Starting with polynomial:
P : -t+1
Extension levels are: 1 25
-------------------------------------------------
Trying to find an order 25 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^26 + 4140972253716543832520800751/6370314939029062417031376*t^25 - 1242378627702950459727622289375/6370314939029062417031376*t^24 + 4762813704477923887169977376250/132714894563105467021487*t^23 - 602545930779550074960546824938750/132714894563105467021487*t^22 + 55680303716935408493589248932864750/132714894563105467021487*t^21 - 3898010858079162175228321043056899750/132714894563105467021487*t^20 + 211629679597918390067304702259899450000/132714894563105467021487*t^19 - 9048279156808009380306935832216348150000/132714894563105467021487*t^18 + 307683684783358250717762891098370410275000/132714894563105467021487*t^17 - 8370287345735053932215359065647921098635000/132714894563105467021487*t^16 + 182656377046831811925815169828141087192960000/132714894563105467021487*t^15 - 3197125115662714867705912185363470653968000000/132714894563105467021487*t^14 + 44770066130205947639488217503389384686256000000/132714894563105467021487*t^13 - 38384656908247323182595347625491696690352000000/10208838043315805155499*t^12 + 337892251706227014719535706950655204394419200000/10208838043315805155499*t^11 - 2323894215517927934576555330017962786746035200000/10208838043315805155499*t^10 + 12308695750044200413744834566009385825054560000000/10208838043315805155499*t^9 - 49263414869040887808441752358314869246919520000000/10208838043315805155499*t^8 + 145305933011815995806422734044926323473157120000000/10208838043315805155499*t^7 - 305446258522866210590225777357835221970207744000000/10208838043315805155499*t^6 + 436959396285914111065227182238173059596309504000000/10208838043315805155499*t^5 - 398064358072792699323128445298766261478220800000000/10208838043315805155499*t^4 + 208406224444427699401959590108818624984473600000000/10208838043315805155499*t^3 - 52461792314331374728044880764544509222297600000000/10208838043315805155499*t^2 + 4283400073920377948856786438125125452066816000000/10208838043315805155499*t - 6650514521066766970245844381658824175616000000/10208838043315805155499
-------------------------------------------------
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:   26 out of 26
Indefinite weights: 0 out of 26
Negative weights:   0 out of 26
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (87.13551145057008375 + 1.3746794500299223687e-255j)  +/-  (8.68e-118, 8.68e-118j)
| (40.612306645767330025 - 1.6406590106963521664e-253j)  +/-  (2.08e-114, 2.08e-114j)
| (75.316697988628794942 - 1.2035096829664616808e-258j)  +/-  (1.35e-116, 1.35e-116j)
| (66.169065990266211109 + 5.774420882058708589e-256j)  +/-  (8.66e-116, 8.66e-116j)
| (58.493291444660217413 + 6.9792482724246838053e-259j)  +/-  (2.82e-115, 2.82e-115j)
| (14.95967791121370029 + 4.9147997792725815088e-266j)  +/-  (6.48e-116, 6.48e-116j)
| (8.3382429864224724091 + 2.577892856463153582e-271j)  +/-  (8.69e-118, 8.69e-118j)
| (12.510894639398484096 - 3.3853148904229096251e-269j)  +/-  (1.85e-116, 1.85e-116j)
| (51.822232505706910799 + 1.1368143738291133315e-267j)  +/-  (7.42e-115, 7.42e-115j)
| (17.66762562177802964 + 4.0847327201261277725e-273j)  +/-  (1.78e-115, 1.78e-115j)
| (3.746494347437049646 + 3.5330538791320922778e-282j)  +/-  (2.48e-120, 2.48e-120j)
| (20.65129137489465965 - 3.8848137031111698768e-276j)  +/-  (4.55e-115, 4.55e-115j)
