Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 10 31
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P2 : 16*t^14 - 3816/7*t^12 + 44964/7*t^10 - 225630/7*t^8 + 68715*t^6 - 108945/2*t^4 + 46845/4*t^2 - 2835/8
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^45 - 2505479092273124086995121620335165330886523528336031926935851768/424635023160733130132146032946621864188665857294391564658621*t^43 + 1253177924028265265417554967432945036394010948222647082195793938136/1273905069482199390396438098839865592565997571883174693975863*t^41 - 961230571120433883668425147770083465572314551632350093385278610549600/9766605532696861993039358757772302876339314717771005987148283*t^39 + 236877677394598710426074641479182910651299567649414112816575642063504705/35810886953221827307810982111831777213244153965160355286210371*t^37 - 3241841520623864261306128105406329193646018733030809745752829830091677265/10231681986634807802231709174809079203784043990045815796060106*t^35 + 114605850882864024849534616807480908522484259593164191309147118346605442905/10231681986634807802231709174809079203784043990045815796060106*t^33 - 1527836729523441151200454231952612768749140146647841380934865349017655438635/5115840993317403901115854587404539601892021995022907898030053*t^31 + 249087371000921859782255436221415679739708635325503701373296515906781742764525/40926727946539231208926836699236316815136175960183263184240424*t^29 - 7818631233771551266424841183980512731613623375401358585315969942225303869101575/81853455893078462417853673398472633630272351920366526368480848*t^27 + 94791734165076819333069287340224612016512629874701239732139184306949503253781275/81853455893078462417853673398472633630272351920366526368480848*t^25 - 887048881492523561772411401338511146292124771037694322368541475867585466814973875/81853455893078462417853673398472633630272351920366526368480848*t^23 + 201685984853301712046667259451398038075340607951038024990032406104920985787272375/2588251569741611459853080581769885648388058558746767632204928*t^21 - 2210061844859151326654239306316508033436803002083796002241733860401886447208875625/5176503139483222919706161163539771296776117117493535264409856*t^19 + 9108897208154768031351292511115116035421378740542451926112001567293472705516746875/5176503139483222919706161163539771296776117117493535264409856*t^17 - 27727997517870741945466340780601048965929374452760503105188514301123607128601873125/5176503139483222919706161163539771296776117117493535264409856*t^15 + 972212950534848376270502734013187587599321534235013118485072060479794177363876093125/82824050231731566715298578616636340748417873879896564230557696*t^13 - 2959942725129121966875276497069053095650609325055580570317341308848043335539961854375/165648100463463133430597157233272681496835747759793128461115392*t^11 + 2975384059992633464178155941151492068541280273017082542982119952887684603852844628125/165648100463463133430597157233272681496835747759793128461115392*t^9 - 915824887927451128648838712207475550721426892271937938516483266596290682249207721875/82824050231731566715298578616636340748417873879896564230557696*t^7 + 4878625787542456685702186341444310132053474219547688215438546771329583504494029009375/1325184803707705067444777257866181451974685982078345027688923136*t^5 - 59454488797338681920246858457230338256375180838530176898692189401749096866357359375/115233461191974353690850196336189691476059650615508263277297664*t^3 + 37893565474375108784742165150937934602836629031782066675464863997108218075773578125/2650369607415410134889554515732362903949371964156690055377846272*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:
| (6.0851223131628006508 - 1.6454944910733631037e-860j)  +/-  (8.12e-246, 8.12e-246j)
| (7.8712429801178351966 - 6.3563558784624774297e-869j)  +/-  (5.01e-248, 5.01e-248j)
| (-5.6066292893916079568 - 1.331627764462087703e-866j)  +/-  (1.8e-245, 1.8e-245j)
