Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 7 36
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : 3/2*t^9 - 151/50*t^7 + 1281/650*t^5 - 651/1430*t^3 + 56/2145*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^45 - 26586068496872073074123759863344482469672626157273780446802265052593508420498263/1597767476645688290825084585167828481165798695056506599856639915970332068166900*t^43 + 30683451118009559634414999809455534767294964588320085048501101868381973006056737115761/356076862077781446804987525565917087484128731381598004337450915033232234379607167100*t^41 - 356600836283814516390607381132641575305748549558228956360243844674284942796767323200055277/1288642163859491055987249855023053939605061878870003177697234861505267456219798337734900*t^39 + 4589853657664877006499311899532788896592204063615139758089733628206521169187485842285109129/7434474022266294553772595317440695805413818531942326025176354970222696862806528871547500*t^37 - 1482176937578988682830724929999378286061531870052563482786188820664523313532663810405858316/1458915601143654576412364134874115037083894496859649999564177185016819545658270450599375*t^35 + 296808275039090793360836242127299253738282130503841259807557175629482529844887538809365489/232265695343015097481635693371278639900300310132954043330253452746619878480568047867575*t^33 - 1554890646208623332768789827894766663801850770241648189773858388109317508938213000550609519/1237615156710435284821501627142560963926233617336004389240676022406476009381795140690275*t^31 + 8636942381990050639011260703269084219481873783796034636571826668896312206200990953767867044/8821299521233953625855383938143785593942303442714073838204818457578073683891518555983875*t^29 - 98603480003976748646520878738238496965718647950280526681496483191095143280151757216205183956563/161694420224218369961929187586175589936962422104948973454294322327406090625731535131184428750*t^27 + 8842533383842198308943847711460294322548824775922144628494846280373299454125918045778808876599/29022075424859707429064213156493054604070178326529302927693852725431862420003096049186948750*t^25 - 8647169859187524496841450190694794718282651349323635903301106837864656996759304963156493575253/70813864036657686126916680101843053233931235116731499143573000650053744304807554360016154950*t^23 + 7105455054858120694460582401403682776106155649407132381132174774413602322482172728532776561447/181652955572295803542960179391684353947910559647267758672643784276224822347115030749606658350*t^21 - 128997726795833618832830933612385992793095931818014398082426224687301768108279837153874853253/12975211112306843110211441385120310996279325689090554190903127448301773024793930767829047025*t^19 + 1414605352845005303097418513050125800611721223702198362328511927518378495341303882419310283613/713636611176876371061629276181617104795362912899980480499672009656597516363666192230597586375*t^17 - 2829501358222027958826300387644442057148491727084415063002748266391937029029702392406079555859/9277275945299392823801180590361022362339717867699746246495736125535767712727660498997768622875*t^15 + 