  Let $\mathbb{F}_q$ be a finite field of order $q$ and integer $n\ge 1$. Let
$\ell$ be a prime such that $\ell^k|(q-1)$ for some integer $k\ge 1$ and $\mu$
be an element of order $\ell^k$ in $\mathbb{F}_q$. In this paper, we determine
the weight distributions of all irreducible $\mu$-constacyclic codes of length
$\ell^n$ over $\mathbb{F}_q$. Explicit expressions for the generator
polynomials and codewords of these codes are also obtained.
