Starting with polynomial:
P : 2*t
Extension levels are: 1 24 42
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P2 : 2*t^25 - 300*t^23 + 18975*t^21 - 664125*t^19 + 113565375/8*t^17 - 386122275/2*t^15 + 13514279625/8*t^13 - 75293843625/8*t^11 + 4141161399375/128*t^9 - 4141161399375/64*t^7 + 17392877877375/256*t^5 - 7905853580625/256*t^3 + 7905853580625/2048*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^67 - 5916977598948764630874254250821757333879879437/3561065251525204731467607869168469441659291*t^65 + 4609577178572112675164169785529174318046805706755/7122130503050409462935215738336938883318582*t^63 - 20165505037782828327421163541792781460837712778625635/128198349054907370332833883290064899899734476*t^61 + 762914850404979908321930370643142727825827031740377475/28488522012201637851740862953347755533274328*t^59 - 7553124481990293657380705644203097694138279895318879387725/2222104716951727752435787310361124931595397584*t^57 + 1485565111913984004262376522691561755050020889984215671905025/4444209433903455504871574620722249863190795168*t^55 - 242691617359830665824388529918556880470048973057662245500125/9287794010247555914047177890746603684829248*t^53 + 890437278134685778303352613022571195383817782261929347753848125/538692052594358243014736317663303013720096384*t^51 - 92338847343136373161922828674633238601424478041113781156298596125/1077384105188716486029472635326606027440192768*t^49 + 7921380141313499136619668514409355189144123508312422131902832873025/2154768210377432972058945270653212054880385536*t^47 - 565859652374422825062878634481027077764748096541010793929554367986425/4309536420754865944117890541306424109760771072*t^45 + 33811986210186187251733723751983327514974906029312899056325434443146625/8619072841509731888235781082612848219521542144*t^43 - 1694812173354746539189636999577503548785755432304135645303175745531133625/17238145683019463776471562165225696439043084288*t^41 + 71363567425158628525575547776689662266960422527512510274240457311800598125/34476291366038927552943124330451392878086168576*t^39 - 194202979815928171075793753986761298672573772385168422728651935448760891625/5304044825544450392760480666223291212013256704*t^37 + 5766296974659758959962876941986006351929462874865528969294555218342248786375/10608089651088900785520961332446582424026513408*t^35 - 143386774750226855522789038217513830244770459176946547812911557823375456991875/21216179302177801571041922664893164848053026816*t^33 + 2976048939881581680855755384078951008888197508126919699771895696116370631156875/42432358604355603142083845329786329696106053632*t^31 - 1769733150885885360690283562648661688399640100537061546970219251493313509259375/2926369558921076078764403126192160668696969216*t^29 + 25208199096145729176812242216548250112920116104718446415589653939244582256874375/5852739117842152157528806252384321337393938432*t^27 - 294386605193553445122507259540438205216561718731853649506219286176689266158039375/11705478235684304315057612504768642674787876864*t^25 + 2792791062320166676239932195922297215019149152130086666869115081909149103781296875/23410956471368608630115225009537285349575753728*t^23 - 21280106714680014373273116995380901838971276609393458237190158539648345365062171875/46821912942737217260230450019074570699151507456*t^21 + 128421352610596332435520742356272730359276491496797648007120846658954151973607734375/93643825885474434520460900038149141398303014912*t^19 - 603194969321853211257048301214608136674672772374758969431305874088639458118780984375/187287651770948869040921800076298282796606029824*t^17 + 2157233866044564080552871563803156653514967036549387851230248611317937726921851421875/374575303541897738081843600152596565593212059648*t^15 - 5710996387010066861469398700313793645430087180113885704097798894390580548448558046875/749150607083795476163687200305193131186424119296*t^13 + 10783732993347405034067943950100278051064517361187711904757781310932715993177587421875/1498301214167590952327374400610386262372848238592*t^11 - 13805375320203379911673828899015564949233851222027401063406799518495004867522723046875/2996602428335181904654748801220772524745696477184*t^9 + 11143441182238159112628191422387377054583455811163262609478441875046875134717336484375/5993204856670363809309497602441545049491392954368*t^7 - 5074614049429138422357103796259820194270549477383562976453089088428668095884073359375/11986409713340727618618995204883090098982785908736*t^5 + 269555714279732911561688563562658819540256974465123876729223486903148928761152734375/5993204856670363809309497602441545049491392954368*t^3 - 35188799793056631270925236729354114050963505844521157257023490879880514774609765625/23972819426681455237237990409766180197965571817472*t
-------------------------------------------------
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: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (9.7279605251187949374 - 1.1703428323425695136e-1756j)  +/-  (3.81e-500, 3.81e-500j)
| (8.0753668338251125712 - 3.7680852570740174959e-1754j)  +/-  (5.12e-497, 5.12e-497j)
| (-9.083862925857441501 - 5.8357960588610828644e-1755j)  +/-  (9.23e-499, 9.23e-499j)
| (7.2262513797618947735 + 3.0254483450757136703e-1752j)  +/-  (7.28e-496, 7.28e-496j)
| (7.6372627922708488517 - 2.9988519206665661744e-1753j)  +/-  (2.27e-496, 2.27e-496j)
| (9.083862925857441501 - 3.180887292112869712e-1756j)  +/-  (9.17e-499, 9.17e-499j)
| (-6.4665895576333171454 - 5.3907451178825220563e-1750j)  +/-  (6.92e-495, 6.92e-495j)
| (-1.1163766518434586402 + 3.6021698146626960024e-1771j)  +/-  (2.35e-504, 2.35e-504j)
| (-2.9487757936815636892 + 2.1967657475284471778e-1764j)  +/-  (4.27e-498, 4.27e-498j)
| (6.8366250377410061047 + 1.2878069810069479746e-1760j)  +/-  (2.49e-495, 2.49e-495j)
| (0.6464636102336935968 - 7.979654998267348881e-1773j)  +/-  (1.04e-506, 1.04e-506j)
| (6.0611430771701372502 - 6.7033939325393469554e-1759j)  +/-  (3.1e-494, 3.1e-494j)
| (-5.0926774642959711482 + 7.3975026020356346065e-1762j)  +/-  (3.07e-495, 3.07e-495j)
| (-7.2262513797618947735 + 1.8588744161223778089e-1774j)  +/-  (7.35e-496, 7.35e-496j)
| (-4.4940414459164940897 + 2.634509499343960321e-1780j)  +/-  (1.19e-495, 1.19e-495j)
| (-5.7451624469755089615 - 1.2208486371778575044e-1794j)  +/-  (9.45e-495, 9.45e-495j)
| (-9.7279605251187949374 + 2.8265933139151460977e-1814j)  +/-  (3.67e-500, 3.67e-500j)
| (6.1642724340524517709 - 1.5530380753358927415e-1807j)  +/-  (2.86e-494, 2.86e-494j)
| (-1.7780011243371474582 - 9.0285949914217179254e-1816j)  +/-  (1.31e-501, 1.31e-501j)
| (4.7853203673522240573 - 3.9089734722713314336e-1810j)  +/-  (1.87e-495, 1.87e-495j)
| (-3.4336506168834276055 + 5.1356300914835133405e-1809j)  +/-  (4.57e-497, 4.57e-497j)
| (-4.7853203673522240573 - 2.4908485342074528472e-1810j)  +/-  (1.91e-495, 1.91e-495j)