131328983294263436957632284872111968299707303302319069561884418060268380821720692664365419919/3710910378119757129520472236144408944935887147079898498598294450214307085091064199599107449150*t^13 - 83892974165696271859816006462856870720257826590482749875520514427717662240350060957368049337/27974555158133553745615867626319390507978226185679234835587142778538622641455714735439425385900*t^11 + 1122868247925142510141241482055517730536498355512094199231493074414717140564278015408321205213/6334965172628243852757193296105600159579432857138815815949779332849064454533289582361782603297900*t^9 - 216149962959760810320950938553984909734052638741752121129992992401554466270998496164923215167/31674825863141219263785966480528000797897164285694079079748896664245322272666447911808913016489500*t^7 + 694226761665955273563444475277818632967191496377332653387814919366300294548031692069368731/4524975123305888466255138068646857256842452040813439868535556666320760324666635415972701859498500*t^5 - 374201012999603080636670880284835195421140391551582364651351412689095853886208757957797/226248756165294423312756903432342862842122602040671993426777833316038016233331770798635092974925*t^3 + 270058309710347928597318330421237828421706565383243608827186807204014019426681182992/49851420849980127170607453298651817236399895364893829060137488696754139170056152887834850994475*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: 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:
| (0.42475175714240062828 + 2.8922172028403165833e-928j)  +/-  (1.58e-247, 1.58e-247j)
| (0.99197845700981455113 - 1.0902714111785455129e-918j)  +/-  (3.95e-240, 3.95e-240j)
| (-0.91737273678523516753 + 5.4198275563378269718e-920j)  +/-  (2.79e-240, 2.79e-240j)
| (0.98040244436512692464 - 6.963548135675251307e-927j)  +/-  (5.24e-240, 5.24e-240j)
| (0.91737273678523516753 + 1.507891215901891143e-926j)  +/-  (3.04e-240, 3.04e-240j)
| (0.94282013727978672949 - 1.2848542931409761126e-926j)  +/-  (4.44e-240, 4.44e-240j)
| (-0.99847263536143578022 - 1.3060084234638197845e-924j)  +/-  (1.46e-240, 1.46e-240j)
| (-0.94282013727978672949 + 5.0006129304451772144e-938j)  +/-  (4.2e-240, 4.2e-240j)
| (-0.96392874096524810675 - 1.120752690174943469e-956j)  +/-  (5.94e-240, 5.94e-240j)
| (-0.99197845700981455113 + 5.4948389616462959365e-980j)  +/-  (3.81e-240, 3.81e-240j)
| (0.8878150578504902195 + 2.617721046575475493e-997j)  +/-  (1.54e-240, 1.54e-240j)
| (-0.21949224231216232471 - 8.6670019018840209377e-1011j)  +/-  (1.34e-251, 1.34e-251j)
| (-0.8878150578504902195 + 2.9578563746815969734e-998j)  +/-  (1.56e-240, 1.56e-240j)
| (-0.77438239838682401527 + 2.9446455276214678743e-1011j)  +/-  (6.04e-242, 6.04e-242j)
| (0.99847263536143578022 + 2.5126884244561124801e-1008j)  +/-  (1.34e-240, 1.34e-240j)
| (0.85419792113301438085 - 2.1615334004143290827e-1013j)  +/-  (5.77e-241, 5.77e-241j)
| (0.81641357233552832956 + 6.9810264416714610618e-1017j)  +/-  (1.93e-241, 1.93e-241j)
| (-0.98040244436512692464 + 3.4895231568343899005e-1019j)  +/-  (5.9e-240, 5.9e-240j)
| (-0.81641357233552832956 + 3.3453679482027856095e-1028j)  +/-  (2.05e-241, 2.05e-241j)
