Starting with polynomial:
P : 2*t
Extension levels are: 1 74
-------------------------------------------------
Trying to find an order 74 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^75 - 2775*t^73 + 1823175*t^71 - 1510196625/2*t^69 + 1771460641125/8*t^67 - 783339895505475/16*t^65 + 16972364402618625/2*t^63 - 4735289668330596375/4*t^61 + 4332790046522495683125/32*t^59 - 823711529955554457091875/64*t^57 + 65732180090453245675931625/64*t^55 - 8873844312211188166250769375/128*t^53 + 2038026243704502882182260033125/512*t^51 - 199883343132557013444798580171875/1024*t^49 + 4197550205783697282340770183609375/512*t^47 - 302503451496811784147358171232115625/1024*t^45 + 149739208490921833152942294759897234375/16384*t^43 - 7953794427488377372770993656952188390625/32768*t^41 + 181169761959457484602005966630577624453125/32768*t^39 - 7065620716418841899478232698592527353671875/65536*t^37 + 470570339713494870505250297726262321754546875/262144*t^35 - 13332826291882354664315425102244099116378828125/524288*t^33 + 39998478875647063992946275306732297349136484375/131072*t^31 - 808664899007647163335652957288283402928194140625/262144*t^29 + 54719658166184124719045850109840510264807803515625/2097152*t^27 - 768264000653225111055403735542160764117901561359375/4194304*t^25 + 4432292311460914102242713858897081331449432084765625/4194304*t^23 - 41532220548133750661755800233368947290989122868359375/8388608*t^21 + 622983308222006259926337003500534209364836843025390625/33554432*t^19 - 3673453300205623118875987158572115510392658626115234375/67108864*t^17 + 4163247073566372868059452113048397578445013109597265625/33554432*t^15 - 14101320733047391972459434576454249862475044403474609375/67108864*t^13 + 549951508588848286925917948481715744636526731735509765625/2147483648*t^11 - 916585847648080478209863247469526241060877886225849609375/4294967296*t^9 + 485251331107807311993457013366219774679288292707802734375/4294967296*t^7 - 291150798664684387196074208019731864807572975624681640625/8589934592*t^5 + 161750443702602437331152337788739924893096097569267578125/34359738368*t^3 - 13114900840751548972796135496384318234575359262373046875/68719476736*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
Positive weights:   75 out of 75
Indefinite weights: 0 out of 75
Negative weights:   0 out of 75
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (9.9067257997991215233 + 1.1671037556371379002e-1205j)  +/-  (2.38e-494, 2.38e-494j)
| (9.4904090577984018241 - 8.0861430787997969097e-1219j)  +/-  (1.04e-493, 1.04e-493j)
| (-10.358570924603207178 + 2.2378341232641486995e-1236j)  +/-  (3.42e-495, 3.42e-495j)
| (-9.9067257997991215233 + 3.250265889698154265e-1265j)  +/-  (2.41e-494, 2.41e-494j)
| (2.3146677482934548559 - 2.3805191228077681376e-1292j)  +/-  (8.13e-500, 8.13e-500j)
| (6.4447429831267426062 + 9.4526556623952383743e-1292j)  +/-  (4.68e-492, 4.68e-492j)
| (9.0995594639401111916 + 3.6825850408024457529e-1322j)  +/-  (3.77e-493, 3.77e-493j)
| (11.478660318722641592 + 4.6963304648685173159e-1340j)  +/-  (1.24e-497, 1.24e-497j)
| (8.7281447480576210417 + 1.5085546229449279407e-1360j)  +/-  (1.07e-492, 1.07e-492j)
