Starting with polynomial:
P : t^44 - 946*t^42 + 407253*t^40 - 105885780*t^38 + 18609425835*t^36 - 2344787655210*t^34 + 219237645762135*t^32 - 15534553185431280*t^30 + 844691329457825850*t^28 - 35477035837228685700*t^26 + 1153003664709932285250*t^24 - 28929910132721937339000*t^22 + 556900770054897293775750*t^20 - 8139318946956191216722500*t^18 + 88951128491735518297038750*t^16 - 711609027933884146376310000*t^14 + 4047276346373966082515263125*t^12 - 15712955227098927143882786250*t^10 + 39282388067747317859706965625*t^8 - 57889835047206573687989212500*t^6 + 43417376285404930265991909375*t^4 - 12404964652972837218854831250*t^2 + 563862029680583509947946875
Extension levels are: 44
-------------------------------------------------
Ending with final polynomial:
P : t^44 - 946*t^42 + 407253*t^40 - 105885780*t^38 + 18609425835*t^36 - 2344787655210*t^34 + 219237645762135*t^32 - 15534553185431280*t^30 + 844691329457825850*t^28 - 35477035837228685700*t^26 + 1153003664709932285250*t^24 - 28929910132721937339000*t^22 + 556900770054897293775750*t^20 - 8139318946956191216722500*t^18 + 88951128491735518297038750*t^16 - 711609027933884146376310000*t^14 + 4047276346373966082515263125*t^12 - 15712955227098927143882786250*t^10 + 39282388067747317859706965625*t^8 - 57889835047206573687989212500*t^6 + 43417376285404930265991909375*t^4 - 12404964652972837218854831250*t^2 + 563862029680583509947946875
-------------------------------------------------
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
Positive weights:   44 out of 44
Indefinite weights: 0 out of 44
Negative weights:   0 out of 44
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (7.193997236488432016 - 8.3134001122182829185e-544j)  +/-  (1.07e-244, 1.07e-244j)
| (-8.9728487036288647298 + 1.0906887112616357576e-556j)  +/-  (7.81e-245, 7.81e-245j)
| (10.339733507643281028 + 2.176427160615121662e-575j)  +/-  (1.15e-245, 1.15e-245j)
| (12.087760709058448891 - 7.2480620816176110085e-578j)  +/-  (1.76e-247, 1.76e-247j)
| (8.9728487036288647298 - 5.2755473079043925053e-574j)  +/-  (6.78e-245, 6.78e-245j)
| (-8.3535922949510002247 - 3.8549524344732999663e-579j)  +/-  (1.07e-244, 1.07e-244j)
| (-7.193997236488432016 + 3.2528182683138698538e-596j)  +/-  (1.04e-244, 1.04e-244j)
| (-12.087760709058448891 + 1.4249955593776889871e-606j)  +/-  (1.69e-247, 1.69e-247j)
| (7.7626863861635528943 - 1.0388339420557617613e-610j)  +/-  (1.27e-244, 1.27e-244j)
| (-10.339733507643281028 + 1.1689119063052201892e-616j)  +/-  (1.2e-245, 1.2e-245j)
| (9.629741154666466764 + 3.3213420146487975542e-631j)  +/-  (2.86e-245, 2.86e-245j)
| (5.0695002345897820947 - 1.5100734348244981408e-630j)  +/-  (9.39e-246, 9.39e-246j)
| (-11.132842524243940487 - 4.9208108287636793746e-636j)  +/-  (2.31e-246, 2.31e-246j)
| (11.132842524243940487 + 1.5929400925053532294e-646j)  +/-  (2.02e-246, 2.02e-246j)
| (-6.6431963997275934439 + 4.3283098021419383999e-670j)  +/-  (8.76e-245, 8.76e-245j)
| (1.6524879894793965418 - 6.041259229572042625e-694j)  +/-  (5.21e-251, 5.21e-251j)
| (2.6067914629874263111 + 1.0612273581947563345e-693j)  +/-  (4.34e-249, 4.34e-249j)
