Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 10 27
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Trying to find an order 10 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P2 : 4*t^12 - 8477/76*t^10 + 155745/152*t^8 - 563535/152*t^6 + 1500975/304*t^4 - 2132865/1216*t^2 + 110565/2432
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^39 - 1699639380422035860256037577242097457139069086751030885127668113/1500637075048149269098881991624565516591054469337454092471740*t^37 + 429038355398161828889365226829014092834850702404758995488208614483/3001274150096298538197763983249131033182108938674908184943480*t^35 - 266524801894579297858460138076877852304268658000950525920206403552/25010617917469154484981366527076091943184241155624234874529*t^33 + 11955739752686559052290081116677820992027048285126439151931313433975637/22809683540731868890303006272693395852184027933929302205570448*t^31 - 6980141574796706827799742155234405169264882622136575795065168664339109935/387764620192441771135151106635787729487128474876798137494697616*t^29 + 115176643142478710710959655623903327755254378329666384904492026276213686823/258509746794961180756767404423858486324752316584532091663131744*t^27 - 8363250599208407524714214059977106889245227514701700379796747864060268710441/1034038987179844723027069617695433945299009266338128366652526976*t^25 + 224490439976626866576254251492728378039515044964962910461158640589651579645025/2068077974359689446054139235390867890598018532676256733305053952*t^23 - 4457950272987217811258900752797397368931558409773362882313239946493232410148525/4136155948719378892108278470781735781196037065352513466610107904*t^21 + 65100226833919698386864763466479028260636450459354111720081347429947781014318875/8272311897438757784216556941563471562392074130705026933220215808*t^19 - 36328817951232693326533790555835867144409653611257517008108782735771584452238025/870769673414606082549111257006681217093902540074213361391601664*t^17 + 16118831651746527488539500069580430975484992231105622715199678977381473939699075/102443490989953656770483677294903672599282651773436866046070784*t^15 - 41967068385153612784794529032567349060705185663024948511005616076786351464027125/102443490989953656770483677294903672599282651773436866046070784*t^13 + 144491275364217657236794189962572293766728030337639753528702270453908978451590875/204886981979907313540967354589807345198565303546873732092141568*t^11 - 617701484603890637377782810605947576933461268949791875174171242766079622363353125/819547927919629254163869418359229380794261214187494928368566272*t^9 + 744438523489061730674210229680924396640027797758851058299742535680153277155724625/1639095855839258508327738836718458761588522428374989856737132544*t^7 - 861997151104789622846530095616976968546854726133670627466957836366972677372729875/6556383423357034033310955346873835046354089713499959426948530176*t^5 + 177595302715239927795297542804004741059911257736318979116767128220130502678180625/13112766846714068066621910693747670092708179426999918853897060352*t^3 - 3754787818672758098787787105763695113486284272662569056150835774027216450529375/13112766846714068066621910693747670092708179426999918853897060352*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (7.2833670655689746837 - 9.1876565201515124433e-337j)  +/-  (4.4e-121, 4.4e-121j)
