Symmetry conjecture for the genus of the central curve

Let $m$ be the size of the symmetric matrices and let $d$ denote the dimension parameter for the central curve. Write $\mathrm{genus}(m,d)$ for its genus. The complementary parameter is $\binom{m+1}{2}-d$. Symmetry conjecture.

$$\mathrm{genus}(m,d)=\mathrm{genus}\left(m,\binom{m+1}{2}-d\right).$$

This conjecture predicts a symmetry in the genus values of central curves associated with semidefinite programming under complementary dimension parameters. The source gives the conjecture after observing a missing table entry that is conjecturally equal to $33$; no resolution is provided here.