  Let $\zeta_k$ be a $k$-th primitive root of unity, $m\geq\phi(k)+1$ an
integer and $\Phi_k(X)\in\mathbb Z [X]$ the $k$-th cyclotomic polynomial. In
this paper we show that the pair $(-m+\zeta_k,\mathcal N)$ is a canonical
number system, with $\mathcal N=\{0,1,\dots,|\Phi_k(m)|\}$. Moreover we also
discuss whether the two bases $-m+\zeta_k$ and $-n+\zeta_k$ are
multiplicatively independent for positive integers $m$ and $n$ and $k$ fixed.
