How to compute a finite field nth root using a provided factorization?

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Bonjour,

if I have a finite field factorization which too complex to be compute
automatically. For example, let s say
218882428718392752222464057452572750886963111572978236626890378946452262085=
83=C2=B9=C2=B2=E2=88=921=3D2
=C3=97 2 =C3=97 2 =C3=97 2 =C3=97 2 =C3=97 3 =C3=97 3 =C3=97 3 =C3=97 5 =C3=
=97 7 =C3=97 11 =C3=97 13 =C3=97 17 =C3=97 29 =C3=97 67 =C3=97 163 =C3=97 2=
29 =C3=97
311 =C3=97 397 =C3=97 983 =C3=97 3769 =C3=97 4051 =C3=97 11003 =C3=97 43913=
 =C3=97 1400587 =C3=97 5830087 =C3=97
32159167 =C3=97 405928799 =C3=97 11465965001 =C3=97 41692944763 =C3=97 1520=
01576931 =C3=97
52920684769483 =C3=97 3005054907817151659 =C3=97 3388996819669187238034903 =
=C3=97
13427688667394608761327070753331941386769 =C3=97
104348903484733242407804502753091803656481823949 =C3=97
641469669835476619879596836179377083193590415350574158759835060588161590591=
53647304344187619
=C3=97 292709098791663788479256587 =C3=97 120512159921899177054359774877548=
4291 =C3=97
1299287670584980812472075235801753046609485536283861463811601644579 =C3=97
641770527576080033169847928211903939472904736144195303864791214519176411228=
05418393835009573667434937689392838890413030823815490004914389366996109
=C3=97 493356762637 =C3=97 493356762637 =C3=97 2126437289207585950861 =C3=
=97
999583392375668473878196519781537317030864416227463205181407249320239784466=
025001570156606898657304482428213741734451272417306338613370083558474075107=
5324811175115719549874430103358645783161654857

Then, how can I provide such a factorization to Pari/gp in order to compute
arbitrary nth roots? I m meaning, doing the reverse of Modexp.

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<div dir=3D"auto"><div dir=3D"auto">Bonjour,</div><div dir=3D"auto"><br></d=
iv>if I have a finite field factorization which too complex to be compute a=
utomatically. For example, let s say 21888242871839275222246405745257275088=
696311157297823662689037894645226208583=C2=B9=C2=B2=E2=88=921=3D2 =C3=97 2 =
=C3=97 2 =C3=97 2 =C3=97 2 =C3=97 3 =C3=97 3 =C3=97 3 =C3=97 5 =C3=97 7 =C3=
=97 11 =C3=97 13 =C3=97 17 =C3=97 29 =C3=97 67 =C3=97 163 =C3=97 229 =C3=97=
 311 =C3=97 397 =C3=97 983 =C3=97 3769 =C3=97 4051 =C3=97 11003 =C3=97 4391=
3 =C3=97 1400587 =C3=97 5830087 =C3=97 32159167 =C3=97 405928799 =C3=97 114=
65965001 =C3=97 41692944763 =C3=97 152001576931 =C3=97 52920684769483 =C3=
=97 3005054907817151659 =C3=97 3388996819669187238034903 =C3=97 13427688667=
394608761327070753331941386769 =C3=97 1043489034847332424078045027530918036=
56481823949 =C3=97 64146966983547661987959683617937708319359041535057415875=
983506058816159059153647304344187619 =C3=97 292709098791663788479256587 =C3=
=97 1205121599218991770543597748775484291 =C3=97 12992876705849808124720752=
35801753046609485536283861463811601644579 =C3=97 64177052757608003316984792=
821190393947290473614419530386479121451917641122805418393835009573667434937=
689392838890413030823815490004914389366996109 =C3=97 493356762637 =C3=97 49=
3356762637 =C3=97 2126437289207585950861 =C3=97 999583392375668473878196519=
781537317030864416227463205181407249320239784466025001570156606898657304482=
428213741734451272417306338613370083558474075107532481117511571954987443010=
3358645783161654857<div dir=3D"auto"><br></div><div dir=3D"auto">Then, how =
can I provide such a factorization to Pari/gp in order to compute arbitrary=
 nth roots? I m meaning, doing the reverse of Modexp.</div></div>

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