I'm looking for a polynomial $f \in \mathbb{Q}$ of degree $3$ that is irreducible over $\mathbb{Q}$, such that the polynomial's splitting field $L/\mathbb{Q}$ has a Galois group $G\text{al}(L/\mathbb{Q}) = G$ with $G$ isomorfic to the cyclic group of order 3.
The question actually asks me to give this polinomial in a seventh root of unity $\zeta$ with $\zeta^7 = 1$. I guess i should be able to write it in $\mathbb{Q}(\zeta)$.
Could anyone help me find this polynomial, or give me a hint?
Thanks!