Starting with polynomial:
P : 16*t^4 - 12*t^2 + 1
Extension levels are: 4 30
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P1 : 16*t^4 - 12*t^2 + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^34 - 132*t^32 + 496*t^30 - 4495/4*t^28 + 27405/16*t^26 - 118755/64*t^24 + 94185/64*t^22 - 444015/512*t^20 + 1562275/4096*t^18 - 2042975/16384*t^16 + 245157/8192*t^14 - 676039/131072*t^12 + 323323/524288*t^10 - 101745/2097152*t^8 + 4845/2097152*t^6 - 969/16777216*t^4 + 153/268435456*t^2 - 1/1073741824
-------------------------------------------------
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: 1
  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:
| (-0.99597429399523902958 - 2.2843216725588841872e-404j)  +/-  (2.22e-117, 2.22e-117j)
| (0.99597429399523902958 - 1.6637917037077328179e-416j)  +/-  (2.28e-117, 2.28e-117j)
| (-0.93623487063973720951 - 1.159639042911732845e-415j)  +/-  (7.61e-117, 7.61e-117j)
| (0.22252093395631440429 - 1.1316810169794970147e-435j)  +/-  (3.63e-125, 3.63e-125j)
| (0.90096886790241912624 + 2.5775028529223250491e-427j)  +/-  (5.79e-117, 5.79e-117j)
| (0.96396286069585329189 + 1.8003009325731938128e-426j)  +/-  (8.6e-117, 8.6e-117j)
| (0.9839295885986296554 + 1.0541083867702149106e-427j)  +/-  (6.33e-117, 6.33e-117j)
| (-0.90096886790241912624 - 1.8698527282379647227e-426j)  +/-  (6.33e-117, 6.33e-117j)
| (-0.96396286069585329189 - 6.2897983310366077767e-436j)  +/-  (9.69e-117, 9.69e-117j)
| (0.93623487063973720951 + 1.891741670097735428e-444j)  +/-  (8.46e-117, 8.46e-117j)
| (0.85844879360186611853 - 4.6594332410974382707e-446j)  +/-  (3.07e-117, 3.07e-117j)
| (-0.9839295885986296554 - 4.4675446864870108224e-444j)  +/-  (7.53e-117, 7.53e-117j)
| (-0.85844879360186611853 + 7.0074575525363462699e-453j)  +/-  (3.05e-117, 3.05e-117j)
| (-0.6910626489868646759 + 2.5584863262322883023e-461j)  +/-  (5.25e-119, 5.25e-119j)
| (-0.13423326581765547604 - 2.4013055242935839349e-468j)  +/-  (2.34e-126, 2.34e-126j)
| (0.75307146600361093353 - 4.8675430347286761231e-459j)  +/-  (2.43e-118, 2.43e-118j)
| (0.8090169943749474241 + 5.9733748088834593407e-460j)  +/-  (8.67e-118, 8.67e-118j)
| (-0.39302503165392361819 - 2.506689831224161067e-464j)  +/-  (1.05e-122, 1.05e-122j)
| (-0.75307146600361093353 + 1.5915998073188507803e-460j)  +/-  (2.35e-118, 2.35e-118j)
| (-0.8090169943749474241 + 6.4206750713015588051e-465j)  +/-  (7.82e-118, 7.82e-118j)
| (0.62348980185873353053 - 1.4089340660034566688e-467j)  +/-  (8.7e-120, 8.7e-120j)
| (0.6910626489868646759 + 2.1504948938719770232e-470j)  +/-  (5.56e-119, 5.56e-119j)
| (0.13423326581765547604 + 2.4403017856856389191e-478j)  +/-  (2.11e-126, 2.11e-126j)
| (-0.55089698145210252269 + 4.362093891653368144e-469j)  +/-  (1.34e-120, 1.34e-120j)
| (-0.47386866247299867071 + 8.1928620687466533219e-471j)  +/-  (1.27e-121, 1.27e-121j)
| (0.044864830350514925458 + 1.0747821369561033668e-477j)  +/-  (9.31e-128, 9.31e-128j)
| (0.47386866247299867071 - 1.4435084646617203202e-471j)  +/-  (1.12e-121, 1.12e-121j)
| (0.3090169943749474241 + 3.3002819530309629293e-474j)  +/-  (5.43e-124, 5.43e-124j)
| (-0.22252093395631440429 + 5.9487529708520649146e-475j)  +/-  (3.63e-125, 3.63e-125j)
| (-0.62348980185873353053 - 2.2619289305117197837e-473j)  +/-  (8.66e-120, 8.66e-120j)