| (0.14285310028475523527 - 1.325092011300607259e-296j)  +/-  (2.38e-126, 2.38e-126j)
| (2.6323097316811975498 - 1.7885578048971388867e-296j)  +/-  (2.66e-121, 2.66e-121j)
| (45.91140348844115999 + 4.2730429598911021492e-289j)  +/-  (1.37e-114, 1.37e-114j)
| (10.307559653070123597 - 4.2287849790159953641e-302j)  +/-  (4.21e-117, 4.21e-117j)
| (0.001583129020456320998 + 6.586028005390517075e-322j)  +/-  (6.61e-129, 6.61e-129j)
| (35.826133392834375588 + 1.0747063986162412535e-309j)  +/-  (2.33e-114, 2.33e-114j)
| (27.531037531814798769 - 1.3352584000871722687e-331j)  +/-  (1.55e-114, 1.55e-114j)
| (23.930824433971589908 - 5.5042552585194274272e-349j)  +/-  (8.79e-115, 8.79e-115j)
| (1.7179982968830053032 + 8.2781119716585638246e-369j)  +/-  (2.15e-122, 2.15e-122j)
| (1 + 6.4253226070061060929e-370j)  +/-  (1.47e-123, 1.47e-123j)
| (6.5933922323283044099 - 1.2060235529352960956e-362j)  +/-  (1.37e-118, 1.37e-118j)
| (31.482954524056955323 - 3.3439903487046997695e-360j)  +/-  (2.07e-114, 2.07e-114j)
| (5.0650249361176568358 + 8.0819405292745862918e-376j)  +/-  (2.03e-119, 2.03e-119j)
| (0.47559109184154913664 - 4.069155743733985039e-381j)  +/-  (8.57e-125, 8.57e-125j)
-------------------------------------------------
The weights are:
| (2.0322703166974146385e-37 - 5.4104315678883964171e-282j)  +/-  (1.64e-40, 7.4e-96j)
| (1.1582025734847967024e-17 + 9.5010769826156407596e-271j)  +/-  (5.38e-33, 2.42e-88j)
| (1.9828456656361950635e-32 + 2.2655350313172660585e-279j)  +/-  (3.35e-39, 1.51e-94j)
| (1.5218584507815307492e-28 - 2.6952072545189134841e-277j)  +/-  (3.48e-38, 1.56e-93j)
| (2.8132629208092591562e-25 + 1.6562445172541479087e-275j)  +/-  (2.62e-37, 1.18e-92j)
| (8.2038442643862976756e-07 - 1.9714566710743457954e-266j)  +/-  (3.44e-27, 1.55e-82j)
| (0.00044385261373078181791 + 3.6448116496917165397e-265j)  +/-  (4.41e-23, 1.99e-78j)
| (8.5668219702221153603e-06 + 5.8155647974878948713e-266j)  +/-  (5.42e-26, 2.44e-81j)
| (1.9520649782759698772e-22 - 6.9591320689207157248e-274j)  +/-  (3.49e-37, 1.57e-92j)
| (6.0365747258820996714e-08 + 5.9789247688435174004e-267j)  +/-  (2.23e-29, 1e-84j)
| (0.028686946913257229204 - 2.5652251201565590405e-264j)  +/-  (3.77e-21, 1.7e-76j)
| (3.361322831521642616e-09 - 1.6217451268212434743e-267j)  +/-  (4.98e-31, 2.24e-86j)
| (0.20572597471798749796 + 6.2564071558604224895e-264j)  +/-  (1.75e-20, 7.86e-76j)
| (0.072888857820904113247 + 3.9690000090467253459e-264j)  +/-  (1.68e-20, 7.57e-76j)
| (6.4265447999735494758e-20 + 2.6711455502417102342e-272j)  +/-  (6.53e-37, 2.94e-92j)
| (6.958316223961219417e-05 - 1.5369196554979158386e-265j)  +/-  (1.44e-27, 6.48e-83j)
| (0.040014224447538748384 - 2.693094708360584232e-264j)  +/-  (7.03e-22, 3.17e-77j)
| (1.2571196596344636977e-15 - 4.1362847349522354411e-270j)  +/-  (8.82e-36, 3.97e-91j)
| (4.1667326468594498114e-12 - 8.7128114910100119162e-269j)  +/-  (1.18e-34, 5.3e-90j)
| (1.3897522039373725996e-10 + 3.9458840566604219269e-268j)  +/-  (8.95e-34, 4.04e-89j)
| (0.14634495643186369814 - 5.4916808652792737338e-264j)  +/-  (4.4e-27, 1.99e-82j)
| (0.22838563618326615167 + 6.7359763784775107635e-264j)  +/-  (7.57e-27, 3.43e-82j)
| (0.0022394906688523041761 - 7.7671739669885862393e-265j)  +/-  (6.43e-30, 2.91e-85j)
| (8.7929878897090532924e-14 + 1.8135884622494307161e-269j)  +/-  (1.23e-35, 5.53e-91j)
| (0.0089809525546723586811 + 1.4885484257447451822e-264j)  +/-  (1.43e-29, 6.51e-85j)
| (0.26621007340898960176 - 7.1771237749898452115e-264j)  +/-  (3.97e-28, 1.67e-83j)