| (-3.9527605169426474808 + 1.5242134595790400724e-1819j)  +/-  (2.82e-496, 2.82e-496j)
| (8.5508105024271155897 - 1.1532465240790414024e-1828j)  +/-  (9.55e-498, 9.55e-498j)
| (-7.6372627922708488517 - 1.9814870801016724343e-1824j)  +/-  (2.42e-496, 2.42e-496j)
| (-1.3272807020730839518 - 2.9721344174066044529e-1843j)  +/-  (2.18e-503, 2.18e-503j)
| (1.7780011243371474582 - 7.3127937202658565158e-1841j)  +/-  (1.25e-501, 1.25e-501j)
| (-8.5508105024271155897 - 1.1975545839015856399e-1833j)  +/-  (9.05e-498, 9.05e-498j)
| (3.6902828769983559016 - 2.2054989091000033596e-1843j)  +/-  (1.25e-496, 1.25e-496j)
| (-0.6464636102336935968 + 1.1084841014540787831e-1855j)  +/-  (9.67e-507, 9.67e-507j)
| (-5.4136363552800338097 + 8.9902446683359539001e-1843j)  +/-  (5.16e-495, 5.16e-495j)
| (2.9487757936815636892 - 1.2252631391844464016e-1859j)  +/-  (4.47e-498, 4.47e-498j)
| (-8.0753668338251125712 - 1.448415082990711255e-1855j)  +/-  (5.07e-497, 5.07e-497j)
| (5.0926774642959711482 - 6.9443344764131432171e-1863j)  +/-  (3.2e-495, 3.2e-495j)
| (-4.2186094443865613814 - 7.7858582373337489399e-1870j)  +/-  (5.82e-496, 5.82e-496j)
| (3.1882949244251047122 + 1.5149181737582271435e-1882j)  +/-  (1.55e-497, 1.55e-497j)
| (1.3272807020730839518 - 1.2274520993051820727e-1889j)  +/-  (2.14e-503, 2.14e-503j)
| (2.0137508784616847862 + 3.5220670047603051867e-1886j)  +/-  (9.75e-501, 9.75e-501j)
| (4.2186094443865613814 - 4.709064108774132374e-1882j)  +/-  (5.77e-496, 5.77e-496j)
| (4.4940414459164940897 - 6.1826783093405034023e-1882j)  +/-  (1.11e-495, 1.11e-495j)
| (-1.5417299316881258215 + 7.1985656437931044031e-1900j)  +/-  (1.67e-502, 1.67e-502j)
| (2.7053202371730259933 - 3.4146646887677394287e-1891j)  +/-  (1.03e-498, 1.03e-498j)
| (3.9527605169426474808 - 1.3343717669750212693e-1891j)  +/-  (2.76e-496, 2.76e-496j)
| (-6.8366250377410061047 - 2.4816056757417342517e-1911j)  +/-  (2.24e-495, 2.24e-495j)
| (6.4665895576333171454 - 4.2754189331767125984e-1934j)  +/-  (7.07e-495, 7.07e-495j)
| (-0.88198275621382135637 - 7.1635407030731100119e-1956j)  +/-  (1.57e-505, 1.57e-505j)
| (-2.4637037273900830247 + 1.0881031714889544577e-1945j)  +/-  (2.45e-499, 2.45e-499j)
| (2.4637037273900830247 - 7.7017969053588195573e-1955j)  +/-  (2.5e-499, 2.5e-499j)
| (-6.0611430771701372502 + 6.3719028534803716063e-1957j)  +/-  (3.12e-494, 3.12e-494j)
| (1.1163766518434586402 - 3.6313393851320086477e-1995j)  +/-  (2.31e-504, 2.31e-504j)
| (-2.7053202371730259933 - 1.4831670072294868309e-1988j)  +/-  (1.01e-498, 1.01e-498j)
| (-0.44014729864530830458 + 2.5878819273026266971e-1997j)  +/-  (9.04e-508, 9.04e-508j)
| (0.88198275621382135637 - 2.2064680556260570468e-1996j)  +/-  (1.61e-505, 1.61e-505j)
| (-6.1642724340524517709 - 6.1636838074512765465e-1984j)  +/-  (3e-494, 3e-494j)
| (5.4136363552800338097 + 2.4888287578493076451e-1997j)  +/-  (5.07e-495, 5.07e-495j)
| (5.7451624469755089615 + 8.8316370698762448403e-2000j)  +/-  (9.09e-495, 9.09e-495j)
| (-2.2364201302672808702 + 1.2757723104715657737e-2004j)  +/-  (5.23e-500, 5.23e-500j)
| (-3.6902828769983559016 - 1.220552777531609396e-2004j)  +/-  (1.2e-496, 1.2e-496j)
| (3.4336506168834276055 - 1.0349449979536419157e-2006j)  +/-  (4.42e-497, 4.42e-497j)
| (0.44014729864530830458 + 3.9881052516792599172e-2017j)  +/-  (9.51e-508, 9.51e-508j)
