Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 10 27
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P2 : t^12 - 8477/152*t^10 + 155745/152*t^8 - 563535/76*t^6 + 1500975/76*t^4 - 2132865/152*t^2 + 110565/152
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 1699639380422035860256037577242097457139069086751030885127668113/3001274150096298538197763983249131033182108938674908184943480*t^37 + 429038355398161828889365226829014092834850702404758995488208614483/3001274150096298538197763983249131033182108938674908184943480*t^35 - 533049603789158595716920276153755704608537316001901051840412807104/25010617917469154484981366527076091943184241155624234874529*t^33 + 11955739752686559052290081116677820992027048285126439151931313433975637/5702420885182967222575751568173348963046006983482325551392612*t^31 - 6980141574796706827799742155234405169264882622136575795065168664339109935/48470577524055221391893888329473466185891059359599767186837202*t^29 + 115176643142478710710959655623903327755254378329666384904492026276213686823/16156859174685073797297962776491155395297019786533255728945734*t^27 - 8363250599208407524714214059977106889245227514701700379796747864060268710441/32313718349370147594595925552982310790594039573066511457891468*t^25 + 224490439976626866576254251492728378039515044964962910461158640589651579645025/32313718349370147594595925552982310790594039573066511457891468*t^23 - 4457950272987217811258900752797397368931558409773362882313239946493232410148525/32313718349370147594595925552982310790594039573066511457891468*t^21 + 65100226833919698386864763466479028260636450459354111720081347429947781014318875/32313718349370147594595925552982310790594039573066511457891468*t^19 - 36328817951232693326533790555835867144409653611257517008108782735771584452238025/1700722018387902504978732923841174252136528398582447971467972*t^17 + 16118831651746527488539500069580430975484992231105622715199678977381473939699075/100042471669876617939925466108304367772736964622496939498116*t^15 - 41967068385153612784794529032567349060705185663024948511005616076786351464027125/50021235834938308969962733054152183886368482311248469749058*t^13 + 144491275364217657236794189962572293766728030337639753528702270453908978451590875/50021235834938308969962733054152183886368482311248469749058*t^11 - 617701484603890637377782810605947576933461268949791875174171242766079622363353125/100042471669876617939925466108304367772736964622496939498116*t^9 + 744438523489061730674210229680924396640027797758851058299742535680153277155724625/100042471669876617939925466108304367772736964622496939498116*t^7 - 861997151104789622846530095616976968546854726133670627466957836366972677372729875/200084943339753235879850932216608735545473929244993878996232*t^5 + 177595302715239927795297542804004741059911257736318979116767128220130502678180625/200084943339753235879850932216608735545473929244993878996232*t^3 - 3754787818672758098787787105763695113486284272662569056150835774027216450529375/100042471669876617939925466108304367772736964622496939498116*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
Positive weights:   39 out of 39
Indefinite weights: 0 out of 39
Negative weights:   0 out of 39
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-9.2982040285931542005 - 2.2130602082981744519e-279j)  +/-  (5.7e-120, 5.7e-120j)
