Create a finite field F of order 81 with \texttt{F.<t>=FiniteField(3\^4)}.
(a) List the elements of F.
(b) Obtain the generators of F with F.gens().
(c) Obtain the first generator of F and save it as u with u = F.0 (alternatively, u = F.gen(0)).
(d) Compute the first 80 powers of u and comment.
(e) The generator you have worked with above is a root of a polynomial over Z3. Obtain this polynomial with F.modulus() and use this observation to explain the entry in your list of powers that is the fourth power of the generator.