| (-6.1070758170297517375 - 1.2337784545017962517e-714j)  +/-  (4.68e-245, 4.68e-245j)
| (-2.1282421191854660575 - 1.249852683844124883e-738j)  +/-  (4.16e-250, 4.16e-250j)
| (-9.629741154666466764 + 2.6845279463875248564e-744j)  +/-  (3.53e-245, 3.53e-245j)
| (4.5644803021991296361 + 1.2697342387415783971e-758j)  +/-  (2.43e-246, 2.43e-246j)
| (3.5752229994251972775 - 5.8617622954497173474e-761j)  +/-  (1.26e-247, 1.26e-247j)
| (6.1070758170297517375 + 5.547383525740907704e-758j)  +/-  (4.12e-245, 4.12e-245j)
| (-7.7626863861635528943 - 2.3959242507759141457e-759j)  +/-  (1.14e-244, 1.14e-244j)
| (-3.0888559941420047415 - 2.8979410422751840739e-770j)  +/-  (2.99e-248, 2.99e-248j)
| (5.5831648296456221311 + 2.2000179074191233583e-766j)  +/-  (2.43e-245, 2.43e-245j)
| (6.6431963997275934439 + 1.1540677704723553325e-765j)  +/-  (9.18e-245, 9.18e-245j)
| (4.0667677904955582945 + 7.0987790220099003708e-769j)  +/-  (5.9e-247, 5.9e-247j)
| (-5.0695002345897820947 + 1.9299520811391471288e-766j)  +/-  (8.53e-246, 8.53e-246j)
| (-0.70672523810634546144 - 4.3612642127649310739e-781j)  +/-  (3.19e-253, 3.19e-253j)
| (-3.5752229994251972775 + 8.0299185029627218517e-774j)  +/-  (1.61e-247, 1.61e-247j)
| (-1.1788598033288554408 - 6.7360064348141058398e-779j)  +/-  (4.46e-252, 4.46e-252j)
| (1.1788598033288554408 - 1.2569619087990056919e-779j)  +/-  (4.55e-252, 4.55e-252j)
| (2.1282421191854660575 - 3.1541857614663364041e-777j)  +/-  (4.35e-250, 4.35e-250j)
| (-0.23547711817192248766 - 4.6266005488807251694e-781j)  +/-  (2.14e-254, 2.14e-254j)
| (-1.6524879894793965418 - 2.0808382959664820481e-777j)  +/-  (4.42e-251, 4.42e-251j)
| (-4.5644803021991296361 + 1.7988163404870781981e-771j)  +/-  (2.87e-246, 2.87e-246j)
| (-2.6067914629874263111 + 2.7269865303029686648e-779j)  +/-  (3.85e-249, 3.85e-249j)
| (0.70672523810634546144 + 2.9469002662699233055e-783j)  +/-  (3.46e-253, 3.46e-253j)
| (-4.0667677904955582945 - 2.0617150123137335566e-775j)  +/-  (6.82e-247, 6.82e-247j)
| (-5.5831648296456221311 - 3.2608299984665897936e-781j)  +/-  (2.46e-245, 2.46e-245j)
| (0.23547711817192248766 + 1.0340913318322791907e-795j)  +/-  (2.14e-254, 2.14e-254j)
| (3.0888559941420047415 - 3.3027127686065475953e-790j)  +/-  (2.4e-248, 2.4e-248j)
| (8.3535922949510002247 - 5.2743912589606336001e-786j)  +/-  (9.88e-245, 9.88e-245j)
-------------------------------------------------
The weights are:
| (1.289064815963905405e-12 + 3.8547277366128556495e-555j)  +/-  (1.97e-78, 3.23e-199j)
| (8.3466769815268154197e-19 + 5.333933094604980296e-560j)  +/-  (2.12e-83, 3.47e-204j)
| (1.809481070701213978e-24 + 4.0361822913876434976e-562j)  +/-  (1.36e-85, 2.22e-206j)
| (8.2152508931746107772e-33 + 1.7481693475243778407e-566j)  +/-  (7.15e-89, 1.17e-209j)
| (8.3466769815268154197e-19 + 4.8476714435294353236e-559j)  +/-  (3.84e-83, 6.29e-204j)
| (1.6934271103574151887e-16 - 7.9001665679387559754e-559j)  +/-  (1.14e-83, 1.86e-204j)
| (1.289064815963905405e-12 - 7.4482316530065661557e-557j)  +/-  (9.27e-82, 1.52e-202j)
| (8.2152508931746107772e-33 + 4.4369021335822545758e-567j)  +/-  (1.32e-91, 2.16e-212j)
