Starting with polynomial:
P : 32*t^5 - 160*t^3 + 120*t
Extension levels are: 5 30
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P1 : 32*t^5 - 160*t^3 + 120*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 32*t^35 - 36667355455313852560/4256846092236523*t^33 + 56643703084468513494960/55338999199074799*t^31 - 3929929157530576676405400/55338999199074799*t^29 + 177448293953340737099814300/55338999199074799*t^27 - 423359817264248763032780310/4256846092236523*t^25 + 9281170339532839691857375875/4256846092236523*t^23 - 291646999300640212199260087875/8513692184473046*t^21 + 3296117890883236042963216906875/8513692184473046*t^19 - 26671328422527460722501960691875/8513692184473046*t^17 + 1220701216787354988249729668551125/68109537475784368*t^15 - 9667412788224924999384295401118125/136219074951568736*t^13 + 51320671215794239602878423977213125/272438149903137472*t^11 - 174250264424743566925960433267053125/544876299806274944*t^9 + 352869158324049282774870833487290625/1089752599612549888*t^7 - 381800909229719498805617740400000625/2179505199225099776*t^5 + 363316518321535437119816600393465625/8718020796900399104*t^3 - 48655971603572547475483629402909375/17436041593800798208*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:
| (4.4871737991773953589 - 1.9915476883208057129e-428j)  +/-  (1.89e-119, 1.89e-119j)
| (2.7964770311687679036 + 1.5834539191227594579e-430j)  +/-  (1.37e-120, 1.37e-120j)
| (5.9743597146209338801 - 1.7182784174753845746e-429j)  +/-  (6.69e-120, 6.69e-120j)
| (-6.5655367354006416806 + 1.5378526814456822002e-428j)  +/-  (2e-120, 2e-120j)
| (2.4031949871126608932 - 3.0192139472589565661e-431j)  +/-  (3.51e-121, 3.51e-121j)
| (3.2000313836191566712 - 1.9967681007243059731e-429j)  +/-  (3.69e-120, 3.69e-120j)
| (7.2753705942326492943 - 1.5123661772267312317e-431j)  +/-  (2.22e-121, 2.22e-121j)
| (-7.2753705942326492943 - 2.0209840014170625729e-430j)  +/-  (2.23e-121, 2.23e-121j)
| (-4.4871737991773953589 + 2.0433739403360109105e-427j)  +/-  (1.98e-119, 1.98e-119j)
| (5.443836788420729291 - 1.1384424067687679254e-435j)  +/-  (1.4e-119, 1.4e-119j)
| (4.0429608327090546096 + 3.6828959133227427254e-435j)  +/-  (1.55e-119, 1.55e-119j)
| (-4.9518852599067314586 - 2.5012555277368020177e-434j)  +/-  (2.18e-119, 2.18e-119j)
| (-5.443836788420729291 + 3.5512056973253801397e-438j)  +/-  (1.39e-119, 1.39e-119j)
| (-1.648969472452039135 + 3.2983902028976201832e-448j)  +/-  (1.6e-122, 1.6e-122j)
| (4.9518852599067314586 - 3.6299936289942050738e-445j)  +/-  (1.96e-119, 1.96e-119j)
| (1.293404401515679164 - 5.5558606229327348241e-450j)  +/-  (2.69e-123, 2.69e-123j)
| (-3.2000313836191566712 - 8.3415201286561861351e-446j)  +/-  (3.78e-120, 3.78e-120j)
| (-5.9743597146209338801 - 6.853011275845346899e-454j)  +/-  (6.73e-120, 6.73e-120j)
| (-1.293404401515679164 + 3.1968083974403294996e-463j)  +/-  (2.6e-123, 2.6e-123j)
| (2.0201828704560856329 - 1.3145139052415669953e-465j)  +/-  (8.14e-122, 8.14e-122j)
| (-4.0429608327090546096 - 7.2562587014619638148e-465j)  +/-  (1.67e-119, 1.67e-119j)
| (0.95857246461381850711 - 1.1786170017771604576e-475j)  +/-  (3.93e-124, 3.93e-124j)
| (6.5655367354006416806 + 1.278980648055786029e-472j)  +/-  (1.74e-120, 1.74e-120j)
| (-2.4031949871126608932 - 3.0922938714955347837e-471j)  +/-  (3.91e-121, 3.91e-121j)
| (-0.95857246461381850711 + 1.3288189145193641638e-477j)  +/-  (3.69e-124, 3.69e-124j)
| (-2.0201828704560856329 + 4.5783134640212513848e-475j)  +/-  (7.17e-122, 7.17e-122j)
| (-2.7964770311687679036 + 7.2460011292003568575e-474j)  +/-  (1.38e-120, 1.38e-120j)
| (0.64145027129324503664 + 5.5375177566315958362e-487j)  +/-  (3.54e-125, 3.54e-125j)