| (4.5071428402131878624 - 2.3442400970184857942e-332j)  +/-  (9.64e-119, 9.64e-119j)
| (-5.4565758930647794857 + 1.9956810192025322929e-336j)  +/-  (4.64e-119, 4.64e-119j)
| (5.4565758930647794857 + 1.1719615047765341154e-335j)  +/-  (4.22e-119, 4.22e-119j)
| (6.5748231214742941682 + 1.3484476295208050113e-340j)  +/-  (3.92e-120, 3.92e-120j)
| (4.9673829470033858293 - 1.2278510492310879172e-336j)  +/-  (7.64e-119, 7.64e-119j)
| (-5.985153350599019693 + 1.7708709154627310437e-343j)  +/-  (1.61e-119, 1.61e-119j)
| (-7.2833670655689746837 + 1.4297963596854658463e-344j)  +/-  (4.32e-121, 4.32e-121j)
| (-6.5748231214742941682 + 5.0191868367033219531e-343j)  +/-  (4.06e-120, 4.06e-120j)
| (5.985153350599019693 + 5.3218426262768368685e-341j)  +/-  (1.77e-119, 1.77e-119j)
| (1.3532153932168790075 + 1.1865124927847927429e-349j)  +/-  (7.69e-123, 7.69e-123j)
| (-1.6884933432663781558 + 1.1309625974422471372e-356j)  +/-  (5.67e-122, 5.67e-122j)
| (-4.9673829470033858293 - 2.9128262926491698837e-352j)  +/-  (6.54e-119, 6.54e-119j)
| (-4.0721983742019086803 - 1.0678033891768110713e-351j)  +/-  (1.1e-118, 1.1e-118j)
| (-0.7071067811865475244 + 3.4506182819740922113e-355j)  +/-  (8.36e-125, 8.36e-125j)
| (3.6783246397895513046 - 9.8794461166495349771e-354j)  +/-  (1.54e-118, 1.54e-118j)
| (-2.7962452403682858841 - 5.8445543028851891737e-369j)  +/-  (7.78e-120, 7.78e-120j)
| (-4.5071428402131878624 - 9.8446546488974965059e-370j)  +/-  (1.02e-118, 1.02e-118j)
| (-1.0312897787599441261 - 4.2410744549843129028e-376j)  +/-  (8.92e-124, 8.92e-124j)
| (-3.1739156793533050567 - 2.4244321909056427773e-369j)  +/-  (5.12e-119, 5.12e-119j)
| (3.4434867091595391902 + 2.84720701583655977e-370j)  +/-  (1.37e-118, 1.37e-118j)
| (0.7071067811865475244 - 2.5486406027326471918e-388j)  +/-  (8.28e-125, 8.28e-125j)
| (2.7962452403682858841 + 2.6106784723982394185e-388j)  +/-  (9.14e-120, 9.14e-120j)
| (-1.3532153932168790075 + 1.2438890043825502373e-405j)  +/-  (8.15e-123, 8.15e-123j)
| (-0.16761481870756104368 - 2.8254669761587997648e-419j)  +/-  (1.16e-126, 1.16e-126j)
| (2.0436541275856649452 - 1.1543930623996965152e-400j)  +/-  (3.19e-121, 3.19e-121j)
| (1.6884933432663781558 + 2.5359963536906181197e-408j)  +/-  (5.17e-122, 5.17e-122j)
| (3.1739156793533050567 - 6.348051734625566238e-414j)  +/-  (4.78e-119, 4.78e-119j)
| (-3.6783246397895513046 + 1.9116058645124026653e-430j)  +/-  (1.61e-118, 1.61e-118j)
| (-2.4148428650197551712 - 1.6946366229289107562e-433j)  +/-  (1.77e-120, 1.77e-120j)
| (-0.38298882146605389681 + 1.5957473724985624333e-441j)  +/-  (7.58e-126, 7.58e-126j)
| (0.16761481870756104368 - 8.3418245610229579177e-440j)  +/-  (1.37e-126, 1.37e-126j)
| (-3.3946125245945129543e-441 + 2.4410213732759035876e-441j)  +/-  (1.63e-439, 1.63e-439j)
| (4.0721983742019086803 - 1.6418443135340943004e-434j)  +/-  (1.09e-118, 1.09e-118j)
| (-2.0436541275856649452 - 2.4760848467199683947e-451j)  +/-  (3.27e-121, 3.27e-121j)
| (-3.4434867091595391902 + 4.2066852143988946218e-447j)  +/-  (1.27e-118, 1.27e-118j)
| (2.4148428650197551712 + 6.2627218152774312233e-448j)  +/-  (1.61e-120, 1.61e-120j)
| (1.0312897787599441261 + 1.0707588163360347028e-459j)  +/-  (9.68e-124, 9.68e-124j)
| (0.38298882146605389681 + 4.3781413897919313148e-461j)  +/-  (7.58e-126, 7.58e-126j)
-------------------------------------------------
The weights are:
| (4.2175727769595684512e-24 + 9.9225679413244423101e-351j)  +/-  (2.36e-32, 1.01e-90j)
| (3.8012574401310846943e-10 + 5.7689805681668599931e-341j)  +/-  (6.86e-25, 2.94e-83j)
| (3.3514577130571290389e-14 + 1.8229838748202426591e-345j)  +/-  (1e-29, 4.29e-88j)
| (3.3514577130571290389e-14 - 1.9129108311588608102e-344j)  +/-  (3.52e-28, 1.51e-86j)
| (6.0158676885651676053e-20 - 3.158337636495889906e-348j)  +/-  (2.21e-31, 9.47e-90j)
| (5.1359368138975699e-12 + 1.0000829836249559297e-342j)  +/-  (9.51e-27, 4.07e-85j)
| (8.6616722624926784603e-17 - 4.5213185904998337592e-347j)  +/-  (8.14e-33, 3.49e-91j)
| (4.2175727769595684512e-24 - 2.3363776576215021413e-351j)  +/-  (9.25e-37, 3.96e-95j)
| (6.0158676885651676053e-20 + 5.8927797615805790485e-349j)  +/-  (9.06e-35, 3.88e-93j)
| (8.6616722624926784603e-17 + 3.2097342964894155447e-346j)  +/-  (4e-32, 1.71e-90j)
| (0.029484432223803898655 - 2.2492337044417522517e-336j)  +/-  (7.19e-17, 3.08e-75j)
| (0.011260524236889318217 + 3.7756164605176016667e-337j)  +/-  (1.18e-19, 5.05e-78j)
| (5.1359368138975699e-12 - 4.8579500990850508074e-344j)  +/-  (1.56e-31, 6.68e-90j)
| (1.4923301070641353001e-08 - 1.7513228095461886803e-341j)  +/-  (3.26e-30, 1.4e-88j)
| (0.11211113952533940892 - 1.0049969770225180957e-335j)  +/-  (1.87e-19, 8e-78j)
| (2.5907783169555125841e-07 + 2.9210530407977466851e-339j)  +/-  (2.12e-29, 9.08e-88j)
| (8.7072931905242411435e-05 - 8.1541253668635101827e-339j)  +/-  (3.53e-27, 1.51e-85j)
| (3.8012574401310846943e-10 + 9.8855100652845457987e-343j)  +/-  (2.95e-31, 1.26e-89j)
| (0.06249929548559794645 + 3.4533175421963661049e-336j)  +/-  (3.03e-20, 1.3e-78j)
| (8.5393228801344546207e-06 + 2.889539040502188077e-339j)  +/-  (1.89e-28, 8.08e-87j)
| (6.8760466410472000151e-07 - 9.1377240903421457523e-339j)  +/-  (4.18e-30, 1.79e-88j)
| (0.11211113952533940892 - 1.3790140059598150436e-335j)  +/-  (1.56e-22, 6.66e-81j)
| (8.7072931905242411435e-05 - 3.4807823358143144099e-338j)  +/-  (1.7e-29, 7.29e-88j)
| (0.029484432223803898655 - 1.2104935291326461034e-336j)  +/-  (2.21e-24, 9.48e-83j)
| (0.059675244045608347616 - 1.1903575838653167207e-334j)  +/-  (1.53e-23, 6.53e-82j)
| (0.0031536435064733809421 - 2.8246662159507743511e-337j)  +/-  (7.34e-28, 3.14e-86j)
| (0.011260524236889318217 + 8.2991238844405120226e-337j)  +/-  (7.82e-27, 3.35e-85j)
| (8.5393228801344546207e-06 + 1.6647323411955881124e-338j)  +/-  (4.36e-30, 1.87e-88j)
| (2.5907783169555125841e-07 + 2.9577169215104855006e-340j)  +/-  (3.46e-32, 1.48e-90j)
| (0.00062459202022999621591 + 2.8819366959620296479e-338j)  +/-  (7.15e-30, 3.05e-88j)
| (0.15072480540793186074 + 4.1663403554986399793e-335j)  +/-  (9.62e-25, 4.09e-83j)
| (0.059675244045608347616 - 1.2823128847595419529e-334j)  +/-  (1.47e-25, 6.24e-84j)
| (0.14073949860449662476 + 1.7363404614614259005e-334j)  +/-  (4.04e-25, 1.72e-83j)
| (1.4923301070641353001e-08 - 3.4544965085837701927e-340j)  +/-  (1.37e-33, 5.82e-92j)
| (0.0031536435064733809421 - 1.0622436601711315856e-337j)  +/-  (1.68e-29, 7.18e-88j)
| (6.8760466410472000151e-07 - 1.2224722132991944114e-339j)  +/-  (5.77e-32, 2.49e-90j)
| (0.00062459202022999621591 + 9.5343364025684871618e-338j)  +/-  (1.16e-30, 4.89e-89j)
| (0.06249929548559794645 + 5.5025211106504155131e-336j)  +/-  (9.25e-29, 3.73e-87j)
| (0.15072480540793186074 + 4.9401521601933849516e-335j)  +/-  (1e-27, 4.7e-86j)
