Intersection theory and Siegel-Veech constants for Prym eigenform loci in $\mathrm{\Omega }{\mathcal{M}}_3(2,2{)}^{\mathrm{o}\mathrm{d}\mathrm{d}}$

We compute the Siegel-Veech constants associated to saddle connections with distinct endpoints on Prym eigenforms for real quadratic orders with non-square discriminant in $\mathrm{\Omega }{\mathcal{M}}_3(2,2{)}^{\mathrm{o}\mathrm{d}\mathrm{d}}$.