 - 12*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/479001600*t^33 - 231390371173195462872963148868484871402830998805107747229049223085034057/136763404540002728964852939851962019641201030136619406533158262156659977190400*t^32 + 10979345329339089866499771869000416777486227925069042931953679680000795169/17095425567500341120606617481495252455150128767077425816644782769582497148800*t^31 - 46758070086257923420043054530571560161013150705945470712667663558581160894267/307717660215006140170919114666914544192702317807393664699606089852484948678400*t^30 + 447242699829073713392764266139557330495003216027869393648407411880759277196703/17779242590200354765430882180755062553356133917760522849310574080365797034752*t^29 - 275676117858669835015777202961268469113644553966870105136219086917975916008371081/88896212951001773827154410903775312766780669588802614246552870401828985173760*t^28 + 1408791922703399335153411772080644353514023753296427910138738883859447876096028919/4762297122375095026454700584130820326791821585114425763208189485812267062880*t^27 - 658518391310689249664004714213353092860364834101649096355280478792554007658345197/29396895817130216212683336939079137819702602377249541748198700529705352240*t^26 + 80589540591144002958266347530335365317211716950256365519753433874963774503456698419/58793791634260432425366673878158275639405204754499083496397401059410704480*t^25 - 186259877464980675819858397090118841449921043140731897089723885300871189971697051315/2713559613888943035016923409761151183357163296361496161372187741203570976*t^24 + 347700746591982747235587155067782724576182365539292131511559930726598592825989997738/122487065904709234219513903912829740915427509905206423950827918873772301*t^23 - 23903895887758961176431814209141342461497928548917160711950010479886213154091479672193/244974131809418468439027807825659481830855019810412847901655837747544602*t^22 + 6173546059950285585288429841601906749330895306396149096714619623684601304909536218184387/2204767186284766215951250270430935336477695178293715631114902539727901418*t^21 - 16476351655172175894252856374219191453524013962688571826175744956445046673926191368361993/244974131809418468439027807825659481830855019810412847901655837747544602*t^20 + 165832081101547815256598981621914955661624739335375067479010274270230453027722513541198700/122487065904709234219513903912829740915427509905206423950827918873772301*t^19 - 8391764272979112574318070503082732721776141170237981104206911137886312424812155155703536480/367461197714127702658541711738489222746282529715619271852483756621316903*t^18 + 39486486819396315304073354354954351199817882557468337285247322260251521579032917737041024580/122487065904709234219513903912829740915427509905206423950827918873772301*t^17 - 465291909299896945883856816894346198895263438612965109699207341579422932818181058627708907180/122487065904709234219513903912829740915427509905206423950827918873772301*t^16 + 4559733303549812732569263969421868984801533696615224018578234009835048520137612784132281895680/122487065904709234219513903912829740915427509905206423950827918873772301*t^15 - 36974416803075755228105058090744803963678412608976442942077226657869775207227379049834555184000/122487065904709234219513903912829740915427509905206423950827918873772301*t^14 + 246488841899764873297789570816561172658936936654954875463135205347797728223811389468931931094400/122487065904709234219513903912829740915427509905206423950827918873772301*t^13 - 103075346109389717614316663719204605579919882290419346090368294523812905672681002744318990710400/9422081992669941093808761839448441608879039223477417226986762990290177*t^12 + 452362000874742270891775852815359492316179995858486538403498664067986591883041104475915082726400/9422081992669941093808761839448441608879039223477417226986762990290177*t^11 - 