# Finding roots of a polynomial over an extension field

Apologies if I am not articulating this very well. I am still in an early learning phase.

I am trying to find the roots of a polynomial s^37 + 7 over a finite field of size 241 and modulus x^32 + 44.

My code is as follows:

`K.<x> = GF(241)[]`

`T.<a> = K.quotient(x^32 + 44)`

`J.<s> = T[]`

`G = s^32 + 7`

`G.roots()`

and here I get : 'root finding with multiplicities for this polynomial not implemented (try the multiplicities=False option)'

I think I expressed this correctly as some sanity-checking with known roots is correctly evaluated as follows:

rootList = [20*a^29, 51*a^13, 221*a^13]

for r in rootList: assert(G(r) == 0)

It does not appear root finding is implemented for G.

Is there some alternative way to find the roots of G?

Thank you.