| (0.23523811119573597713 - 2.8627305735990371487e-2018j)  +/-  (7.58e-509, 7.58e-509j)
| (-3.1882949244251047122 - 8.9233655370041204547e-2013j)  +/-  (1.48e-497, 1.48e-497j)
| (-2.0137508784616847862 - 1.6083503323181894479e-2016j)  +/-  (8.97e-501, 8.97e-501j)
| (-2.1031571519748117956e-2053 - 7.2270709326344062947e-2052j)  +/-  (4.84e-2050, 4.84e-2050j)
| (1.5417299316881258215 + 1.6707422307651427423e-2016j)  +/-  (1.73e-502, 1.73e-502j)
| (2.2364201302672808702 - 4.0646782285281537805e-2016j)  +/-  (5.15e-500, 5.15e-500j)
| (-0.23523811119573597713 + 1.7835786122554997506e-2024j)  +/-  (6.74e-509, 6.74e-509j)
-------------------------------------------------
The weights are:
| (3.3453155837419049134e-42 + 1.7071196250804715383e-1784j)  +/-  (2.24e-188, 3.06e-435j)
| (1.2245251160049266847e-29 - 5.7501763567775667917e-1777j)  +/-  (2.75e-183, 3.75e-430j)
| (4.7196171366828768236e-37 + 1.060739866470421884e-1780j)  +/-  (5.07e-189, 6.9e-436j)
| (4.7293063551882728635e-24 - 2.6843702939841981427e-1773j)  +/-  (8.64e-181, 1.18e-427j)
| (1.1134095375317224252e-26 + 4.4330628435438252883e-1775j)  +/-  (4.26e-182, 5.8e-429j)
| (4.7196171366828768236e-37 - 1.7791948188652399737e-1781j)  +/-  (1.81e-187, 2.47e-434j)
| (1.3962277315501116653e-19 - 8.4931366288029641852e-1768j)  +/-  (2.05e-182, 2.79e-429j)
| (0.036212803466364620633 + 8.0080924057431254255e-1757j)  +/-  (7.06e-137, 9.62e-384j)
| (2.2744975254180034046e-05 + 2.4022633468674055906e-1759j)  +/-  (4.77e-162, 6.5e-409j)
| (1.0778164926908600763e-21 + 1.2188234739868616864e-1771j)  +/-  (2.56e-180, 3.49e-427j)
| (0.083185270147084775674 + 1.2314440246034210146e-1756j)  +/-  (4.22e-139, 5.76e-386j)
| (1.4527638223111282026e-17 - 5.4734067589118630876e-1768j)  +/-  (1.9e-178, 2.59e-425j)
| (9.673866265433893178e-13 + 1.1302512052498455693e-1764j)  +/-  (2.51e-177, 3.43e-424j)
| (4.7293063551882728635e-24 + 4.5847187199233081857e-1772j)  +/-  (1.49e-186, 2.03e-433j)
| (2.7025777785559110254e-10 + 4.8338230961013716052e-1763j)  +/-  (6.92e-175, 9.43e-422j)
| (8.7397637177783845009e-16 + 3.3496621605850481536e-1766j)  +/-  (1.36e-180, 1.85e-427j)
| (3.3453155837419049134e-42 - 8.4990799178664444296e-1784j)  +/-  (1.18e-195, 1.61e-442j)
| (2.571332463655617024e-18 + 2.4142902394363866611e-1768j)  +/-  (2.19e-181, 2.99e-428j)
| (0.005741494938711787824 - 1.7031272056150779469e-1757j)  +/-  (1.58e-157, 2.16e-404j)
| (1.9187428188677731656e-11 - 1.1443950558997096106e-1764j)  +/-  (3.21e-178, 4.38e-425j)
| (1.0750784355407846113e-06 + 2.250602920607844357e-1760j)  +/-  (9.51e-171, 1.3e-417j)
| (1.9187428188677731656e-11 - 7.6446862598811137125e-1764j)  +/-  (4.66e-177, 6.35e-424j)
| (2.4382344071237108327e-08 + 1.2750360926773578125e-1761j)  +/-  (8.66e-174, 1.18e-420j)
| (4.9649326629257146819e-33 + 4.6309884325806988816e-1779j)  +/-  (1.43e-191, 1.94e-438j)
| (1.1134095375317224252e-26 - 5.4129716338294531308e-1774j)  +/-  (6.91e-190, 9.42e-437j)
| (0.019836677931395164785 - 5.8337434049602267016e-1757j)  +/-  (1.77e-157, 2.41e-404j)
| (0.005741494938711787824 - 9.689450918339450481e-1758j)  +/-  (5.54e-165, 7.55e-412j)
| (4.9649326629257146819e-33 - 3.3524737563361457888e-1778j)  +/-  (1.42e-193, 1.94e-440j)
| (1.7914666592354821848e-07 - 1.5245160470280419022e-1761j)  +/-  (1.08e-178, 1.47e-425j)
| (0.083185270147084775674 + 1.5047927203488243239e-1756j)  +/-  (1.56e-157, 2.12e-404j)