143896333549277156902507075394959597918349090810063354394411235844839120236264795719205881702400/856552908424540099437160167222585600807185383952492475180614817299107*t^10 + 395302291132644363824872220095216843256020784240401030609060619130323988895798036467637200000000/856552908424540099437160167222585600807185383952492475180614817299107*t^9 - 836272842502057167097567384197681589788114227525052283591738293627244803484888194971108880768000/856552908424540099437160167222585600807185383952492475180614817299107*t^8 + 1329414618991200310840870781745843062593593824930834676838729627685280195346329715138055061504000/856552908424540099437160167222585600807185383952492475180614817299107*t^7 - 1538373928632268794602921829775867132191400002887194467818861513325201559350859313055977478144000/856552908424540099437160167222585600807185383952492475180614817299107*t^6 + 1242028691284241936532245991986980366254526666284369084243294997212878396916723038396427577344000/856552908424540099437160167222585600807185383952492475180614817299107*t^5 - 659745001440190703010493659336143300198070743241187106295337906811382075596436760856116377600000/856552908424540099437160167222585600807185383952492475180614817299107*t^4 + 211844591549522676096301678630504131884734699264271332134760076721305201597451035170332426240000/856552908424540099437160167222585600807185383952492475180614817299107*t^3 - 36237805817980803688877596290304726145390526090612846452625698874426658904452474571944427520000/856552908424540099437160167222585600807185383952492475180614817299107*t^2 + 2730729145889130231433971717546441415108091290720836705200289863845311718936466852324229120000/856552908424540099437160167222585600807185383952492475180614817299107*t - 63129772020184538034943811825711543957873907208602128147862027173221577320242796974981120000/856552908424540099437160167222585600807185383952492475180614817299107
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (93.551178069372863862 - 1.5132584894640503768e-601j)  +/-  (3.95e-244, 3.95e-244j)
| (64.24786154326179611 - 1.0117475671221988155e-601j)  +/-  (4.13e-241, 4.13e-241j)
| (81.478734778765280474 + 3.7615434167971048873e-622j)  +/-  (8.87e-243, 8.87e-243j)
| (57.399126229876987754 + 9.3413564890970579725e-660j)  +/-  (1.67e-240, 1.67e-240j)
| (35.502737955530880276 - 5.5084502534344358765e-694j)  +/-  (1.34e-238, 1.34e-238j)
| (72.116828845037914955 + 1.4194043867366006758e-708j)  +/-  (7.7e-242, 7.7e-242j)
| (19.48042028474031866 - 1.1185875293847202189e-712j)  +/-  (4.25e-240, 4.25e-240j)
| (51.32585343233548139 - 1.5110002067197079383e-721j)  +/-  (5.11e-240, 5.11e-240j)
| (5.6208189301795707627 - 8.7819648928071745944e-735j)  +/-  (3.03e-244, 3.03e-244j)
| (8.1926039030086924357 - 2.2008302061251352051e-733j)  +/-  (8.02e-243, 8.02e-243j)
| (4.5992276394183484846 + 3.7523148513331625859e-736j)  +/-  (6.38e-245, 6.38e-245j)
| (14.981132841120411206 + 1.5318144014867968622e-729j)  +/-  (8.85e-241, 8.85e-241j)
| (37.099121044466920337 - 1.8623045099056897425e-731j)  +/-  (1.24e-238, 1.24e-238j)
| (25.154963911439720593 - 1.0495212742688015608e-738j)  +/-  (1.36e-239, 1.36e-239j)
| (6.8445254531151773478 - 2.6605757622824946804e-748j)  +/-  (1.67e-243, 1.67e-243j)
| (22.15109037939700567 - 6.9010745548094085929e-743j)  +/-  (7.91e-240, 7.91e-240j)
| (9.6213168424568670439 + 2.7915018129002119403e-752j)  +/-  (3.41e-242, 3.41e-242j)
| (2.0676007724866038691 - 7.6215792236699441499e-758j)  +/-  (1.03e-247, 1.03e-247j)
| (41.016195928374940132 + 6.4873406904594080728e-748j)  +/-  (3.66e-239, 3.66e-239j)
| (28.487967250984000313 - 4.1175012414833143801e-761j)  +/-  (2.51e-239, 2.51e-239j)
| (0.61175748451513066539 - 1.4229835319028062689e-788j)  +/-  (5.14e-251, 5.14e-251j)
| (1.5126102697764187868 + 2.3774484108085923841e-785j)  +/-  (1.31e-248, 1.31e-248j)
| (17.116855187462255728 - 3.8888716984768759227e-776j)  +/-  (2.14e-240, 2.14e-240j)
