Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 10 23
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 23 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^35 - 87831838483004721172497261052311145174474953329557/85234197309576834168121491413625209611480810988*t^33 + 330160321281965263939728981404654588857847177567137077/2897962708525612361716130708063257126790347573592*t^31 - 41562525783158140029842358092122133390747595146556558675/5795925417051224723432261416126514253580695147184*t^29 + 23282701522672331249466521994835054036722622004392985589855/81142955838717146128051659825771199550129732060576*t^27 - 178748345971783060462267701080839460580635393327183443576095/23183701668204898893729045664506057014322780588736*t^25 + 46478103318336452119582769678051486794453310216189159586510195/324571823354868584512206639303084798200518928242304*t^23 - 172819000466514476203622334958166112195892320769769450873590155/92734806672819595574916182658024228057291122354944*t^21 + 3161611611675967210588641194216256574998006115984074079021847025/185469613345639191149832365316048456114582244709888*t^19 - 2127867094249190507622389874239412190275913891497153384522438075/19523117194277809594719196349057732222587604706304*t^17 + 1103546319452758578773421162727814801667276412139807598582096525/2296837316973859952319905452830321437951482906624*t^15 - 6557634813306287837798832824369238217848292987034154793472767275/4593674633947719904639810905660642875902965813248*t^13 + 25402123650516251192238570101935041647141509762484167378255455825/9187349267895439809279621811321285751805931626496*t^11 - 61205267201423971693659221335495600186660601260168226337481377375/18374698535790879618559243622642571503611863252992*t^9 + 85981214363605155272889912466336366834316787276086682915916489125/36749397071581759237118487245285143007223726505984*t^7 - 63961412666440002918388375946288503688243234452574380427984980875/73498794143163518474236974490570286014447453011968*t^5 + 20307084658707043834465430148286508319890465031133838662266839625/146997588286327036948473948981140572028894906023936*t^3 - 476879449806310210796004990029132812063040705802943023196579125/146997588286327036948473948981140572028894906023936*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: 1
  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:
| (8.2327484894970929527 - 1.2008990225112494399e-421j)  +/-  (8.05e-123, 8.05e-123j)
| (6.494468350953160388 - 4.3896100190276252503e-419j)  +/-  (1.97e-121, 1.97e-121j)
| (-3.6783246397895513046 - 2.2068907857941252431e-422j)  +/-  (2.44e-120, 2.44e-120j)
| (5.7873333506408867913 - 3.3761737239558058927e-422j)  +/-  (1.08e-120, 1.08e-120j)
| (-5.7873333506408867913 + 2.3701599105768995478e-429j)  +/-  (1.14e-120, 1.14e-120j)
| (-2.3957665934203341845 - 7.2838962455884369426e-430j)  +/-  (2.82e-121, 2.82e-121j)
| (-8.2327484894970929527 - 3.1018319622197621182e-431j)  +/-  (8.14e-123, 8.14e-123j)
| (-6.494468350953160388 - 1.7648004398929138806e-429j)  +/-  (2.21e-121, 2.21e-121j)
| (-5.1914893928968576118 + 4.669582515970298585e-428j)  +/-  (2.67e-120, 2.67e-120j)
| (-4.6533018359160458712 + 2.9204777374273482238e-428j)  +/-  (3.5e-120, 3.5e-120j)
| (0.91220592321268213398 - 1.2174126693833683104e-431j)  +/-  (8.83e-124, 8.83e-124j)
| (0.7071067811865475244 + 3.395655667173750339e-430j)  +/-  (1.17e-122, 1.17e-122j)
| (-1.3532153932168790075 - 1.8888067736382788317e-431j)  +/-  (4.18e-123, 4.18e-123j)
| (5.1914893928968576118 + 3.3697253663325239582e-428j)  +/-  (2.58e-120, 2.58e-120j)
| (0.16761481870756104368 - 4.4943760552751128597e-441j)  +/-  (6.71e-127, 6.71e-127j)
| (2.3957665934203341845 - 8.0830792140676956167e-435j)  +/-  (2.87e-121, 2.87e-121j)
| (-2.7962452403682858841 + 3.4534793874253149329e-435j)  +/-  (6.88e-121, 6.88e-121j)
| (4.1522920031735537427 - 8.7049080592295898986e-438j)  +/-  (3.88e-120, 3.88e-120j)
| (-0.91220592321268213398 + 1.4733149881222198382e-451j)  +/-  (9.59e-124, 9.59e-124j)
| (-4.1522920031735537427 - 5.3994283509765345785e-447j)  +/-  (4.15e-120, 4.15e-120j)
| (2.7962452403682858841 - 6.8872509516816744104e-447j)  +/-  (6.48e-121, 6.48e-121j)
| (0.71036469065990305664 + 8.8987235681304933027e-456j)  +/-  (1.26e-122, 1.26e-122j)