| (10.865483112083049681 + 1.0860829323495275343e-1400j)  +/-  (2.78e-496, 2.78e-496j)
| (7.0567764692174773906 - 1.6509015446707714331e-1435j)  +/-  (6.65e-492, 6.65e-492j)
| (-9.0995594639401111916 + 5.1965573517466541132e-1453j)  +/-  (3.72e-493, 3.72e-493j)
| (-3.9014116643261456799 + 2.3710482278589521484e-1456j)  +/-  (1.98e-495, 1.98e-495j)
| (-1.5379625916624639517 - 1.0186540985432286512e-1464j)  +/-  (1.14e-502, 1.14e-502j)
| (-6.4447429831267426062 + 7.0725710223636556986e-1454j)  +/-  (4.67e-492, 4.67e-492j)
| (10.358570924603207178 + 1.2056986494427362569e-1455j)  +/-  (3.36e-495, 3.36e-495j)
| (6.7477619079872564198 + 1.1416680707628213219e-1466j)  +/-  (6.51e-492, 6.51e-492j)
| (-9.4904090577984018241 + 2.3577993946335865872e-1480j)  +/-  (1.11e-493, 1.11e-493j)
| (-1.7960090360977112959 - 4.0345016047713231233e-1488j)  +/-  (1.14e-501, 1.14e-501j)
| (-2.3146677482934548559 + 2.9508081651269909179e-1486j)  +/-  (7.87e-500, 7.87e-500j)
| (2.5755454098889713413 - 5.566934436033071663e-1485j)  +/-  (5.48e-499, 5.48e-499j)
| (-5.2804469030361733377 + 8.6482708201143420646e-1480j)  +/-  (4.87e-493, 4.87e-493j)
| (4.1720952149448501977 - 1.0758543237699453671e-1479j)  +/-  (1.05e-494, 1.05e-494j)
| (-11.478660318722641592 - 4.2353078956665170705e-1485j)  +/-  (1.12e-497, 1.12e-497j)
| (-7.3726025317424623165 - 1.4175004918984315661e-1478j)  +/-  (5.71e-492, 5.71e-492j)
| (-4.9989827149592104258 + 1.0846625320811244288e-1479j)  +/-  (2.14e-493, 2.14e-493j)
| (1.5379625916624639517 - 4.8795074742525916341e-1489j)  +/-  (1.12e-502, 1.12e-502j)
| (4.7206279897915652586 - 1.5042642249524896276e-1477j)  +/-  (7.97e-494, 7.97e-494j)
| (-7.0567764692174773906 - 3.849045347039233927e-1480j)  +/-  (6.5e-492, 6.5e-492j)
| (-2.05486751778580179 - 8.6756064723619551514e-1491j)  +/-  (1.16e-500, 1.16e-500j)
| (7.3726025317424623165 + 2.2911780329643711905e-1480j)  +/-  (5.92e-492, 5.92e-492j)
| (-10.865483112083049681 + 1.6480419227116437194e-1492j)  +/-  (2.74e-496, 2.74e-496j)
| (1.0238111346569745485 + 2.2456587515406822758e-1501j)  +/-  (6.66e-505, 6.66e-505j)
| (-7.6962341998287289119 - 3.8498097824187249416e-1488j)  +/-  (4.62e-492, 4.62e-492j)
| (-5.8540732676978864666 - 8.7379796737919261567e-1489j)  +/-  (2.23e-492, 2.23e-492j)
| (-4.4450872824012323375 - 7.7258981990581788907e-1491j)  +/-  (2.98e-494, 2.98e-494j)
| (-4.7206279897915652586 - 3.4138866820663868491e-1490j)  +/-  (8.69e-494, 8.69e-494j)
| (3.9014116643261456799 + 2.6374987253726767023e-1491j)  +/-  (1.97e-495, 1.97e-495j)
| (4.4450872824012323375 - 2.9312027774483411897e-1490j)  +/-  (3.09e-494, 3.09e-494j)
| (-8.7281447480576210417 - 3.7201719730295824458e-1489j)  +/-  (1.13e-492, 1.13e-492j)
| (-3.3661131093032384298 + 7.9796676039823607115e-1493j)  +/-  (1.25e-496, 1.25e-496j)
| (8.3721912199266994284 - 7.6626333797741189871e-1488j)  +/-  (2.43e-492, 2.43e-492j)
| (8.0289066873027559309 + 3.9638161800464475224e-1504j)  +/-  (4.84e-492, 4.84e-492j)
| (0.7674683331048162346 + 1.3422672673557071068e-1555j)  +/-  (5.24e-506, 5.24e-506j)
| (5.8540732676978864666 + 1.1189296037397737209e-1540j)  +/-  (2.11e-492, 2.11e-492j)
