\\ \hline \\
D_m\textup{ - quiver} & \left(s+\frac43\right)^{m-3}\cdot(s+1)^{2m-4}\cdot\left(s+\frac23\right)^{m-3} \\ \hline \\
E_6\textup{ - quiver} & (s+\frac75)\cdot(s+\frac43)^4\cdot(s+\frac65)\cdot(s+1)^{10}\cdot(s+\frac45)\cdot(s+\frac23)^4\cdot(s+\frac35) \\ \hline \\
\star_m\textup{ - quiver} &  \prod_{l=0}^{m-3}\left(s+\frac{2(m-1)-l}{m}\right)^{l+1}\cdot(s+1)^{2(m-1)}\cdot\prod_{l=0}^{m-3}\left(s+\frac{m-1-l}{m}\right)^{m-l-2}\\ \hline \\
\textup{discriminant in }S^3(({{\mathds C}}^2)^*) & \left(s+\frac76\right)\cdot\left(s+1\right)^2\cdot\left(s+\frac56\right) \\ \hline \\
\textup{discriminant of }\\\textup{Sl}(3,{{\mathds C}})\times \operatorname{Gl}(2,{{\mathds C}})\textup{ action}\\\textup{on Sym}(3,{{\mathds C}})\times\textup{Sym}(3,{{\mathds C}})& \left(s+\frac54\right)^2\cdot\left(s+\frac76\right)^2\cdot\left(s+1\right)^4\cdot
\left(s+\frac56\right)^2\cdot\left(s+\frac34\right)^2
\end{array}$$

Notice that the examples $E_6$ and the last two discriminants are obtained by direct calculations in Singular ([@Singular]). On the other hand, the closed formulas for the star quiver and the $D$-series follows from rather involved combinatorial arguments, the details of which will appear in [@CompQuiver]. The Bernstein polynomials for $D_4$ (which is equal to $\star_3$) and the bracelet are also calculated in [@GS]. The one for $A_n$ is of course completely obvious and well known. It would be of interest to complete these calculations by the Bernstein polynomials of quiver representations for the highest roots of the Dynkin quivers $E_7$ and $E_8$, however, this seems to be out of reach of computer algebra for the moment (remember from [@BM] that the linear free divisors associated to these roots for $E_7$ resp. $E_8$ are of degree $46$ resp. $118$).

Let us finish this note with a remark and a conjecture exploiting further 