Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 8 23
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Trying to find an order 8 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Trying to find an order 23 Kronrod extension for:
P2 : 35/8*t^12 - 87219/8284*t^10 + 102069/11336*t^8 - 891429/269230*t^6 + 24664563/47599864*t^4 - 792603/23799932*t^2 + 30429/47599864
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^35 - 4044919947170060412234577744319258448018898382798751939285017895849448073/113679553841204601080213963276120624183714623441482817959974000968830072*t^33 + 12304431051462329185629714353634421600039241180695148798953346030292815036777/93596165995925121556042829764005980577925039966820853453711927464336759280*t^31 - 17867620165749883499623397028071916638341968067312997921112151479280380127482639/61180693839336387790466663055738575971103667791645231207576363252521461649360*t^29 + 7101739859530976262016844152382075795264544608170716466226023512807476587207107693/16318367822319550329629642715039237418499547254081926323813902405457017443372400*t^27 - 1130722010172653348069903741966166351905261199682006160577130773772632355381570317/2460307763980486049698007670882838872327624047538505814975019131899673399154608*t^25 + 40971859457503546519676717797740400855208003126875901217306000116583618093435874023/115634464907082844335806360531493426999398330234309773303825899199284649760266576*t^23 - 3345065988185116206928894180307140352868159539757171730498431929858788688237514797/16519209272440406333686622933070489571342618604901396186260842742754949965752368*t^21 + 1424922652240613422195912642145568902151547684424549152068468999468099194224085025/16519209272440406333686622933070489571342618604901396186260842742754949965752368*t^19 - 118801128424259053282995359065988051984758846008799396498939686693742946650080003/4347160334852738508864900771860655150353320685500367417437063879672355254145360*t^17 + 74549292136212240546325127366161237304383318807885980981040710341528285048051357/11682536765427779622983153502865861488092369371621995799129185115287556388871312*t^15 - 46858479042263260861360396236065984876083724003109359873625575235797946596375568611/43369470652189727220387793520472366464294905897251389071633911542985838500953267248*t^13 + 73693785057975703861415949056052071659098940063608925330268549615822627509430193/569580289991234691449745881131907251876293323228442257976430357975423770181374992*t^11 - 18968340026165507338497410973030755395430208999928515435291304302722002301448577/1796368606895432488418429317416015178994463557874317890541049590537874967495105744*t^9 + 9258193959146349150774798258966101837827400830410497983896835228434396978274083/16680565635457587392456843661720140947805733037404380412166889054994553269597410480*t^7 - 1657524886388088365013782045818562159258486472586668215268581268722894710291311/96747280685654006876249693237976817497273251616945406390567956518968408963664980784*t^5 + 25367191170078443472880331193597938474789499668455174714995335673085233771897/96747280685654006876249693237976817497273251616945406390567956518968408963664980784*t^3 - 238819177050725744668791662714502359228587066179854049664388318422338607407/179673521273357441341606573156242661066364610145755754725340490678084188075377821456*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:
| (-0.99884297579022614604 + 2.2723655638572794592e-438j)  +/-  (6.08e-117, 6.08e-117j)
| (-0.99089327061916926742 + 3.8743613482068231691e-439j)  +/-  (1.34e-116, 1.34e-116j)
| (-0.90813994197979583444 - 1.8121234436927685691e-439j)  +/-  (3.85e-117, 3.85e-117j)
| (0.90813994197979583444 - 2.3542999513539759257e-438j)  +/-  (3.9e-117, 3.9e-117j)
| (0.5012491364137743572 - 1.851367100382244707e-446j)  +/-  (5.15e-121, 5.15e-121j)
| (0.94558845994204580589 - 2.465633768140377373e-440j)  +/-  (7.74e-117, 7.74e-117j)
| (0.99089327061916926742 - 6.7073251332053605063e-441j)  +/-  (1.33e-116, 1.33e-116j)
| (-0.94558845994204580589 + 9.2612718760587156275e-444j)  +/-  (7.73e-117, 7.73e-117j)
| (-0.9732162594524303742 - 4.2152009753782709554e-446j)  +/-  (1.19e-116, 1.19e-116j)
| (0.9732162594524303742 - 5.1754857712397614495e-444j)  +/-  (1.21e-116, 1.21e-116j)
| (0.86113631159405257522 - 1.0902156044745594734e-447j)  +/-  (1.56e-117, 1.56e-117j)
| (0.99884297579022614604 - 1.1811059018427725493e-447j)  +/-  (6.36e-117, 6.36e-117j)
| (-0.86113631159405257522 - 1.9051497891643217866e-453j)  +/-  (1.47e-117, 1.47e-117j)
| (-0.80497769557985231531 - 2.0588077348707038457e-453j)  +/-  (4.24e-118, 4.24e-118j)
| (-0.096144508783968409195 + 1.834042944236469152e-455j)  +/-  (1.4e-126, 1.4e-126j)
| (0.80497769557985231531 + 4.7709137598769666509e-452j)  +/-  (4.5e-118, 4.5e-118j)
| (0.58757432536053971849 + 7.6507690534361425452e-455j)  +/-  (3.24e-120, 3.24e-120j)
| (-0.3399810435848562648 - 1.7328384344909813493e-455j)  +/-  (9.73e-122, 9.73e-122j)
| (-0.74020101558163220772 - 1.2710633202698799263e-454j)  +/-  (1e-118, 1e-118j)
| (-0.35241611849142175407 + 3.2895138214960682943e-459j)  +/-  (1.78e-121, 1.78e-121j)
| (0.24740203806840584977 - 3.1724677793193494448e-455j)  +/-  (7.37e-124, 7.37e-124j)
| (0.74020101558163220772 - 6.0569729513121616163e-459j)  +/-  (9.91e-119, 9.91e-119j)
| (0.18035397587349104032 - 9.5506733303624994321e-462j)  +/-  (4.46e-125, 4.46e-125j)
| (-0.58757432536053971849 - 1.8624024167178971628e-467j)  +/-  (3.08e-120, 3.08e-120j)
| (-0.5012491364137743572 + 1.0485948746488636624e-468j)  +/-  (5.26e-121, 5.26e-121j)
| (0.096144508783968409195 + 1.5988659339287047464e-468j)  +/-  (1.65e-126, 1.65e-126j)
| (0.6674742407002819824 - 4.8381760202085067518e-473j)  +/-  (2.01e-119, 2.01e-119j)
| (0.3399810435848562648 - 7.2413670065219538819e-484j)  +/-  (1.04e-121, 1.04e-121j)
| (-0.18035397587349104032 - 3.1625900348860743619e-495j)  +/-  (5.02e-125, 5.02e-125j)
| (-0.6674742407002819824 + 4.5673585998472275677e-499j)  +/-  (2.02e-119, 2.02e-119j)
| (-0.24740203806840584977 - 3.6862260019793254769e-502j)  +/-  (6.59e-124, 6.59e-124j)
| (0.35241611849142175407 + 5.621526452468118393e-508j)  +/-  (1.44e-121, 1.44e-121j)
| (0.40643846808514921201 + 1.3125093922619055236e-511j)  +/-  (1.36e-121, 1.36e-121j)
| (8.6342356818233918856e-520 - 2.6506211420238594276e-520j)  +/-  (3.16e-518, 3.16e-518j)