| (-3.1011122385952585394 + 5.8591801627014014463e-1575j)  +/-  (2.12e-497, 2.12e-497j)
| (5.5653520540734329259 - 8.7444765916197630375e-1573j)  +/-  (9.16e-493, 9.16e-493j)
| (3.3661131093032384298 - 2.9297451475786558268e-1584j)  +/-  (1.24e-496, 1.24e-496j)
| (1.2806034800245348639 + 3.002482801985834401e-1591j)  +/-  (8.66e-504, 8.66e-504j)
| (-6.7477619079872564198 + 3.4584725326576674867e-1578j)  +/-  (6.84e-492, 6.84e-492j)
| (-6.1470388825769429487 + 4.3620163586851920478e-1580j)  +/-  (3.26e-492, 3.26e-492j)
| (-1.0238111346569745485 - 3.4771136661929959188e-1603j)  +/-  (6.66e-505, 6.66e-505j)
| (-5.5653520540734329259 - 3.1708481630957025658e-1589j)  +/-  (8.75e-493, 8.75e-493j)
| (2.05486751778580179 + 2.541912284551906962e-1609j)  +/-  (1.17e-500, 1.17e-500j)
| (-8.3721912199266994284 - 1.4711948190923683892e-1598j)  +/-  (2.55e-492, 2.55e-492j)
| (-0.7674683331048162346 + 4.1255826101117504173e-1622j)  +/-  (4.96e-506, 4.96e-506j)
| (-0.51146046221189689802 + 3.5300301215569456765e-1623j)  +/-  (3.6e-507, 3.6e-507j)
| (6.1470388825769429487 + 1.9737691495366374807e-1606j)  +/-  (3.26e-492, 3.26e-492j)
| (-8.0289066873027559309 + 2.7527568421812976998e-1621j)  +/-  (4.83e-492, 4.83e-492j)
| (0.25567482833134799806 - 1.3326065839760111429e-1687j)  +/-  (9.22e-509, 9.22e-509j)
| (4.9989827149592104258 - 7.3544641602444691653e-1631j)  +/-  (2.15e-493, 2.15e-493j)
| (-3.6328178485882914931 + 2.2414847809550212218e-1651j)  +/-  (5.03e-496, 5.03e-496j)
| (-0.25567482833134799806 + 6.7865128081531092085e-1678j)  +/-  (1.01e-508, 1.01e-508j)
| (5.2804469030361733377 + 4.0977318032495061734e-1661j)  +/-  (4.74e-493, 4.74e-493j)
| (3.1011122385952585394 - 1.7848630404973554086e-1680j)  +/-  (2.11e-497, 2.11e-497j)
| (0.51146046221189689802 - 8.4070268988876615114e-1699j)  +/-  (3.53e-507, 3.53e-507j)
| (7.6962341998287289119 - 3.2903645042231552443e-1682j)  +/-  (4.41e-492, 4.41e-492j)
| (-2.5755454098889713413 - 4.0597554149617806859e-1705j)  +/-  (5.79e-499, 5.79e-499j)
| (-4.1720952149448501977 - 9.3774627722722212581e-1699j)  +/-  (1.02e-494, 1.02e-494j)
| (-1.2639585867619033137e-1742 + 6.1502332260914244988e-1743j)  +/-  (1.05e-1740, 1.05e-1740j)
| (3.6328178485882914931 + 1.5134657588538148194e-1701j)  +/-  (5.3e-496, 5.3e-496j)
| (1.7960090360977112959 - 3.0548745863346716996e-1711j)  +/-  (1.07e-501, 1.07e-501j)
| (2.8376432363425030718 - 8.179049696799814679e-1708j)  +/-  (4.34e-498, 4.34e-498j)
| (-2.8376432363425030718 + 1.6784647561898617411e-1707j)  +/-  (4.36e-498, 4.36e-498j)
| (-1.2806034800245348639 + 5.0764216544007651062e-1713j)  +/-  (8.8e-504, 8.8e-504j)
-------------------------------------------------
The weights are:
| (5.8043087959232874624e-44 - 6.7110445005248123993e-1248j)  +/-  (4.79e-166, 2.69e-410j)
| (1.7379568545505588668e-40 + 8.9039013662284192049e-1247j)  +/-  (1.07e-164, 6.03e-409j)
| (6.73196777064783938e-48 + 3.6000022172998114102e-1252j)  +/-  (1.66e-169, 9.33e-414j)
| (5.8043087959232874624e-44 - 3.4190058004650422409e-1250j)  +/-  (4.24e-168, 2.38e-412j)
| (0.00069200902322717366738 + 9.7427392561140529695e-1230j)  +/-  (2.19e-124, 1.23e-368j)