| (3.4494255126788579724e-14 - 1.7303694208465420818e-1765j)  +/-  (1.57e-181, 2.14e-428j)
| (2.2744975254180034046e-05 + 8.9823698739383017484e-1760j)  +/-  (2.32e-175, 3.16e-422j)
| (1.2245251160049266847e-29 + 5.2352256221849382255e-1776j)  +/-  (4.91e-192, 6.69e-439j)
| (9.673866265433893178e-13 + 1.3463540902469569771e-1765j)  +/-  (7.06e-184, 9.62e-431j)
| (2.8345407629907212974e-09 - 2.6638838987586071405e-1762j)  +/-  (9.81e-178, 1.34e-424j)
| (5.218292908407346157e-06 - 2.6955632037207475776e-1760j)  +/-  (5.9e-177, 8.03e-424j)
| (0.019836677931395164785 - 3.847944888253595895e-1757j)  +/-  (8.75e-166, 1.19e-412j)
| (0.0022360488937579182053 + 4.7045112820343445954e-1758j)  +/-  (3.41e-171, 4.65e-418j)
| (2.8345407629907212974e-09 - 5.6121611058165241381e-1763j)  +/-  (1.12e-181, 1.53e-428j)
| (2.7025777785559110254e-10 + 8.7131549458309837737e-1764j)  +/-  (1.16e-182, 1.58e-429j)
| (0.011923097891739002234 + 3.3693730286743264096e-1757j)  +/-  (1.91e-170, 2.61e-417j)
| (9.159411756440705287e-05 - 2.787180170313590367e-1759j)  +/-  (9.09e-177, 1.24e-423j)
| (2.4382344071237108327e-08 + 3.0800012250258017834e-1762j)  +/-  (6.6e-181, 8.99e-428j)
| (1.0778164926908600763e-21 - 4.3207852231055640878e-1770j)  +/-  (7.75e-192, 1.06e-438j)
| (1.3962277315501116653e-19 - 5.86072859788169416e-1770j)  +/-  (3.45e-190, 4.71e-437j)
| (0.062407154743508148744 - 1.0404767760935972203e-1756j)  +/-  (1.44e-170, 1.96e-417j)
| (0.00030732780727216082746 + 1.8657434649408055386e-1758j)  +/-  (4.19e-179, 5.71e-426j)
| (0.00030732780727216082746 + 8.3680283191788481122e-1759j)  +/-  (3.19e-178, 4.35e-425j)
| (1.4527638223111282026e-17 - 1.6837207095954160636e-1766j)  +/-  (2.04e-189, 2.78e-436j)
| (0.036212803466364620633 + 5.6515716524663684801e-1757j)  +/-  (1.15e-174, 1.56e-421j)
| (9.159411756440705287e-05 - 6.7919230197939774937e-1759j)  +/-  (4.06e-181, 5.54e-428j)
| (0.090294522229804079265 - 1.9397654232667499457e-1756j)  +/-  (6.38e-175, 8.7e-422j)
| (0.062407154743508148744 - 7.9087298258566099046e-1757j)  +/-  (3.84e-175, 5.24e-422j)
| (2.571332463655617024e-18 + 1.0037545289878017971e-1766j)  +/-  (9.1e-190, 1.24e-436j)
| (3.4494255126788579724e-14 - 1.5377580942665470385e-1766j)  +/-  (3.35e-189, 4.56e-436j)
| (8.7397637177783845009e-16 + 1.9855854190256190942e-1767j)  +/-  (4.49e-190, 6.12e-437j)
| (0.00083762965192812521166 - 4.4789673117721130253e-1758j)  +/-  (7.89e-182, 1.07e-428j)
| (1.7914666592354821848e-07 - 5.5712478696564374688e-1761j)  +/-  (1.93e-185, 2.63e-432j)
| (1.0750784355407846113e-06 + 6.9013849105210448238e-1761j)  +/-  (8.07e-185, 1.1e-431j)
| (0.090294522229804079265 - 1.6926965487372574155e-1756j)  +/-  (1.79e-179, 2.44e-426j)
| (0.11870839810003173601 + 1.7731899338927361977e-1756j)  +/-  (9.34e-180, 1.27e-426j)
| (5.218292908407346157e-06 - 7.93184402154431862e-1760j)  +/-  (2.09e-184, 2.85e-431j)
| (0.0022360488937579182053 + 8.9553852332910842925e-1758j)  +/-  (5.06e-182, 6.91e-429j)
| (0.1363774701604824189 - 1.7173392073158503395e-1756j)  +/-  (3.27e-181, 4.47e-428j)
| (0.011923097891739002234 + 2.0727856555813623324e-1757j)  +/-  (1.34e-182, 1.83e-429j)
| (0.00083762965192812521166 - 2.1782121915206517719e-1758j)  +/-  (1.05e-183, 1.41e-430j)
| (0.11870839810003173601 + 1.9069705390362785023e-1756j)  +/-  (1.11e-181, 1.53e-428j)