Starting with polynomial:
P : -t+1
Extension levels are: 1 25
-------------------------------------------------
Trying to find an order 25 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^26 + 4140972253716543832520800751/6370314939029062417031376*t^25 - 1242378627702950459727622289375/6370314939029062417031376*t^24 + 4762813704477923887169977376250/132714894563105467021487*t^23 - 602545930779550074960546824938750/132714894563105467021487*t^22 + 55680303716935408493589248932864750/132714894563105467021487*t^21 - 3898010858079162175228321043056899750/132714894563105467021487*t^20 + 211629679597918390067304702259899450000/132714894563105467021487*t^19 - 9048279156808009380306935832216348150000/132714894563105467021487*t^18 + 307683684783358250717762891098370410275000/132714894563105467021487*t^17 - 8370287345735053932215359065647921098635000/132714894563105467021487*t^16 + 182656377046831811925815169828141087192960000/132714894563105467021487*t^15 - 3197125115662714867705912185363470653968000000/132714894563105467021487*t^14 + 44770066130205947639488217503389384686256000000/132714894563105467021487*t^13 - 38384656908247323182595347625491696690352000000/10208838043315805155499*t^12 + 337892251706227014719535706950655204394419200000/10208838043315805155499*t^11 - 2323894215517927934576555330017962786746035200000/10208838043315805155499*t^10 + 12308695750044200413744834566009385825054560000000/10208838043315805155499*t^9 - 49263414869040887808441752358314869246919520000000/10208838043315805155499*t^8 + 145305933011815995806422734044926323473157120000000/10208838043315805155499*t^7 - 305446258522866210590225777357835221970207744000000/10208838043315805155499*t^6 + 436959396285914111065227182238173059596309504000000/10208838043315805155499*t^5 - 398064358072792699323128445298766261478220800000000/10208838043315805155499*t^4 + 208406224444427699401959590108818624984473600000000/10208838043315805155499*t^3 - 52461792314331374728044880764544509222297600000000/10208838043315805155499*t^2 + 4283400073920377948856786438125125452066816000000/10208838043315805155499*t - 6650514521066766970245844381658824175616000000/10208838043315805155499
-------------------------------------------------
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:   26 out of 26
Indefinite weights: 0 out of 26
Negative weights:   0 out of 26
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (87.13551145057008375 + 1.3746794500299223687e-255j)  +/-  (8.68e-118, 8.68e-118j)
| (40.612306645767330025 - 1.6406590106963521664e-253j)  +/-  (2.08e-114, 2.08e-114j)
| (75.316697988628794942 - 1.2035096829664616808e-258j)  +/-  (1.35e-116, 1.35e-116j)
| (66.169065990266211109 + 5.774420882058708589e-256j)  +/-  (8.66e-116, 8.66e-116j)
| (58.493291444660217413 + 6.9792482724246838053e-259j)  +/-  (2.82e-115, 2.82e-115j)
| (14.95967791121370029 + 4.9147997792725815088e-266j)  +/-  (6.48e-116, 6.48e-116j)
| (8.3382429864224724091 + 2.577892856463153582e-271j)  +/-  (8.69e-118, 8.69e-118j)
| (12.510894639398484096 - 3.3853148904229096251e-269j)  +/-  (1.85e-116, 1.85e-116j)
| (51.822232505706910799 + 1.1368143738291133315e-267j)  +/-  (7.42e-115, 7.42e-115j)
| (17.66762562177802964 + 4.0847327201261277725e-273j)  +/-  (1.78e-115, 1.78e-115j)
| (3.746494347437049646 + 3.5330538791320922778e-282j)  +/-  (2.48e-120, 2.48e-120j)
| (20.65129137489465965 - 3.8848137031111698768e-276j)  +/-  (4.55e-115, 4.55e-115j)