| (3.911506869286660161 - 1.7377723970400432535e-863j)  +/-  (2.88e-245, 2.88e-245j)
| (-7.1781844631140710939 - 2.121451784452428176e-871j)  +/-  (6.05e-247, 6.05e-247j)
| (7.1781844631140710939 + 8.2896623918235253297e-871j)  +/-  (5.65e-247, 5.65e-247j)
| (-3.0486879132310133212 + 4.0763398650218632114e-868j)  +/-  (1.6e-245, 1.6e-245j)
| (-4.3102628661200666105 + 3.3984748326921662555e-870j)  +/-  (3.08e-245, 3.08e-245j)
| (6.6017612215807822881 + 3.5667012432805707151e-870j)  +/-  (2.99e-246, 2.99e-246j)
| (3.2526743547415744393 - 3.1185971626213488771e-877j)  +/-  (2.95e-245, 2.95e-245j)
| (1.3049918145723915256 - 3.6479808556067102468e-896j)  +/-  (8.57e-250, 8.57e-250j)
| (3.5348577777640336012 - 1.0951587268465881327e-892j)  +/-  (2.98e-245, 2.98e-245j)
| (-6.6017612215807822881 + 2.0620089772356760019e-901j)  +/-  (2.89e-246, 2.89e-246j)
| (-3.911506869286660161 - 2.1267024208209431504e-899j)  +/-  (3.14e-245, 3.14e-245j)
| (-4.7243815902336158237 - 7.8217752269483561611e-907j)  +/-  (3.24e-245, 3.24e-245j)
| (0.8347251619815422063 + 1.0546518933940972065e-920j)  +/-  (2.33e-251, 2.33e-251j)
| (-7.8712429801178351966 - 1.0914217599357561459e-917j)  +/-  (4.98e-248, 4.98e-248j)
| (1.0363502036603261655 + 3.5238789779919167409e-919j)  +/-  (1.41e-250, 1.41e-250j)
| (5.1552114942842835114 - 1.147828419654361022e-913j)  +/-  (2.63e-245, 2.63e-245j)
| (3.0486879132310133212 - 3.1153357043944079357e-922j)  +/-  (1.73e-245, 1.73e-245j)
| (-3.5348577777640336012 - 6.6315305821628874528e-930j)  +/-  (2.86e-245, 2.86e-245j)
| (1.6506801238857845559 + 3.0198231446841526895e-941j)  +/-  (9.27e-249, 9.27e-249j)
| (-5.1552114942842835114 - 6.3231861041859507001e-937j)  +/-  (2.56e-245, 2.56e-245j)
| (-0.8347251619815422063 - 2.7042882064097509604e-945j)  +/-  (2.27e-251, 2.27e-251j)
| (-2.0361363785587461639 + 4.4939386439498448558e-940j)  +/-  (3.75e-247, 3.75e-247j)
| (5.6066292893916079568 - 6.4439708336901099894e-947j)  +/-  (1.75e-245, 1.75e-245j)
| (-6.0851223131628006508 + 6.5571844787880484812e-955j)  +/-  (8.48e-246, 8.48e-246j)
| (2.0361363785587461639 + 2.4680257017069710923e-956j)  +/-  (3.58e-247, 3.58e-247j)
| (-2.3166778458612639611 - 1.780382158397004654e-954j)  +/-  (1.74e-246, 1.74e-246j)
| (-0.18980675578014987883 + 3.2935729312127594802e-967j)  +/-  (2.77e-254, 2.77e-254j)
| (-2.176951312681095309 + 3.5921102050081510489e-958j)  +/-  (1.57e-246, 1.57e-246j)
| (2.3166778458612639611 - 1.6387143994756280323e-961j)  +/-  (1.77e-246, 1.77e-246j)
| (4.3102628661200666105 + 2.0125607476004200938e-966j)  +/-  (3.22e-245, 3.22e-245j)
| (-1.6506801238857845559 - 1.2826317934142397258e-977j)  +/-  (8.55e-249, 8.55e-249j)
| (-1.0363502036603261655 + 3.6902514282961356134e-979j)  +/-  (1.46e-250, 1.46e-250j)
| (-3.2526743547415744393 + 1.1617529494956373558e-974j)  +/-  (2.9e-245, 2.9e-245j)
| (2.7082856041986238156 + 4.1566910714474607276e-977j)  +/-  (3.39e-246, 3.39e-246j)
| (4.7243815902336158237 + 1.4262778492880363388e-982j)  +/-  (3.1e-245, 3.1e-245j)
| (2.176951312681095309 - 5.2426466886132469322e-988j)  +/-  (1.47e-246, 1.47e-246j)
| (-2.7082856041986238156 + 7.0104854124877266563e-992j)  +/-  (3.52e-246, 3.52e-246j)
| (-0.52464762327529031788 + 4.710230888850731996e-999j)  +/-  (6.98e-253, 6.98e-253j)
| (-1.3049918145723915256 + 1.685622766906453101e-996j)  +/-  (8.88e-250, 8.88e-250j)
| (0.18980675578014987883 + 4.7023233412452957706e-1000j)  +/-  (2.95e-254, 2.95e-254j)
| (0.52464762327529031788 - 3.0110425715087657733e-998j)  +/-  (6.71e-253, 6.71e-253j)
| (-2.8206490952989310766e-1123 + 1.5508325826029601487e-1123j)  +/-  (1.45e-1121, 1.45e-1121j)
-------------------------------------------------
The weights are:
| (2.316332909736108927e-17 + 2.9644765486637909359e-876j)  +/-  (1.69e-91, 5.48e-213j)
