Starting with polynomial:
P : t
Extension levels are: 1 6 30
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : t^7 - 21/13*t^5 + 105/143*t^3 - 35/429*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^37 - 19944450506125491474555725506986657/2193874699098371736365588642099257*t^35 + 11907690248195282591317342971110813850/313724081971067158300279175820193751*t^33 - 8253592974312346806657769053406349950/85561113264836497718257957041871023*t^31 + 290118902286244654028453995297476088830/1739742636385008786937911793184710801*t^29 - 21303915579818200477443734210877270454618/102644815546715518429336795797897937259*t^27 + 28804127317654168865183082137012091112194/150019345799045757704415316935389292917*t^25 - 20160235952416026830398832469559995318450/150019345799045757704415316935389292917*t^23 + 570518084388431596220444054292602158504800/7951025327349425158334011797575632524601*t^21 - 232623049149210078440061747710695803508800/7951025327349425158334011797575632524601*t^19 + 3791054066250393023225946173788814712090/418475017228917113596526936714506974979*t^17 - 41388205799759719587147698604326119971630/19668325809759104339036766025581827824013*t^15 + 7068794392867000651202586946943034535450/19668325809759104339036766025581827824013*t^13 - 728793365950827706863697507029524386950/16642429531334626748415725098569238928011*t^11 + 883550098083304351148503992107059360185150/242726808818237106648052729521705337176144433*t^9 - 11483784383176702021352922164718720510270/59536764427114762008012933656267346854525993*t^7 + 2633132894124615010893821509692751616805/450778359233868912346383640540309911898553947*t^5 - 37401668860355446843932502710127229325/450778359233868912346383640540309911898553947*t^3 + 157724205505896542453249967182843100/450778359233868912346383640540309911898553947*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:
| (-0.99784612344852210871 + 4.7009583849709685517e-843j)  +/-  (1.98e-243, 1.98e-243j)
| (-0.98868775153792583362 - 1.7514708121586798599e-844j)  +/-  (5.26e-243, 5.26e-243j)
| (-0.91927944102079721186 - 8.9763285383650184272e-847j)  +/-  (4.08e-243, 4.08e-243j)
| (0.99784612344852210871 - 8.4616779542945857684e-853j)  +/-  (1.87e-243, 1.87e-243j)
| (0.94910791234275852453 - 2.9830764001748977867e-871j)  +/-  (6e-243, 6e-243j)
| (0.91927944102079721186 + 7.8898634532048888535e-894j)  +/-  (4.08e-243, 4.08e-243j)
| (0.083003770784361174585 - 2.3100011879153943271e-916j)  +/-  (1.88e-254, 1.88e-254j)
| (-0.84148519136966672985 - 1.2145811990021185203e-904j)  +/-  (9e-244, 9e-244j)
| (-0.97235933101661391008 - 3.4987598163030488094e-905j)  +/-  (6.79e-243, 6.79e-243j)
| (0.98868775153792583362 + 6.2324361031944931857e-918j)  +/-  (5.35e-243, 5.35e-243j)
| (0.8832767929424487679 + 1.6992430802450716265e-938j)  +/-  (2.01e-243, 2.01e-243j)
| (0.97235933101661391008 + 3.1125105334152075251e-952j)  +/-  (6.88e-243, 6.88e-243j)
| (-0.94910791234275852453 + 1.680402280861900686e-959j)  +/-  (6.68e-243, 6.68e-243j)
| (-0.8832767929424487679 - 1.7652839258876481374e-963j)  +/-  (2.05e-243, 2.05e-243j)
| (0.32766326206750472751 - 2.1259706585984325298e-972j)  +/-  (1.3e-250, 1.3e-250j)
| (0.84148519136966672985 - 9.7073218999785967477e-964j)  +/-  (8.51e-244, 8.51e-244j)
| (0.79418608920443608857 + 1.0761547125975737383e-969j)  +/-  (2.74e-244, 2.74e-244j)
| (-0.32766326206750472751 - 9.9988975599985329293e-977j)  +/-  (1.34e-250, 1.34e-250j)
| (-0.79418608920443608857 + 8.7816246352738803878e-971j)  +/-  (2.8e-244, 2.8e-244j)
| (-0.74153118559939443986 + 1.1995143371004867727e-970j)  +/-  (7.5e-245, 7.5e-245j)
| (0.74153118559939443986 - 2.6203065564143095012e-972j)  +/-  (7.49e-245, 7.49e-245j)
| (0.6836267794908846579 + 4.3345171749934002571e-974j)  +/-  (1.33e-245, 1.33e-245j)
| (0.24736277927426844744 - 1.911304733805583728e-979j)  +/-  (7.22e-252, 7.22e-252j)
| (-0.6836267794908846579 + 1.3195134293962306285e-972j)  +/-  (1.35e-245, 1.35e-245j)
| (-0.55301677795294993595 + 4.0790609976494285044e-974j)  +/-  (2.61e-247, 2.61e-247j)
| (-7.5282068694985008005e-987 - 1.7290801295235149113e-986j)  +/-  (6.98e-985, 6.98e-985j)
| (0.62066801549804592241 + 2.2909736785021118677e-975j)  +/-  (2.13e-246, 2.13e-246j)