| (1.5510392996203341843e-19 - 3.1986830888859110721e-1237j)  +/-  (2.55e-155, 1.44e-399j)
| (2.3504511766040101569e-37 - 1.6888741866260468499e-1245j)  +/-  (9.54e-165, 5.37e-409j)
| (2.3964180523247840393e-58 - 2.7690548699473688507e-1256j)  +/-  (1.35e-173, 7.58e-418j)
| (1.6854799461897554852e-34 + 3.0973270223150985425e-1244j)  +/-  (2.51e-164, 1.41e-408j)
| (1.6462690981313147968e-52 + 3.7629326484568353917e-1253j)  +/-  (1.52e-171, 8.58e-416j)
| (4.1583350763978992287e-23 - 6.3622000881452780737e-1239j)  +/-  (8.67e-160, 4.88e-404j)
| (2.3504511766040101569e-37 - 7.1723767691795213594e-1247j)  +/-  (1.94e-171, 1.09e-415j)
| (3.7303464887411851309e-08 + 3.933002347572480149e-1232j)  +/-  (3.73e-149, 2.1e-393j)
| (0.013654017656194762919 - 2.8708531553809849175e-1229j)  +/-  (3.17e-124, 1.78e-368j)
| (1.5510392996203341843e-19 - 6.7723493447035847944e-1238j)  +/-  (5.79e-163, 3.26e-407j)
| (6.73196777064783938e-48 - 1.6146044106059785392e-1250j)  +/-  (1.81e-170, 1.02e-414j)
| (2.9011639637145324892e-21 + 4.7943109334595927418e-1238j)  +/-  (9.09e-160, 5.12e-404j)
| (1.7379568545505588668e-40 + 1.9110261567269056659e-1248j)  +/-  (1.36e-172, 7.63e-417j)
| (0.0057928040339243874553 + 1.8286970948097803839e-1229j)  +/-  (4.82e-131, 2.71e-375j)
| (0.00069200902322717366738 + 6.0522919683442261728e-1230j)  +/-  (8.37e-138, 4.71e-382j)
| (0.00019407605941249404897 - 5.3431430089796154406e-1230j)  +/-  (8.79e-141, 4.95e-385j)
| (1.2414235683278477463e-13 - 6.5233064736607959809e-1235j)  +/-  (5.93e-159, 3.33e-403j)
| (4.2284372216695220929e-09 - 3.1883737007404848458e-1232j)  +/-  (1.39e-152, 7.82e-397j)
| (2.3964180523247840393e-58 + 2.0353959992788806523e-1257j)  +/-  (1.67e-180, 9.39e-425j)
| (4.4644186836303139056e-25 + 1.0872773046089941452e-1240j)  +/-  (7.86e-168, 4.42e-412j)
| (2.2152228704211189204e-12 + 2.8076360511222262271e-1234j)  +/-  (7.26e-159, 4.09e-403j)
| (0.013654017656194762919 - 3.9260305213363755102e-1229j)  +/-  (7.05e-135, 3.97e-379j)
| (3.2793584144169020244e-11 - 3.1048345354874823295e-1233j)  +/-  (8.17e-158, 4.59e-402j)
| (4.1583350763978992287e-23 - 1.0688799750593731757e-1239j)  +/-  (6.72e-167, 3.78e-411j)
| (0.0021450616332283533694 - 1.0887184332240588038e-1229j)  +/-  (4.56e-141, 2.57e-385j)
| (4.4644186836303139056e-25 + 7.4137757111524007463e-1240j)  +/-  (4.38e-167, 2.46e-411j)
| (1.6462690981313147968e-52 - 1.736810566294965242e-1254j)  +/-  (2.72e-179, 1.53e-423j)
| (0.050742442003969058946 - 7.1304167422721299822e-1229j)  +/-  (7.81e-132, 4.39e-376j)
| (3.4918525679334391583e-27 - 9.4390213526325944997e-1242j)  +/-  (2.08e-169, 1.17e-413j)
| (2.1459659314638432789e-16 - 2.6134722942688812234e-1236j)  +/-  (1.06e-163, 5.99e-408j)
| (4.0587560354841126466e-10 + 3.9470663369251340012e-1233j)  +/-  (4.17e-159, 2.34e-403j)
| (3.2793584144169020244e-11 - 1.1008126156340474792e-1233j)  +/-  (8.26e-160, 4.65e-404j)
| (3.7303464887411851309e-08 + 9.0432300187640218001e-1232j)  +/-  (8.96e-160, 5.04e-404j)
| (4.0587560354841126466e-10 + 1.0371898123641273373e-1232j)  +/-  (9.38e-162, 5.28e-406j)
| (1.6854799461897554852e-34 + 1.9589354968500743017e-1245j)  +/-  (1.04e-174, 5.83e-419j)