| (-0.40643846808514921201 + 1.3430065846232771979e-513j)  +/-  (1.38e-121, 1.38e-121j)
-------------------------------------------------
The weights are:
| (0.0035783161129047237778 + 2.19314809130923905e-438j)  +/-  (1.9e-17, 6.54e-73j)
| (0.012705475150886710871 - 2.7300268367450915018e-438j)  +/-  (1.49e-17, 5.1e-73j)
| (0.042281354876594927073 + 4.8180098347729801698e-439j)  +/-  (1.59e-18, 5.46e-74j)
| (0.042281354876594927073 + 3.682256000669843643e-439j)  +/-  (5.54e-19, 1.9e-74j)
| (0.089440527459790156371 + 6.2569820118237565886e-438j)  +/-  (2.67e-19, 9.18e-75j)
| (0.032571541053790848943 + 2.0260167064011026673e-438j)  +/-  (2.55e-19, 8.75e-75j)
| (0.012705475150886710871 + 4.5658645949612641588e-439j)  +/-  (4.28e-20, 1.47e-75j)
| (0.032571541053790848943 - 7.7805925998354759386e-439j)  +/-  (4.81e-19, 1.65e-74j)
| (0.022661435561542535001 + 9.3149346498688390285e-439j)  +/-  (9.54e-19, 3.27e-74j)
| (0.022661435561542535001 - 8.5772895520946344979e-439j)  +/-  (2.56e-20, 8.79e-76j)
| (0.051659261236686895222 - 2.8383272924190372193e-438j)  +/-  (1.75e-21, 6.02e-77j)
| (0.0035783161129047237778 - 1.5214799422633431177e-439j)  +/-  (1.11e-20, 3.82e-76j)
| (0.051659261236686895222 - 2.6311412010025539861e-439j)  +/-  (5.44e-22, 1.87e-77j)
| (0.060568393163662404313 + 3.7578179692832348385e-439j)  +/-  (1.07e-22, 3.69e-78j)
| (0.09298209806225260727 + 1.428269485610107321e-437j)  +/-  (5.71e-25, 1.96e-80j)
| (0.060568393163662404313 + 1.8292915303361191915e-438j)  +/-  (3.54e-23, 1.22e-78j)
| (0.083214797115677346867 - 3.0237580478656857242e-438j)  +/-  (4.62e-24, 1.59e-79j)
| (0.22566162932837561194 - 1.3760261142310272863e-436j)  +/-  (1.85e-25, 6.34e-81j)
| (0.06887336876757824708 - 5.0109089031969244399e-439j)  +/-  (1.83e-25, 6.29e-81j)
| (-0.16377158390581035418 + 1.4187489585901908636e-436j)  +/-  (1.68e-25, 5.77e-81j)
| (0.071170310745930190563 + 3.6215217751701957387e-437j)  +/-  (3.11e-27, 1.07e-82j)
| (0.06887336876757824708 - 1.7133990658131290292e-438j)  +/-  (2.18e-26, 7.47e-82j)
| (0.072427526105215291545 - 2.6897197018814539856e-437j)  +/-  (2.22e-27, 7.61e-83j)
| (0.083214797115677346867 - 1.3330618265711155967e-438j)  +/-  (4.72e-28, 1.62e-83j)
| (0.089440527459790156371 + 3.2193913086255927377e-438j)  +/-  (4.63e-28, 1.59e-83j)
| (0.09298209806225260727 + 1.6046820414647836878e-437j)  +/-  (1.92e-28, 6.58e-84j)
| (0.076449482253911448919 + 2.027034299032475672e-438j)  +/-  (2.25e-28, 7.74e-84j)
| (0.22566162932837561194 - 2.1075425235137583037e-436j)  +/-  (7.85e-29, 2.7e-84j)
| (0.072427526105215291545 - 2.1585220740078173336e-437j)  +/-  (1.6e-29, 5.49e-85j)
| (0.076449482253911448919 + 7.4672175614143197447e-439j)  +/-  (3.07e-30, 1.05e-85j)
| (0.071170310745930190563 + 2.6707006155527764852e-437j)  +/-  (1.54e-29, 5.28e-85j)
| (-0.16377158390581035418 + 2.2101530060498070279e-436j)  +/-  (2.03e-29, 6.98e-85j)
| (0.10873911819442646572 - 3.3715850793561922109e-437j)  +/-  (3e-30, 1.03e-85j)
| (0.097573897433167885407 - 1.2247859856227984677e-437j)  +/-  (6.86e-31, 2.39e-86j)
| (0.10873911819442646572 - 2.0060703178189224305e-437j)  +/-  (8.96e-31, 2.95e-86j)