| (0.40584515137739716691 + 1.7763785833167043209e-979j)  +/-  (1.91e-249, 1.91e-249j)
| (-0.24736277927426844744 + 9.461136163279479504e-981j)  +/-  (6.97e-252, 6.97e-252j)
| (-0.62066801549804592241 - 1.0294263819931700382e-977j)  +/-  (2.21e-246, 2.21e-246j)
| (-0.16561533960274229959 + 1.0414300285417933234e-984j)  +/-  (3.68e-253, 3.68e-253j)
| (0.48119644370188802369 - 2.8048654964285833583e-978j)  +/-  (2.65e-248, 2.65e-248j)
| (0.55301677795294993595 + 7.8849764484337492103e-980j)  +/-  (2.48e-247, 2.48e-247j)
| (-0.083003770784361174585 - 1.5177738480238393739e-986j)  +/-  (2.13e-254, 2.13e-254j)
| (-0.48119644370188802369 + 4.6898448335524032587e-980j)  +/-  (2.69e-248, 2.69e-248j)
| (-0.40584515137739716691 - 5.631273453697115538e-981j)  +/-  (2.04e-249, 2.04e-249j)
| (0.16561533960274229959 - 2.6951978170454632788e-985j)  +/-  (3.39e-253, 3.39e-253j)
-------------------------------------------------
The weights are:
| (0.0055233890375594599817 + 6.0276536780817417615e-843j)  +/-  (6.02e-78, 5.99e-197j)
| (0.012774881318304376365 - 1.0224835984029247338e-842j)  +/-  (4.52e-78, 4.5e-197j)
| (0.032984273377196113203 + 6.080956017413875289e-843j)  +/-  (1.13e-78, 1.13e-197j)
| (0.0055233890375594599817 + 1.3325312166926301044e-845j)  +/-  (7.04e-80, 7.01e-199j)
| (0.026604240521257812184 - 1.6414803085862500655e-844j)  +/-  (5.78e-80, 5.75e-199j)
| (0.032984273377196113203 + 2.484557450837453983e-844j)  +/-  (2.7e-80, 2.69e-199j)
| (0.082877613582536741195 - 2.0504043266190474776e-843j)  +/-  (2.15e-81, 2.14e-200j)
| (0.044580500545529285986 + 5.5041555065505526557e-843j)  +/-  (1.2e-80, 1.19e-199j)
| (0.019840306608032177794 + 7.6588684334381340389e-843j)  +/-  (1.52e-79, 1.51e-198j)
| (0.012774881318304376365 - 4.7784377463930942243e-845j)  +/-  (1.95e-80, 1.94e-199j)
| (0.038955182334462597699 - 3.5070592083683294845e-844j)  +/-  (1.55e-81, 1.55e-200j)
| (0.019840306608032177794 + 9.7784699118566686501e-845j)  +/-  (1.85e-80, 1.84e-199j)
| (0.026604240521257812184 - 6.5933746869416773296e-843j)  +/-  (3.92e-81, 3.89e-200j)
| (0.038955182334462597699 - 5.7686311011772150703e-843j)  +/-  (1.04e-81, 1.03e-200j)
| (0.079358260246263605714 + 1.4786530564616118012e-843j)  +/-  (9e-85, 8.96e-204j)
| (0.044580500545529285986 + 4.67304260761479322e-844j)  +/-  (5.45e-83, 5.43e-202j)
| (0.049994006957314969876 - 5.9083334546662194536e-844j)  +/-  (8.74e-84, 8.69e-203j)
| (0.079358260246263605714 + 2.9249906959903517817e-843j)  +/-  (1.83e-86, 1.82e-205j)
| (0.049994006957314969876 - 5.2037749313288626377e-843j)  +/-  (7.87e-85, 7.83e-204j)
| (0.055300648389456925753 + 4.8425537695714237533e-843j)  +/-  (1.3e-85, 1.3e-204j)
| (0.055300648389456925753 + 7.1308320184866186987e-844j)  +/-  (8.12e-86, 8.08e-205j)
| (0.060476983761351915134 - 8.2964977221375780611e-844j)  +/-  (1.28e-86, 1.27e-205j)
| (0.081129899764044997566 - 1.6575124200117594983e-843j)  +/-  (3.82e-88, 3.8e-207j)
| (0.060476983761351915134 - 4.4421709136791740079e-843j)  +/-  (8.34e-88, 8.3e-207j)
| (0.069834373713649097773 - 3.6846040005273148665e-843j)  +/-  (5.28e-89, 5.25e-208j)
| (0.083066028892579217223 + 2.2434388384599030398e-843j)  +/-  (1.32e-89, 1.31e-208j)
| (0.065380003545605083425 + 9.4211385773796562755e-844j)  +/-  (7.97e-89, 7.92e-208j)
| (0.076885977280834051781 - 1.3195630617928264006e-843j)  +/-  (1.13e-89, 1.12e-208j)
| (0.081129899764044997566 - 2.750471967377502502e-843j)  +/-  (2.05e-90, 2.04e-209j)
| (0.065380003545605083425 + 4.0444934139025581203e-843j)  +/-  (9.92e-90, 9.87e-209j)
| (0.08226739095185697825 + 2.5883032659852295054e-843j)  +/-  (1.27e-90, 1.26e-209j)
| (0.073699053618454201709 + 1.1801486934032609825e-843j)  +/-  (1.81e-90, 1.8e-209j)
| (0.069834373713649097773 - 1.0564789388174854124e-843j)  +/-  (2.21e-90, 2.19e-209j)
| (0.082877613582536741195 - 2.4225583419388439896e-843j)  +/-  (2.39e-91, 2.38e-210j)
| (0.073699053618454201709 + 3.3793941307282528492e-843j)  +/-  (3.39e-92, 3.38e-211j)
| (0.076885977280834051781 - 3.1294672512733234353e-843j)  +/-  (3e-92, 3.01e-211j)
| (0.08226739095185697825 + 1.851292795649807831e-843j)  +/-  (3.12e-92, 2.9e-211j)