| (4.6533018359160458712 + 1.4057534459664505189e-457j)  +/-  (3.36e-120, 3.36e-120j)
| (-2.0436541275856649452 + 3.1638931454045462242e-472j)  +/-  (1.07e-121, 1.07e-121j)
| (3.2264230923546439326 - 5.9623875562790021393e-469j)  +/-  (1.6e-120, 1.6e-120j)
| (3.6783246397895513046 + 9.5302795346447298423e-480j)  +/-  (2.44e-120, 2.44e-120j)
| (1.7182012865338907978 - 5.0575881143836843119e-483j)  +/-  (2.49e-122, 2.49e-122j)
| (-3.2264230923546439326 - 1.718994830203959312e-481j)  +/-  (1.62e-120, 1.62e-120j)
| (-0.16761481870756104368 + 9.5013670889730046953e-488j)  +/-  (6.71e-127, 6.71e-127j)
| (-0.71036469065990305664 - 1.4551659679997817198e-480j)  +/-  (1.27e-122, 1.27e-122j)
| (-1.7182012865338907978 + 1.5926049158327661301e-485j)  +/-  (2.49e-122, 2.49e-122j)
| (2.6099236831543319712e-500 + 4.908013875150762691e-500j)  +/-  (1.95e-498, 1.95e-498j)
| (1.3532153932168790075 - 3.8554575292221549774e-486j)  +/-  (4e-123, 4e-123j)
| (2.0436541275856649452 + 2.1372021163853851255e-487j)  +/-  (9.21e-122, 9.21e-122j)
| (-0.7071067811865475244 - 3.5453843934136434506e-486j)  +/-  (1.28e-122, 1.28e-122j)
-------------------------------------------------
The weights are:
| (3.5780940805939205415e-28 - 1.1723386416363409497e-441j)  +/-  (7.87e-42, 1.61e-101j)
| (2.1909730226027946265e-19 + 1.0782782424749609053e-436j)  +/-  (1.71e-38, 3.49e-98j)
| (3.4710119536953028874e-07 - 3.9586188387743473747e-428j)  +/-  (5.47e-32, 1.11e-91j)
| (1.0224469592284425024e-15 - 5.8808819466355169365e-435j)  +/-  (3.7e-37, 7.55e-97j)
| (1.0224469592284425024e-15 + 2.0668434110651124346e-434j)  +/-  (8.3e-39, 1.69e-98j)
| (0.00068836209924980539842 + 3.4364926285075838119e-426j)  +/-  (1.12e-27, 2.28e-87j)
| (3.5780940805939205415e-28 + 3.6254750559418169704e-441j)  +/-  (1.29e-44, 2.63e-104j)
| (2.1909730226027946265e-19 - 1.4179041742013641823e-436j)  +/-  (8.03e-41, 1.64e-100j)
| (6.2574837399567902388e-13 - 1.168059948457011285e-432j)  +/-  (5.38e-38, 1.1e-97j)
| (1.1516608812730394277e-10 + 4.1833748222651873775e-431j)  +/-  (5.79e-37, 1.18e-96j)
| (0.16237234131706341341 + 7.7864766050806504103e-424j)  +/-  (2.61e-25, 5.33e-85j)
| (8.5023057635739871786 + 7.5732549531241094559e-422j)  +/-  (2.21e-25, 4.51e-85j)
| (0.035280554345004396332 - 1.1328724801313230989e-424j)  +/-  (1.74e-26, 3.56e-86j)
| (6.2574837399567902388e-13 + 2.3012504616421810442e-433j)  +/-  (1.28e-40, 2.61e-100j)
| (0.29909799493403518597 - 2.4166859973105315066e-423j)  +/-  (8.64e-28, 1.76e-87j)
| (0.00068836209924980539842 + 7.4787591409983432275e-427j)  +/-  (8.18e-34, 1.67e-93j)
| (9.4748477982440614722e-05 - 7.0421153738377693326e-427j)  +/-  (9.79e-34, 2e-93j)
| (8.9213626876284414905e-09 + 8.8350908757882643563e-431j)  +/-  (3.3e-39, 6.73e-99j)
| (0.16237234131706341341 + 1.2790963133044997115e-423j)  +/-  (8.87e-29, 1.81e-88j)
| (8.9213626876284414905e-09 - 1.3547526990064278292e-429j)  +/-  (6.51e-37, 1.33e-96j)
| (9.4748477982440614722e-05 - 9.9582957189591646166e-428j)  +/-  (4.72e-36, 9.62e-96j)
| (-8.4328291857873979202 - 7.6058040296707520272e-422j)  +/-  (2.17e-26, 4.43e-86j)
| (1.1516608812730394277e-10 - 5.4088937872899889125e-432j)  +/-  (2.11e-40, 4.3e-100j)
| (0.0028322953000650992362 - 1.3605353203530246886e-425j)  +/-  (6.22e-34, 1.27e-93j)
| (7.5057998972159853767e-06 + 1.1298772849512208742e-428j)  +/-  (7.95e-38, 1.62e-97j)
| (3.4710119536953028874e-07 - 1.1035762007997513993e-429j)  +/-  (8.56e-39, 1.75e-98j)
| (0.0099852962824786327578 + 1.4394159620229471223e-425j)  +/-  (3.26e-35, 6.63e-95j)
| (7.5057998972159853767e-06 + 1.6482783453648788201e-427j)  +/-  (6.3e-38, 1.28e-97j)
| (0.29909799493403518597 - 2.6425829162070940352e-423j)  +/-  (2.5e-32, 5.08e-92j)
| (-8.4328291857873979202 - 1.1158174343009904722e-421j)  +/-  (5.14e-33, 1.04e-92j)
| (0.0099852962824786327578 + 3.8836901400676096324e-425j)  +/-  (4.8e-36, 1.03e-95j)
| (-0.15967206496143272882 + 4.1319444714010843291e-423j)  +/-  (1.18e-33, 2.54e-93j)
| (0.035280554345004396332 - 5.3167927807938846725e-425j)  +/-  (4.07e-36, 8.74e-96j)
| (0.0028322953000650992362 - 3.9842562263879581006e-426j)  +/-  (2.1e-37, 4.5e-97j)
| (8.5023057635739871786 + 1.109041136081088188e-421j)  +/-  (4.9e-33, 9.92e-93j)