| (1.8985180410046434985e-14 + 2.2869068873622560144e-556j)  +/-  (5.33e-83, 8.73e-204j)
| (1.809481070701213978e-24 + 7.2413368360070244517e-563j)  +/-  (1.34e-88, 2.2e-209j)
| (1.9815155999927581913e-21 - 1.7249764943035458317e-560j)  +/-  (2.25e-86, 3.69e-207j)
| (5.3341521628083075531e-07 + 3.2448351508359109688e-553j)  +/-  (2.95e-79, 4.83e-200j)
| (4.1536348608094469517e-28 - 1.0496454695745333803e-564j)  +/-  (2.71e-90, 4.44e-211j)
| (4.1536348608094469517e-28 - 4.8838385163975077397e-564j)  +/-  (1.71e-89, 2.81e-210j)
| (5.6565652041022443301e-11 + 5.1303198348824593951e-556j)  +/-  (1.96e-83, 3.22e-204j)
| (0.048334227295384228157 - 3.7446858372316007622e-551j)  +/-  (2.91e-68, 4.77e-189j)
| (0.0064079902183447021216 - 1.6471333412372191296e-551j)  +/-  (1.03e-73, 1.69e-194j)
| (1.6830458054045261776e-09 - 2.9112355744151827484e-555j)  +/-  (4.48e-83, 7.33e-204j)
| (0.019765680833827600822 - 1.4234810826822480565e-551j)  +/-  (2.4e-73, 3.92e-194j)
| (1.9815155999927581913e-21 - 2.4974241201996547759e-561j)  +/-  (6.11e-88, 1e-208j)
| (5.9805064978714269961e-06 - 8.778272769152959989e-553j)  +/-  (1.48e-80, 2.42e-201j)
| (0.00032690297263291108826 - 4.7158936814514431219e-552j)  +/-  (1.15e-78, 1.88e-199j)
| (1.6830458054045261776e-09 + 3.5625902993596633391e-554j)  +/-  (5.86e-84, 9.59e-205j)
| (1.8985180410046434985e-14 + 8.6953710192180998236e-558j)  +/-  (8.69e-87, 1.42e-207j)
| (0.0016368797268343002832 - 3.7137341243626962317e-552j)  +/-  (7.45e-81, 1.22e-201j)
| (3.5220801394023272e-08 - 1.0996774485533926149e-553j)  +/-  (3.45e-83, 5.66e-204j)
| (5.6565652041022443301e-11 - 1.288836621753579036e-554j)  +/-  (5.52e-85, 9.04e-206j)
| (5.0550243435022374764e-05 + 2.1459418000820214552e-552j)  +/-  (2.97e-81, 4.86e-202j)
| (5.3341521628083075531e-07 - 5.6212695977342223119e-554j)  +/-  (4.84e-86, 7.93e-207j)
| (0.14656144417140921121 + 4.5736099233335341782e-551j)  +/-  (3.82e-78, 6.25e-199j)
| (0.00032690297263291108826 + 1.584678759029758999e-552j)  +/-  (4.15e-84, 6.8e-205j)
| (0.094144716794965634412 - 3.4589187538968055144e-551j)  +/-  (7.63e-79, 1.25e-199j)
| (0.094144716794965634412 + 4.8146916941694080422e-551j)  +/-  (1.13e-78, 1.85e-199j)
| (0.019765680833827600822 + 2.6195564261903711085e-551j)  +/-  (9.84e-81, 1.61e-201j)
| (0.18276505685973116563 - 5.431309548794687908e-551j)  +/-  (9.5e-79, 1.56e-199j)
| (0.048334227295384228157 + 2.3457012207797422045e-551j)  +/-  (7.36e-81, 1.21e-201j)
| (5.9805064978714269961e-06 + 1.9630616994719164817e-553j)  +/-  (5.93e-86, 9.71e-207j)
| (0.0064079902183447021216 + 7.7093178970927637121e-552j)  +/-  (2.95e-83, 4.83e-204j)
| (0.14656144417140921121 - 5.5701106289859445452e-551j)  +/-  (9.75e-82, 1.6e-202j)
| (5.0550243435022374764e-05 - 5.9594995282490522046e-553j)  +/-  (1.74e-85, 2.85e-206j)
| (3.5220801394023272e-08 + 1.3863767728978866329e-554j)  +/-  (2.21e-87, 3.61e-208j)
| (0.18276505685973116563 + 5.7989018237910089867e-551j)  +/-  (6.66e-83, 1.06e-203j)
| (0.0016368797268343002832 + 9.3024285119549186289e-552j)  +/-  (1.89e-85, 2.8e-206j)
| (1.6934271103574151887e-16 - 1.0592365510005058052e-557j)  +/-  (1.69e-92, 3.03e-213j)