| (-0.85419792113301438085 + 1.0674726628888723472e-1032j)  +/-  (5.7e-241, 5.7e-241j)
| (0.77438239838682401527 + 1.6881434495028283099e-1036j)  +/-  (5.7e-242, 5.7e-242j)
| (0.72825217804086960894 + 3.0292453158297326131e-1038j)  +/-  (1.43e-242, 1.43e-242j)
| (0.21949224231216232471 - 4.694641573294335224e-1049j)  +/-  (1.29e-251, 1.29e-251j)
| (-0.72825217804086960894 + 3.7916747910686857175e-1039j)  +/-  (1.42e-242, 1.42e-242j)
| (-0.67856584166127026741 - 1.2291833596863766233e-1039j)  +/-  (3e-243, 3e-243j)
| (9.5730718956971563317e-1054 + 3.9176185951349192112e-1054j)  +/-  (4.65e-1052, 4.65e-1052j)
| (0.67856584166127026741 - 2.1736903789617414109e-1039j)  +/-  (2.92e-243, 2.92e-243j)
| (0.96392874096524810675 - 2.5058757935285293154e-1043j)  +/-  (5.89e-240, 5.89e-240j)
| (-0.48506777681797552947 + 6.8266113375826138437e-1049j)  +/-  (3.1e-246, 3.1e-246j)
| (-0.62678086968133933539 - 1.1667312156793217813e-1046j)  +/-  (6.11e-244, 6.11e-244j)
| (-0.29036229308829455553 + 3.3017554671512811835e-1055j)  +/-  (3.14e-250, 3.14e-250j)
| (0.48506777681797552947 + 1.9824489686931726264e-1050j)  +/-  (2.87e-246, 2.87e-246j)
| (0.62678086968133933539 + 6.8509778931623289524e-1049j)  +/-  (6.15e-244, 6.15e-244j)
| (0.073802992867587466334 - 1.1020603399184331489e-1058j)  +/-  (2.4e-254, 2.4e-254j)
| (-0.57735026918962576451 - 1.5729407392422711621e-1048j)  +/-  (1.35e-244, 1.35e-244j)
| (-0.42475175714240062828 + 6.4758068706844990835e-1052j)  +/-  (1.69e-247, 1.69e-247j)
| (0.14713006178315640604 + 1.0750866679625499923e-1057j)  +/-  (5.47e-253, 5.47e-253j)
| (0.5347011718497663018 - 3.5766801921958219957e-1049j)  +/-  (2.76e-245, 2.76e-245j)
| (0.35910615152001549131 + 4.8025851750112280747e-1054j)  +/-  (8.43e-249, 8.43e-249j)
| (-0.35910615152001549131 + 7.3633404809444512877e-1054j)  +/-  (7.75e-249, 7.75e-249j)
| (-0.5347011718497663018 + 1.3116112444882634111e-1051j)  +/-  (3e-245, 3e-245j)
| (-0.14713006178315640604 - 6.4640091424948783032e-1059j)  +/-  (4.97e-253, 4.97e-253j)
| (0.29036229308829455553 + 1.1527981043515766654e-1055j)  +/-  (3.22e-250, 3.22e-250j)
| (0.57735026918962576451 - 3.8226214424530438525e-1054j)  +/-  (1.39e-244, 1.39e-244j)
| (-0.073802992867587466334 + 1.0556750341034353267e-1063j)  +/-  (2.4e-254, 2.4e-254j)
-------------------------------------------------
The weights are:
| (0.063557817497010129577 - 8.112370921757662062e-919j)  +/-  (1.24e-69, 1.37e-185j)
| (0.0090581926834297944957 + 6.7636303770118744664e-919j)  +/-  (5.66e-70, 6.27e-186j)
| (0.027528435849888030317 + 5.7671468258602639715e-920j)  +/-  (2.52e-71, 2.79e-187j)
| (0.014062871732302391312 - 1.7823943550946865721e-918j)  +/-  (4.24e-70, 4.69e-186j)
| (0.027528435849888030317 + 1.0948739987156619842e-918j)  +/-  (9.11e-71, 1.01e-186j)
| (0.023326011669615781149 - 1.1357819185665168836e-918j)  +/-  (1.31e-70, 1.45e-186j)
| (0.0039167523259649188978 - 7.5577395304375603026e-922j)  +/-  (5.19e-73, 5.74e-189j)
| (0.023326011669615781149 + 1.1240670684761457383e-920j)  +/-  (1.32e-72, 1.46e-188j)
| (0.018840085076780642319 + 4.2299847481857765705e-921j)  +/-  (5.55e-73, 6.14e-189j)