| (2.8337513377435072286 + 7.219261418983766548e-795j)  +/-  (1.01e-246, 1.01e-246j)
| (45.886150257789927222 - 2.1195756985244232734e-791j)  +/-  (1.36e-239, 1.36e-239j)
| (13.00605499330634772 + 6.5857319612294814957e-805j)  +/-  (3.07e-241, 3.07e-241j)
| (0.11572211735802067527 + 1.4059841892019202533e-825j)  +/-  (2.51e-253, 2.51e-253j)
| (11.207534825590461298 - 4.1088199200683396142e-812j)  +/-  (1.03e-241, 1.03e-241j)
| (0.039843513719523835138 - 1.9161184631518316589e-833j)  +/-  (1.48e-254, 1.48e-254j)
| (3.7045571390429433836 + 7.2094694128604479335e-822j)  +/-  (9.55e-246, 9.55e-246j)
| (32.119124457542600446 + 1.0360898908469116291e-825j)  +/-  (5.58e-239, 5.58e-239j)
| (1.0620545221533065809 + 2.9144883742574469687e-855j)  +/-  (1.12e-249, 1.12e-249j)
| (0.26877039528001958243 - 1.3790801059791247629e-857j)  +/-  (1.88e-252, 1.88e-252j)
-------------------------------------------------
The weights are:
| (3.3922418601321289624e-40 + 1.4595591476266737503e-637j)  +/-  (1.22e-100, 1.04e-218j)
| (9.1447444325686241133e-28 + 5.6852667425880592537e-629j)  +/-  (7.19e-96, 6.15e-214j)
| (4.2738887391562915983e-35 - 2.1952250693093753314e-634j)  +/-  (4.21e-99, 3.6e-217j)
| (7.5882893952852877527e-25 - 9.1516892650548610217e-628j)  +/-  (5.86e-95, 5e-213j)
| (8.4384126511778989471e-16 + 1.6809889232832974847e-621j)  +/-  (1.16e-90, 9.88e-209j)
| (4.0714088637749846025e-31 + 1.0836792601166402268e-631j)  +/-  (7.12e-98, 6.08e-216j)
| (8.692178203071074587e-09 - 9.8849669841738078148e-618j)  +/-  (2.09e-85, 1.78e-203j)
| (2.939621022424207329e-22 + 2.3894799244739977599e-626j)  +/-  (2.61e-94, 2.23e-212j)
| (0.0040887204453391374943 - 2.4921030643416176412e-613j)  +/-  (1.68e-73, 1.44e-191j)
| (0.000383181489894415375 - 3.7213423774845756798e-614j)  +/-  (1.86e-77, 1.59e-195j)
| (0.0093392908366809608327 + 5.4916109825640073129e-613j)  +/-  (5.26e-72, 4.5e-190j)
| (6.3933973661846829437e-07 - 2.4722147535010461197e-616j)  +/-  (1.3e-83, 1.11e-201j)
| (1.9921803250081620964e-16 - 6.1506909950425507869e-622j)  +/-  (6.9e-92, 5.89e-210j)
| (3.7706648621207228549e-11 - 2.243241000657832384e-619j)  +/-  (4.05e-89, 3.46e-207j)
| (0.0013866609191431364484 + 9.6844063500954815378e-614j)  +/-  (2.53e-78, 2.16e-196j)
| (6.8031843405571076825e-10 + 1.558569340735522339e-618j)  +/-  (5.79e-88, 4.94e-206j)
| (9.8737582635024253389e-05 + 1.3308329604337825249e-614j)  +/-  (6.72e-82, 5.74e-200j)
| (0.08501506618629322503 - 2.8373120319831988317e-612j)  +/-  (3.46e-74, 2.96e-192j)
| (7.0252393175838949001e-18 + 2.1060886968984483822e-623j)  +/-  (4.09e-94, 3.5e-212j)
| (1.4824838119373420053e-12 + 3.2223643941959396884e-620j)  +/-  (6.67e-91, 5.69e-209j)
| (0.22299114905640181418 + 4.0856994173972810746e-612j)  +/-  (1.65e-76, 1.41e-194j)
| (0.100864815726767173 + 4.3676126570158054759e-612j)  +/-  (1.64e-76, 1.4e-194j)
| (8.2265563466882486333e-08 + 5.350871266467853468e-617j)  +/-  (3.21e-87, 2.74e-205j)
| (0.049334097224345334442 + 1.5566662416386028605e-612j)  +/-  (8.64e-80, 7.38e-198j)
| (6.0802490190302896481e-20 - 6.8157887383958826478e-625j)  +/-  (6.65e-96, 5.68e-214j)
| (4.2578320118420869598e-06 + 1.035044725583795615e-615j)  +/-  (2.29e-86, 1.95e-204j)
| (0.051257845376771737615 + 5.2106099438988080101e-612j)  +/-  (2.12e-81, 1.8e-199j)
| (2.2982713294868256431e-05 - 4.0002971186660215041e-615j)  +/-  (9.94e-86, 8.49e-204j)
| (0.090154735004980837021 - 2.1744749354667862617e-612j)  +/-  (1.18e-81, 9.99e-200j)
| (0.02176404619061700602 - 9.5333868854592845717e-613j)  +/-  (5.17e-83, 4.43e-201j)
| (4.2010247609710543254e-14 - 5.4748870754841946752e-621j)  +/-  (2.92e-92, 2.49e-210j)
| (0.16110770560487161824 - 4.5696871037259780311e-612j)  +/-  (2.1e-82, 1.83e-200j)
| (0.20218597679292295441 - 5.0554977733388595694e-612j)  +/-  (4.05e-82, 3.31e-200j)