| (5.7589581694700072331 + 4.1691205818702545443e-280j)  +/-  (1.59e-118, 1.59e-118j)
| (9.2982040285931542005 - 2.4128469685348865602e-281j)  +/-  (5.9e-120, 5.9e-120j)
| (-10.300236483869175435 - 2.6256435313212307636e-281j)  +/-  (6.35e-121, 6.35e-121j)
| (7.7167636320902943423 + 1.033084027533281603e-279j)  +/-  (6.07e-119, 6.07e-119j)
| (-8.4642850412999055551 - 2.7257860868234765054e-279j)  +/-  (2.47e-119, 2.47e-119j)
| (6.3740625321822819242 - 3.9934430888952583348e-282j)  +/-  (1.39e-118, 1.39e-118j)
| (4.8698256059449177862 + 1.539074539243122558e-282j)  +/-  (1.86e-118, 1.86e-118j)
| (-6.3740625321822819242 - 1.3100715425962863402e-280j)  +/-  (1.41e-118, 1.41e-118j)
| (4.488594599570059626 + 7.4984207743310168772e-294j)  +/-  (6.45e-119, 6.45e-119j)
| (10.300236483869175435 + 1.0216385999742182824e-296j)  +/-  (5.91e-121, 5.91e-121j)
| (-7.0249403331530214827 + 1.2990570851831040093e-292j)  +/-  (1.06e-118, 1.06e-118j)
| (2.3878901860240018729 + 1.5223635485539111453e-303j)  +/-  (7.8e-122, 7.8e-122j)
| (-4.488594599570059626 - 1.2190494045432912335e-306j)  +/-  (6.43e-119, 6.43e-119j)
| (-7.7167636320902943423 + 4.0101827066501491597e-315j)  +/-  (5.82e-119, 5.82e-119j)
| (-2.3878901860240018729 + 1.6191637921264333645e-316j)  +/-  (8.05e-122, 8.05e-122j)
| (8.4642850412999055551 + 4.7359426940893502565e-321j)  +/-  (2.66e-119, 2.66e-119j)
| (1.9137355618993510628 - 1.25708683583350748e-324j)  +/-  (1.05e-122, 1.05e-122j)
| (-1.9137355618993510628 - 6.8368611077118790046e-320j)  +/-  (1.05e-122, 1.05e-122j)
| (-2.8901633840314029187 + 1.5598043837114158693e-326j)  +/-  (4.17e-121, 4.17e-121j)
| (3.4151035307108390776 + 1.7537022596510507211e-334j)  +/-  (2.3e-120, 2.3e-120j)
| (1.4584639918590616358 - 1.3571140566341102938e-333j)  +/-  (1.4e-123, 1.4e-123j)
| (2.8901633840314029187 - 3.5949433137595488708e-334j)  +/-  (4.2e-121, 4.2e-121j)
| (2.3176569144660065272e-333 + 1.341191529373562741e-333j)  +/-  (1.04e-331, 1.04e-331j)
| (3.9544879426500450264 + 1.6601927917324258048e-334j)  +/-  (1.18e-119, 1.18e-119j)
| (-5.7589581694700072331 - 1.6304629378645530223e-338j)  +/-  (1.59e-118, 1.59e-118j)
| (-4.8698256059449177862 + 2.0084424977578718241e-348j)  +/-  (1.92e-118, 1.92e-118j)
| (-3.4151035307108390776 - 1.4278761409958263794e-354j)  +/-  (2.17e-120, 2.17e-120j)
| (7.0249403331530214827 + 9.1880901450666218774e-358j)  +/-  (1.03e-118, 1.03e-118j)
| (-1 + 7.9803327379733589913e-364j)  +/-  (1.09e-124, 1.09e-124j)
| (-3.9544879426500450264 + 8.3066640908849657249e-358j)  +/-  (1.12e-119, 1.12e-119j)
| (1 + 1.3656294023141516518e-370j)  +/-  (1.01e-124, 1.01e-124j)
| (0.54162798555458137652 + 2.8845941439963495499e-373j)  +/-  (1.25e-125, 1.25e-125j)
| (-5.2019365924015129919 + 2.5475051895815069806e-372j)  +/-  (2.15e-118, 2.15e-118j)
| (-0.54162798555458137652 + 1.2694682109164177445e-382j)  +/-  (1.12e-125, 1.12e-125j)
| (-0.23704314987094039888 + 2.2625809451921899499e-382j)  +/-  (2e-126, 2e-126j)
| (0.23704314987094039888 - 3.0837057159589705099e-382j)  +/-  (1.7e-126, 1.7e-126j)
| (5.2019365924015129919 - 2.5641562188675012963e-380j)  +/-  (2.29e-118, 2.29e-118j)
| (-1.4584639918590616358 + 1.1313033447176137364e-384j)  +/-  (1.42e-123, 1.42e-123j)
-------------------------------------------------
The weights are:
| (6.0158676885651676053e-20 + 2.5217433791222519517e-296j)  +/-  (1.78e-31, 7.77e-91j)
