Symmetry conjecture for spectra of logarithmic Brieskorn lattices of reductive linear free divisors

Let $D\subset V=\mathbb{C}^n$ be a reductive linear free divisor, with defining equation $h$. Its logarithmic Brieskorn lattice is $(G_0(h),\nabla)$, and its spectrum at $\theta=0$ is denoted by $\operatorname{Sp}_{\theta=0}(G_0(h),\nabla)$. Spectrum symmetry conjecture. The spectrum of $(G_0(h),\nabla)$ at $\theta=0$ is symmetric around $\frac{n-1}{2}$. This conjecture is based on computations for examples and is related to the symmetry result cited in the source; its validity for all reductive linear free divisors remains open.