# Represent field element in normal basis

Hi there

I'm having a normal basis, which is a basis of Fpn over Fp where (n=2)
NB = [zeta, zeta**p]
and a point
P = E2.change_ring(Fpn).random_element()
I would like to find a,b in Fp such that
P = a*NB[0] + b*NB[1]

Naive solutions result is memory overflow, and the Solve() function can't give me solutions with a,b in Fp. Any ideas?

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