| (1.7994911753710221612e-06 + 2.8418147131334766631e-1231j)  +/-  (3.24e-157, 1.82e-401j)
| (7.1330216612233448644e-32 - 4.8937841861696582746e-1243j)  +/-  (1.07e-174, 6e-419j)
| (1.9224696335568582429e-29 + 6.565392739665870131e-1242j)  +/-  (5.52e-174, 3.11e-418j)
| (0.080191351631714854551 + 8.7123953755770652733e-1229j)  +/-  (2.13e-146, 1.2e-390j)
| (2.1459659314638432789e-16 - 1.0163815272142101453e-1235j)  +/-  (3.57e-169, 2.01e-413j)
| (9.9266904057990784813e-06 - 6.8105445643397941295e-1231j)  +/-  (7.48e-160, 4.21e-404j)
| (5.7208165983180591026e-15 + 4.8987644581482965902e-1235j)  +/-  (1.48e-168, 8.31e-413j)
| (1.7994911753710221612e-06 + 5.7668831165850550907e-1231j)  +/-  (2.56e-162, 1.44e-406j)
| (0.028134132060466145086 + 5.4674632161497380615e-1229j)  +/-  (1.19e-151, 6.71e-396j)
| (2.9011639637145324892e-21 + 9.093678166894179414e-1239j)  +/-  (7.49e-172, 4.21e-416j)
| (6.4762025047971534469e-18 + 4.4572607249483841949e-1237j)  +/-  (2.94e-170, 1.65e-414j)
| (0.050742442003969058946 - 5.7946726522500554289e-1229j)  +/-  (1.61e-154, 9.05e-399j)
| (5.7208165983180591026e-15 + 1.3745643995560522387e-1235j)  +/-  (1.08e-168, 6.08e-413j)
| (0.0021450616332283533694 - 1.6585637014638265134e-1229j)  +/-  (1.18e-160, 6.66e-405j)
| (7.1330216612233448644e-32 - 4.1083840207798408909e-1244j)  +/-  (1.93e-178, 1.08e-422j)
| (0.080191351631714854551 + 7.4595630824798731013e-1229j)  +/-  (6.08e-157, 3.42e-401j)
| (0.11113485782850290627 - 8.9974150035794802612e-1229j)  +/-  (6.37e-157, 3.58e-401j)
| (6.4762025047971534469e-18 + 1.9032386574149486036e-1236j)  +/-  (3.59e-173, 2.02e-417j)
| (1.9224696335568582429e-29 + 6.8738138877695962908e-1243j)  +/-  (2.46e-177, 1.38e-421j)
| (0.13514066563165885894 + 1.071033706628215736e-1228j)  +/-  (8.25e-159, 4.64e-403j)
| (2.2152228704211189204e-12 + 8.5273014235076449494e-1234j)  +/-  (4.87e-171, 2.74e-415j)
| (2.8015351120256180515e-07 - 1.099205086919040739e-1231j)  +/-  (8.93e-168, 5.02e-412j)
| (0.13514066563165885894 + 1.0171416452738742738e-1228j)  +/-  (1.3e-160, 7.3e-405j)
| (1.2414235683278477463e-13 - 2.1414744813235795531e-1234j)  +/-  (9.91e-172, 5.57e-416j)
| (9.9266904057990784813e-06 - 1.3017262859476704424e-1230j)  +/-  (2.33e-168, 1.31e-412j)
| (0.11113485782850290627 - 9.9770194896887873851e-1229j)  +/-  (1.71e-162, 9.61e-407j)
| (3.4918525679334391583e-27 - 7.5166408824345279917e-1241j)  +/-  (1.24e-178, 6.99e-423j)
| (0.00019407605941249404897 - 3.1381745028509016188e-1230j)  +/-  (9.87e-168, 5.56e-412j)
| (4.2284372216695220929e-09 - 1.2986986141140720813e-1232j)  +/-  (6.46e-170, 3.63e-414j)
| (0.14423866742684052088 - 1.077942088286532422e-1228j)  +/-  (1.24e-164, 6.98e-409j)
| (2.8015351120256180515e-07 - 2.372163469500658795e-1231j)  +/-  (1.61e-169, 9.05e-414j)
| (0.0057928040339243874553 + 2.6385778001164829782e-1229j)  +/-  (4.66e-167, 2.62e-411j)
| (4.7200416271767593941e-05 + 2.732716516157173059e-1230j)  +/-  (1.48e-168, 8.31e-413j)
| (4.7200416271767593941e-05 + 1.5157909050225501892e-1230j)  +/-  (3.48e-169, 1.99e-413j)
| (0.028134132060466145086 + 4.2157520621505355133e-1229j)  +/-  (1.43e-167, 7.8e-412j)
