the (known) quasi-unipotency of the monodromy acting on the cohomology of the Milnor fibre of an isolated hypersurface singularity. In our case, the rationality of the roots of $b_h(s)$ is known, but we deduce information on the (a priori unknown) monodromy of the logarithmic Brieskorn lattice $G_0(h)$. Moreover, we can use the results of [@GS] to obtain a symmetry property of the spectrum at infinity of the logarithmic Brieskorn lattice, which was conjectured in [@dGMS corollary 5.6].

\[cor:MondromySymmetryAtZero\] The monodromy of the logarithmic Brieskorn lattice, i.e. of the local system associated to $G_0(h)[\theta^{-1}]:=G_0(h)\otimes_{{{\mathds C}}[\theta]}{{\mathds C}}[\theta,\theta^{-1}]$ is quasi-unipotent. Moreover, let $\alpha_1,\ldots,\alpha_n$ be the spectral numbers of $G_0(h)$ at infinity (i.e., the numbers $\nu_i$ from proposition \[prop:recalldGMS\]), written as a non-decreasing sequence. Then $\alpha_i+\alpha_{n+1-i}=n-1$.

The eigenvalues of this monodromy are simply the exponentials of either the numbers $\nu_i$ or $\nu_i':=i-1-\nu_i$ from proposition \[prop:recalldGMS\] (or any other integer shift of them). The numbers $\nu_i'$ are the roots of the Bernstein polynomial of $h$ shifted by one, as shown in theorem \[theo:BernsteinEqualResidueGM\]. These are known to be rational by [@Ka1]. Similarly, if we denote the roots of $b_h$ by $\alpha'_1,\ldots,\alpha'_n$, with $\alpha'_i\leq \alpha'_j$ if $i\leq j$, then we know from [@GS theorem 2.5.] that 