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Methinks it's trivlal:

sage: R.<k>=PolynomialRing(GF(17))
sage: L=(k^2-8).roots();L
[(12, 1), (5, 1)]
sage: [u[0]^2 for u in L]
[8, 8]

Methinks it's trivlal:

sage: R.<k>=PolynomialRing(GF(17))
sage: L=(k^2-8).roots();L
[(12, 1), (5, 1)]
sage: [u[0]^2 for u in L]
[8, 8]

Works because:

sage: [u[0].parent() for u in L]
[Finite Field of size 17, Finite Field of size 17]