  We derive some new signed Mahonian polynomials over the complex reflection
group $G(r,1,n)=C_r\wr\mathfrak{S}_n$, where the "sign" is taken to be any of
the $2r$ $1$-dim characters and the "Mahonian" statistics are the
$\mathsf{lmaj}$ defined by Bagno and the $\mathsf{sor}$ defined by Eu et al.
Various new signed Mahonian polynomials over Coxeter groups of types $B_n$ and
$D_n$ are derived as well. We also investigate the signed counting polynomials
on $G(r,1,n)$ for those statistics with the distribution $[r]_q[2r]_q\cdots
[nr]_q$.