| (1.4923301070641353001e-08 - 2.9550734896360521582e-287j)  +/-  (4.93e-24, 2.15e-83j)
| (6.0158676885651676053e-20 - 7.1221063943807734427e-296j)  +/-  (3.28e-32, 1.43e-91j)
| (4.2175727769595684512e-24 - 1.0090391475099458959e-298j)  +/-  (6.58e-34, 2.87e-93j)
| (3.3514577130571290389e-14 - 5.6045779528471922177e-292j)  +/-  (2.79e-29, 1.22e-88j)
| (8.6616722624926784603e-17 - 3.7871008512680600873e-294j)  +/-  (4.45e-31, 1.94e-90j)
| (3.8012574401310846943e-10 - 6.0984941237045555812e-289j)  +/-  (2.34e-26, 1.02e-85j)
| (6.8760466410472000151e-07 - 4.4569893746350873494e-286j)  +/-  (2.42e-23, 1.05e-82j)
| (3.8012574401310846943e-10 - 1.9650026691428594717e-289j)  +/-  (6.41e-29, 2.79e-88j)
| (8.5393228801344546207e-06 + 7.0809899620216038555e-286j)  +/-  (8.46e-23, 3.69e-82j)
| (4.2175727769595684512e-24 + 2.4114687163143107285e-298j)  +/-  (2.75e-35, 1.2e-94j)
| (5.1359368138975699e-12 - 5.5480602416440796719e-291j)  +/-  (2.86e-30, 1.25e-89j)
| (0.011260524236889318217 + 2.671127798553722065e-284j)  +/-  (1.45e-18, 6.3e-78j)
| (8.5393228801344546207e-06 + 2.3723554873282672145e-287j)  +/-  (1.12e-26, 4.87e-86j)
| (3.3514577130571290389e-14 + 1.4137268461681681281e-292j)  +/-  (2.13e-31, 9.26e-91j)
| (0.011260524236889318217 + 8.4342589135196626165e-285j)  +/-  (6.76e-21, 2.94e-80j)
| (8.6616722624926784603e-17 + 6.26995042623071489e-294j)  +/-  (5.83e-33, 2.54e-92j)
| (0.029484432223803898655 - 7.0139764211583169285e-284j)  +/-  (1.13e-18, 4.94e-78j)
| (0.029484432223803898655 - 2.877187039071129578e-284j)  +/-  (1.54e-19, 6.71e-79j)
| (0.0031536435064733809421 - 2.1726803707468106799e-285j)  +/-  (4.07e-23, 1.77e-82j)
| (0.00062459202022999621591 + 3.3565098990512626022e-285j)  +/-  (3.31e-24, 1.44e-83j)
| (0.06249929548559794645 + 1.6688590585736780986e-283j)  +/-  (8.23e-19, 3.59e-78j)
| (0.0031536435064733809421 - 9.4511841145559239562e-285j)  +/-  (4.1e-23, 1.79e-82j)
| (0.14073949860449662476 + 4.8303659170779923783e-282j)  +/-  (7.05e-20, 3.07e-79j)
| (8.7072931905242411435e-05 - 1.3177875328462237119e-285j)  +/-  (2.31e-25, 1.01e-84j)
| (1.4923301070641353001e-08 + 8.1577047178415403601e-289j)  +/-  (2.47e-31, 1.08e-90j)
| (6.8760466410472000151e-07 - 1.8408877475621455755e-288j)  +/-  (3.47e-30, 1.51e-89j)
| (0.00062459202022999621591 + 5.1455412497665515106e-286j)  +/-  (2.17e-28, 9.44e-88j)
| (5.1359368138975699e-12 + 1.664379644501795513e-290j)  +/-  (2.02e-34, 8.8e-94j)
| (0.11211113952533940892 - 2.6064191019132890806e-283j)  +/-  (1.39e-24, 6.04e-84j)
| (8.7072931905242411435e-05 - 1.1465907930123786574e-286j)  +/-  (1.92e-29, 8.35e-89j)
| (0.11211113952533940892 - 4.0717374059966426899e-283j)  +/-  (2.1e-25, 9.19e-85j)
| (0.15072480540793186074 + 1.4201856784845837418e-282j)  +/-  (3.85e-25, 1.68e-84j)
| (2.5907783169555125841e-07 - 2.3350843786750362809e-288j)  +/-  (4.68e-31, 2.04e-90j)
| (0.15072480540793186074 + 1.1182178295492818651e-282j)  +/-  (6.23e-26, 2.73e-85j)
| (0.059675244045608347616 - 3.2615039809045376384e-282j)  +/-  (1.19e-25, 5.26e-85j)
| (0.059675244045608347616 - 3.6198817976360042312e-282j)  +/-  (9.95e-26, 4.36e-85j)
| (2.5907783169555125841e-07 + 1.7661685433689571115e-286j)  +/-  (4.4e-32, 2.07e-91j)
| (0.06249929548559794645 + 8.6068409278162301254e-284j)  +/-  (8.4e-28, 3.21e-87j)