| (-0.3090169943749474241 - 5.4285430091516666429e-478j)  +/-  (5.54e-124, 5.54e-124j)
| (0.39302503165392361819 - 3.2967009883339131093e-474j)  +/-  (1.18e-122, 1.18e-122j)
| (0.55089698145210252269 - 1.5461847898784772484e-474j)  +/-  (1.57e-120, 1.57e-120j)
| (-0.044864830350514925458 + 1.0399743786208104167e-481j)  +/-  (9.31e-128, 9.31e-128j)
-------------------------------------------------
The weights are:
| (0.00022957730573386206578 - 9.7505385646538682026e-406j)  +/-  (1.75e-21, 2.42e-77j)
| (0.00022957730573386206578 + 2.6327407158801892679e-408j)  +/-  (4.94e-22, 6.85e-78j)
| (0.0035275504856627009495 + 1.3488680627974603901e-405j)  +/-  (6.26e-22, 8.68e-78j)
| (0.027156698112891701803 + 5.0910855152420792441e-406j)  +/-  (3.26e-22, 4.52e-78j)
| (0.0053787171163038067068 + 6.4771155647906393889e-407j)  +/-  (1.11e-22, 1.53e-78j)
| (0.0020221600914019125925 + 2.3568429790203633119e-407j)  +/-  (7.59e-23, 1.05e-78j)
| (0.00091093041943232557845 - 1.0509894534953527913e-407j)  +/-  (6.8e-23, 9.44e-79j)
| (0.0053787171163038067068 - 1.2932650885818407494e-405j)  +/-  (6.42e-24, 8.9e-80j)
| (0.0020221600914019125925 - 1.4430044662476293022e-405j)  +/-  (5.6e-24, 7.77e-80j)
| (0.0035275504856627009495 - 4.1703870228329208105e-407j)  +/-  (2.7e-23, 3.75e-79j)
| (0.0075161619646714475613 - 9.2585838610797908289e-407j)  +/-  (1.53e-24, 2.12e-80j)
| (0.00091093041943232557845 + 1.7276122833945456607e-405j)  +/-  (4.21e-24, 5.84e-80j)
| (0.0075161619646714475613 + 1.2484471331569817971e-405j)  +/-  (2.65e-25, 3.68e-81j)
| (0.014926640433578784649 - 1.1182665142149785134e-405j)  +/-  (1.03e-26, 1.43e-82j)
| (0.028056612295655047027 + 7.4373071989819961849e-406j)  +/-  (1.06e-27, 1.46e-83j)
| (0.012368096202604921771 - 1.6153213855263519254e-406j)  +/-  (9.55e-27, 1.32e-82j)
| (0.0098711857946436082271 + 1.2492560928069910377e-406j)  +/-  (4.66e-26, 6.47e-82j)
| (0.02415803784266949537 - 9.1524665269389307021e-406j)  +/-  (8.39e-29, 1.16e-84j)
| (0.012368096202604921771 + 1.1631280885988726556e-405j)  +/-  (1.16e-27, 1.61e-83j)
| (0.0098711857946436082271 - 1.2061023394213535091e-405j)  +/-  (2.9e-27, 4.03e-83j)
| (0.01746458477080449149 - 2.4634525455823319848e-406j)  +/-  (9.71e-30, 1.35e-85j)
| (0.014926640433578784649 + 2.0211322806365730926e-406j)  +/-  (4.44e-29, 6.16e-85j)
| (0.028056612295655047027 - 5.6706688049294888702e-406j)  +/-  (4.34e-31, 6.03e-87j)
| (0.019900357595056051688 - 1.0213690265642439891e-405j)  +/-  (1.36e-30, 1.89e-86j)
| (0.02215567116360146461 + 9.6935709467960076722e-406j)  +/-  (9.61e-31, 1.33e-86j)
| (0.028513918485646271851 + 6.2579279009119250938e-406j)  +/-  (8.3e-32, 1.15e-87j)
| (0.02215567116360146461 - 3.4432712410682878905e-406j)  +/-  (1.67e-32, 2.32e-88j)
| (0.025843099919642106059 - 4.5237047755344628982e-406j)  +/-  (2.26e-32, 3.14e-88j)
| (0.027156698112891701803 - 8.0204750873385471646e-406j)  +/-  (9.59e-33, 1.33e-88j)
| (0.01746458477080449149 + 1.0710440390451386723e-405j)  +/-  (2.29e-32, 3.17e-88j)
| (0.025843099919642106059 + 8.5935404230900551586e-406j)  +/-  (8.73e-33, 1.21e-88j)
| (0.02415803784266949537 + 3.9729846077870718435e-406j)  +/-  (8.31e-34, 1.17e-89j)
| (0.019900357595056051688 + 2.9387589560603273781e-406j)  +/-  (6.27e-34, 9.01e-90j)
| (0.028513918485646271851 - 6.848313938169383912e-406j)  +/-  (9.55e-34, 1.24e-89j)