| (5.578400074357974314e-28 + 9.0593081613338873743e-884j)  +/-  (9.47e-97, 3.08e-218j)
| (5.8320845163584317361e-15 - 4.1006211446548750702e-878j)  +/-  (5.94e-92, 1.93e-213j)
| (4.9916310441666403064e-08 + 5.5281001946252749507e-870j)  +/-  (7.34e-85, 2.39e-206j)
| (1.4646746843005020762e-23 + 4.0268795467646344665e-883j)  +/-  (8.14e-97, 2.65e-218j)
| (1.4646746843005020762e-23 - 5.5440608107771465933e-881j)  +/-  (3.64e-95, 1.18e-216j)
| (1.4947113024929710894e-05 - 1.0364435776422870885e-870j)  +/-  (1.24e-82, 4.03e-204j)
| (1.9588571593495915047e-09 + 8.5088593867826796373e-875j)  +/-  (3.35e-88, 1.09e-209j)
| (3.6059652472952912775e-20 + 1.2887014176015340791e-878j)  +/-  (8.97e-94, 2.92e-215j)
| (2.6576600747324878625e-06 + 1.1607484828433927781e-868j)  +/-  (5.93e-84, 1.93e-205j)
| (0.033495920143954602312 - 8.9152322929123848976e-867j)  +/-  (1.81e-72, 5.87e-194j)
| (7.4999640566779584958e-07 - 2.8873367454359850796e-869j)  +/-  (6.38e-85, 2.08e-206j)
| (3.6059652472952912775e-20 - 3.4980247382058572092e-881j)  +/-  (6.71e-97, 2.18e-218j)
| (4.9916310441666403064e-08 - 1.1908931449278720755e-874j)  +/-  (9.09e-89, 2.96e-210j)
| (4.8237865879403675836e-11 - 9.745454124363206593e-876j)  +/-  (1.45e-91, 4.73e-213j)
| (0.073680445640246857891 - 2.0084633264448668226e-866j)  +/-  (2.18e-75, 7.09e-197j)
| (5.578400074357974314e-28 - 1.3272311483169031343e-885j)  +/-  (2.08e-101, 6.77e-223j)
| (0.037453831902234247855 + 1.8152821452467009204e-866j)  +/-  (2.15e-75, 7.01e-197j)
| (7.1329233056915107664e-13 + 4.5917504636471006954e-874j)  +/-  (3.87e-94, 1.26e-215j)
| (1.4947113024929710894e-05 - 2.1521702443737755724e-868j)  +/-  (1.26e-86, 4.1e-208j)
| (7.4999640566779584958e-07 - 1.7931621301647172194e-872j)  +/-  (8.02e-89, 2.61e-210j)
| (0.0132907357193743071 + 4.5809686564485644685e-867j)  +/-  (2.21e-82, 7.2e-204j)
| (7.1329233056915107664e-13 + 7.4529479300196450423e-877j)  +/-  (1.87e-93, 6.07e-215j)
| (0.073680445640246857891 - 6.3694877784009077316e-867j)  +/-  (9.18e-81, 2.99e-202j)
| (0.0043694309796016788292 - 3.7356497619154961832e-868j)  +/-  (1.89e-85, 6.15e-207j)
| (5.8320845163584317361e-15 - 3.0299243221611976698e-875j)  +/-  (4.63e-96, 1.51e-217j)
| (2.316332909736108927e-17 + 1.5098206513025137452e-879j)  +/-  (1.86e-96, 6.07e-218j)
| (0.0043694309796016788292 - 7.6760252745262007138e-867j)  +/-  (5.79e-86, 1.88e-207j)
| (0.0013038992850615751029 - 1.1875996267356930538e-868j)  +/-  (3.55e-87, 1.15e-208j)
| (0.17545323563604234965 - 2.1261077902775659042e-866j)  +/-  (2.26e-83, 7.36e-205j)
| (-0.0014474215066759942073 + 3.606399321357504059e-868j)  +/-  (1.48e-86, 4.82e-208j)
| (0.0013038992850615751029 - 4.1382750369456456615e-867j)  +/-  (5.67e-88, 1.84e-209j)
| (1.9588571593495915047e-09 + 1.9114460255012107964e-871j)  +/-  (4.15e-94, 1.35e-215j)
| (0.0132907357193743071 + 4.2832988870911557123e-868j)  +/-  (1.52e-87, 4.94e-209j)
| (0.037453831902234247855 + 4.3155881452601776834e-867j)  +/-  (1.68e-86, 5.45e-208j)
| (2.6576600747324878625e-06 + 2.9045205399272565748e-871j)  +/-  (1.2e-90, 3.89e-212j)
| (0.00013480687435709422935 + 4.4701867848896993568e-868j)  +/-  (8.41e-90, 2.74e-211j)
| (4.8237865879403675836e-11 - 8.2600777995434667952e-873j)  +/-  (1.78e-95, 5.78e-217j)
| (-0.0014474215066759942073 + 9.5940955277935673917e-867j)  +/-  (3.69e-88, 1.2e-209j)
| (0.00013480687435709422935 + 5.4379547801507612067e-870j)  +/-  (1.08e-90, 3.44e-212j)
| (0.14327681579414141852 + 8.1153074282098585408e-867j)  +/-  (3.29e-88, 1.11e-209j)
| (0.033495920143954602312 - 1.4265493107153313646e-867j)  +/-  (1.03e-88, 3.26e-210j)
| (0.17545323563604234965 - 2.7514273171758121758e-866j)  +/-  (1.2e-88, 4e-210j)
| (0.14327681579414141852 + 1.6604578887839798583e-866j)  +/-  (6.72e-89, 1.95e-210j)
| (0.037939785676063836442 + 3.539616051243534883e-866j)  +/-  (1.33e-88, 5.1e-210j)
