the spectrum of $(G(*D),\nabla)$, one shows the same statement by analyzing the construction of a good basis of $G(*D)$ from a good basis of $G_0(h)$ using algorithm 2 of [@dGMS lemma 4.11].

Notice that for the normal crossing case, the integer $k$ from above is equal to zero, i.e., the block mentioned above is the whole spectrum. This is not true in general, hence, the Frobenius structures constructed in [@dGMS] are not, a priori, mirrors of quantum cohomology algebras of orbifolds, as zero is not, in general, an element of the spectrum. Still the analogy with the orbifold quantum cohomology, i.e., the fact that there is a block of increasing integer spectral numbers corresponding to the “untwisted sector” (see, e.g., [@Ir2 section 2.1.]) is rather intriguing.

**Examples of Bernstein polynomials:** We use the main result and the computations of spectral numbers in [@dGMS] to obtain the roots of the Bernstein polynomials for the following reductive linear free divisors. The definitions of the two last discriminants can be found in [@GMNS], example in 1.4(2) (this one is also called “bracelet”) and [@sk], proposition 11, respectively.\

$$\begin{array}{c|c}
\textup{\textbf{linear free divisor}} &  \textup{\textbf{Bernstein polynomial of \textit{h}}}\\ \hline \\
A_n\textup{ - quiver} & (s+1)^n 