| (0.0090581926834297944957 + 2.5610545525313678317e-921j)  +/-  (3.63e-73, 4.02e-189j)
| (0.031578588219958689315 - 1.0809336149502550455e-918j)  +/-  (3.26e-74, 3.6e-190j)
| (0.071709335956454726203 + 1.9130679244610985577e-919j)  +/-  (3.97e-76, 4.4e-192j)
| (0.031578588219958689315 - 1.2939242251120095542e-919j)  +/-  (4.42e-74, 4.89e-190j)
| (0.04413158438984733982 + 1.5981634542608931857e-919j)  +/-  (1.71e-75, 1.89e-191j)
| (0.0039167523259649188978 + 4.1914523643045216159e-919j)  +/-  (1.51e-74, 1.67e-190j)
| (0.035677321265763871235 + 1.0683239930167817037e-918j)  +/-  (3.55e-75, 3.93e-191j)
| (0.03990816784711137505 - 1.0557521428197541171e-918j)  +/-  (6.53e-76, 7.23e-192j)
| (0.014062871732302391312 - 4.4789016520432105001e-921j)  +/-  (1.19e-74, 1.32e-190j)
| (0.03990816784711137505 - 1.3580541895401948809e-919j)  +/-  (1.15e-76, 1.27e-192j)
| (0.035677321265763871235 + 1.2214678335494930707e-919j)  +/-  (3.43e-76, 3.8e-192j)
| (0.04413158438984733982 + 1.0608263143943768733e-918j)  +/-  (9.7e-78, 1.07e-193j)
| (0.048044309591937465983 - 1.1145873651824986758e-918j)  +/-  (1.29e-78, 1.43e-194j)
| (0.071709335956454726203 + 2.9440569356365066581e-919j)  +/-  (4.37e-81, 4.84e-197j)
| (0.048044309591937465983 - 1.9870653119429971825e-919j)  +/-  (1.02e-78, 1.13e-194j)
| (0.051115285744687845614 + 2.6739651569938917496e-919j)  +/-  (1.11e-79, 1.22e-195j)
| (0.073881946107648608061 - 1.9195447270136483265e-919j)  +/-  (2.1e-82, 2.33e-198j)
| (0.051115285744687845614 + 1.2682101869814568576e-918j)  +/-  (2.02e-80, 2.23e-196j)
| (0.018840085076780642319 + 1.2707885055900940439e-918j)  +/-  (1.51e-78, 1.68e-194j)
| (0.056096628196383426438 + 5.0141082549826482552e-919j)  +/-  (2.51e-82, 2.78e-198j)
| (0.051787239314369397853 - 4.0025114955653451652e-919j)  +/-  (4.99e-81, 5.52e-197j)
| (0.069928067901440182073 - 2.1303738309891990799e-919j)  +/-  (6.15e-83, 6.8e-199j)
| (0.056096628196383426438 + 1.3842176376634314416e-918j)  +/-  (2.49e-83, 2.76e-199j)
| (0.051787239314369397853 - 1.6171300111393731966e-918j)  +/-  (1.66e-82, 1.84e-198j)
| (0.073644912582955412976 + 2.1089698625932382387e-919j)  +/-  (2.11e-84, 2.34e-200j)
| (0.045585519382300855022 + 6.09255536995225067e-919j)  +/-  (5.9e-83, 6.53e-199j)
| (0.063557817497010129577 - 3.3925573528973355888e-919j)  +/-  (5.86e-84, 6.48e-200j)
| (0.07292809537774209562 - 2.4282275048911512812e-919j)  +/-  (6.58e-85, 7.29e-201j)
| (0.04322468266470640683 - 2.0936445227949837808e-918j)  +/-  (1.19e-84, 1.32e-200j)
| (0.067409121675524917868 + 5.2758236165244535744e-919j)  +/-  (2.46e-85, 2.71e-201j)
| (0.067409121675524917868 + 2.5574455437113406413e-919j)  +/-  (2.34e-85, 2.56e-201j)
| (0.04322468266470640683 - 6.6898046643247512995e-919j)  +/-  (1.35e-84, 1.48e-200j)
| (0.07292809537774209562 - 1.823193149341654417e-919j)  +/-  (1.4e-86, 1.53e-202j)
| (0.069928067901440182073 - 3.7932084789665215394e-919j)  +/-  (1.49e-86, 1.77e-202j)
| (0.045585519382300855022 + 2.1373381200342985057e-918j)  +/-  (4.85e-86, 6.02e-202j)
| (0.073644912582955412976 + 1.8278958734899855582e-919j)  +/-  (8.59e-87, 9.13e-203j)