| (-3.6148880225954548669 - 1.7428129245125466002e-483j)  +/-  (7.69e-120, 7.69e-120j)
| (-0.64145027129324503664 - 3.6414142921137770691e-495j)  +/-  (3.54e-125, 3.54e-125j)
| (1.389657497209293208e-507 - 6.5310442640627960958e-507j)  +/-  (2.34e-505, 2.34e-505j)
| (0.32488479740304182769 - 9.9275918909713214547e-496j)  +/-  (3.62e-126, 3.62e-126j)
| (1.648969472452039135 + 3.927568805876865428e-493j)  +/-  (1.49e-122, 1.49e-122j)
| (3.6148880225954548669 - 2.7033060667182319724e-493j)  +/-  (7.46e-120, 7.46e-120j)
| (-0.32488479740304182769 + 6.7075008890600967218e-502j)  +/-  (3.62e-126, 3.62e-126j)
-------------------------------------------------
The weights are:
| (4.6097662557545466136e-10 + 1.1433999831656324291e-436j)  +/-  (3.46e-28, 7.96e-87j)
| (9.0230553318848784231e-05 - 1.912656953323807113e-433j)  +/-  (1.18e-21, 2.71e-80j)
| (9.8850994161068998369e-17 - 8.0463395350178996793e-441j)  +/-  (7.04e-33, 1.62e-91j)
| (6.8112785432033285407e-20 - 3.0000873575433706577e-442j)  +/-  (4.13e-36, 9.52e-95j)
| (0.00067972905160785349282 + 4.5420164701714477341e-433j)  +/-  (1.69e-20, 3.88e-79j)
| (8.2384093221061490034e-06 + 4.7955872555432674163e-434j)  +/-  (5.14e-24, 1.18e-82j)
| (4.7456008330932688705e-24 - 9.2436825220638640315e-445j)  +/-  (1.48e-36, 3.41e-95j)
| (4.7456008330932688705e-24 + 1.5737990074790160704e-444j)  +/-  (3.64e-38, 8.38e-97j)
| (4.6097662557545466136e-10 + 4.5499896434714561608e-436j)  +/-  (1.67e-32, 3.84e-91j)
| (3.8679294968337051153e-14 + 2.1311965367727525282e-439j)  +/-  (2.07e-32, 4.77e-91j)
| (1.9574690099418951812e-08 - 9.5688462773357575024e-436j)  +/-  (1.43e-28, 3.29e-87j)
| (6.0321811890228792013e-12 + 1.9891456342903058219e-437j)  +/-  (4.86e-34, 1.12e-92j)
| (3.8679294968337051153e-14 - 6.6589506597483971666e-439j)  +/-  (2.37e-35, 5.47e-94j)
| (0.013549931729645334154 - 6.7216757566907922118e-433j)  +/-  (2.17e-25, 5e-84j)
| (6.0321811890228792013e-12 - 3.1773444291767641717e-438j)  +/-  (1.41e-32, 3.24e-91j)
| (0.036628248681828682623 - 2.4783449136589857783e-432j)  +/-  (1.74e-23, 4.02e-82j)
| (8.2384093221061490034e-06 - 1.6146434327151790123e-434j)  +/-  (1.37e-31, 3.15e-90j)
| (9.8850994161068998369e-17 + 1.8640711423007576718e-440j)  +/-  (7.37e-37, 1.7e-95j)
| (0.036628248681828682623 + 1.1860455336714708436e-432j)  +/-  (8.19e-26, 1.89e-84j)
| (0.0035972141212609487698 - 8.6156890069850024474e-433j)  +/-  (5.14e-28, 1.19e-86j)
| (1.9574690099418951812e-08 - 1.6195796918090070974e-435j)  +/-  (2.85e-33, 6.57e-92j)
| (0.072938082276899393499 + 3.4988123971732598481e-432j)  +/-  (1.19e-26, 2.75e-85j)
| (6.8112785432033285407e-20 + 1.5495257985869273395e-442j)  +/-  (2.43e-38, 5.6e-97j)
| (0.00067972905160785349282 - 1.3348419542469607883e-433j)  +/-  (9.79e-31, 2.26e-89j)
| (0.072938082276899393499 - 1.615470093014110335e-432j)  +/-  (5.41e-28, 1.25e-86j)
| (0.0035972141212609487698 + 3.2082547577239611768e-433j)  +/-  (6.17e-30, 1.42e-88j)
| (9.0230553318848784231e-05 + 4.906564681864046886e-434j)  +/-  (1e-31, 2.31e-90j)
| (0.11727240762826873729 - 3.7919843535799991114e-432j)  +/-  (3.67e-29, 8.57e-88j)
| (5.019644714041299729e-07 + 4.932468205878104543e-435j)  +/-  (2.33e-33, 5.36e-92j)
| (0.11727240762826873729 + 1.4271115693859454432e-432j)  +/-  (1.05e-29, 2.37e-88j)
| (0.1844609959801014002 - 1.292704570874727612e-432j)  +/-  (8.94e-30, 2.1e-88j)
| (0.16300489755158830661 + 2.9094789444262014069e-432j)  +/-  (9.32e-30, 2.24e-88j)
| (0.013549931729645334154 + 1.4951287510270619184e-432j)  +/-  (1.18e-31, 2.8e-90j)
| (5.019644714041299729e-07 + 9.7942488417904726709e-435j)  +/-  (6.04e-35, 1.54e-93j)
| (0.16300489755158830661 - 3.4822496874517890623e-433j)  +/-  (2.37e-30, 4.65e-89j)