| (0.14285310028475523527 - 1.325092011300607259e-296j)  +/-  (2.38e-126, 2.38e-126j)
| (2.6323097316811975498 - 1.7885578048971388867e-296j)  +/-  (2.66e-121, 2.66e-121j)
| (45.91140348844115999 + 4.2730429598911021492e-289j)  +/-  (1.37e-114, 1.37e-114j)
| (10.307559653070123597 - 4.2287849790159953641e-302j)  +/-  (4.21e-117, 4.21e-117j)
| (0.001583129020456320998 + 6.586028005390517075e-322j)  +/-  (6.61e-129, 6.61e-129j)
| (35.826133392834375588 + 1.0747063986162412535e-309j)  +/-  (2.33e-114, 2.33e-114j)
| (27.531037531814798769 - 1.3352584000871722687e-331j)  +/-  (1.55e-114, 1.55e-114j)
| (23.930824433971589908 - 5.5042552585194274272e-349j)  +/-  (8.79e-115, 8.79e-115j)
| (1.7179982968830053032 + 8.2781119716585638246e-369j)  +/-  (2.15e-122, 2.15e-122j)
| (1 + 6.4253226070061060929e-370j)  +/-  (1.47e-123, 1.47e-123j)
| (6.5933922323283044099 - 1.2060235529352960956e-362j)  +/-  (1.37e-118, 1.37e-118j)
| (31.482954524056955323 - 3.3439903487046997695e-360j)  +/-  (2.07e-114, 2.07e-114j)
| (5.0650249361176568358 + 8.0819405292745862918e-376j)  +/-  (2.03e-119, 2.03e-119j)
| (0.47559109184154913664 - 4.069155743733985039e-381j)  +/-  (8.57e-125, 8.57e-125j)
-------------------------------------------------
The weights are:
| (2.0322703166974146385e-37 - 5.4104315678883964171e-282j)  +/-  (1.64e-40, 7.4e-96j)
| (1.1582025734847967024e-17 + 9.5010769826156407596e-271j)  +/-  (5.38e-33, 2.42e-88j)
| (1.9828456656361950635e-32 + 2.2655350313172660585e-279j)  +/-  (3.35e-39, 1.51e-94j)
| (1.5218584507815307492e-28 - 2.6952072545189134841e-277j)  +/-  (3.48e-38, 1.56e-93j)
| (2.8132629208092591562e-25 + 1.6562445172541479087e-275j)  +/-  (2.62e-37, 1.18e-92j)
| (8.2038442643862976756e-07 - 1.9714566710743457954e-266j)  +/-  (3.44e-27, 1.55e-82j)
| (0.00044385261373078181791 + 3.6448116496917165397e-265j)  +/-  (4.41e-23, 1.99e-78j)
| (8.5668219702221153603e-06 + 5.8155647974878948713e-266j)  +/-  (5.42e-26, 2.44e-81j)
| (1.9520649782759698772e-22 - 6.9591320689207157248e-274j)  +/-  (3.49e-37, 1.57e-92j)
| (6.0365747258820996714e-08 + 5.9789247688435174004e-267j)  +/-  (2.23e-29, 1e-84j)
| (0.028686946913257229204 - 2.5652251201565590405e-264j)  +/-  (3.77e-21, 1.7e-76j)
| (3.361322831521642616e-09 - 1.6217451268212434743e-267j)  +/-  (4.98e-31, 2.24e-86j)
| (0.20572597471798749796 + 6.2564071558604224895e-264j)  +/-  (1.75e-20, 7.86e-76j)
| (0.072888857820904113247 + 3.9690000090467253459e-264j)  +/-  (1.68e-20, 7.57e-76j)
| (6.4265447999735494758e-20 + 2.6711455502417102342e-272j)  +/-  (6.53e-37, 2.94e-92j)
| (6.958316223961219417e-05 - 1.5369196554979158386e-265j)  +/-  (1.44e-27, 6.48e-83j)
| (0.040014224447538748384 - 2.693094708360584232e-264j)  +/-  (7.03e-22, 3.17e-77j)
| (1.2571196596344636977e-15 - 4.1362847349522354411e-270j)  +/-  (8.82e-36, 3.97e-91j)
| (4.1667326468594498114e-12 - 8.7128114910100119162e-269j)  +/-  (1.18e-34, 5.3e-90j)
| (1.3897522039373725996e-10 + 3.9458840566604219269e-268j)  +/-  (8.95e-34, 4.04e-89j)
| (0.14634495643186369814 - 5.4916808652792737338e-264j)  +/-  (4.4e-27, 1.99e-82j)
| (0.22838563618326615167 + 6.7359763784775107635e-264j)  +/-  (7.57e-27, 3.43e-82j)
| (0.0022394906688523041761 - 7.7671739669885862393e-265j)  +/-  (6.43e-30, 2.91e-85j)
| (8.7929878897090532924e-14 + 1.8135884622494307161e-269j)  +/-  (1.23e-35, 5.53e-91j)
| (0.0089809525546723586811 + 1.4885484257447451822e-264j)  +/-  (1.43e-29, 6.51e-85j)
| (0.26621007340898960176 - 7.1771237749898452115e-264j)  +/-  (3.97e-28, 1.67e-83j)
