Let $\Lambda$ be an $n$ dimensional sublattice of the integer lattice $\mathbb{Z}^n$. The quotient $\mathbb{Z}^n/\Lambda$ has order $\det{\Lambda}$.

What is the best/standard way to compute a set of coset representatives for this quotient?

Let $\Lambda$ be an $n$ dimensional sublattice of the integer lattice $\mathbb{Z}^n$. The quotient $\mathbb{Z}^n/\Lambda$ has order $\sqrt{\det{\Lambda}}$.

What is the best/standard way to compute a set of coset representatives for this quotient?

Edit: I initially forgot to take the square root of $\det{\Lambda}$, which is likely the reason for KCronrad's initial comment.