\[\prod_{j=1}^{h}\theta\left(\sum_{k=1}^{h}T_{jk}\mathbf{z}_{k}\middle|%
\boldsymbol{{\Omega}}\right)=\frac{1}{\mathcal{D}^{g}}\sum_{\mathbf{A}\in%
\mathcal{K}}\sum_{\mathbf{B}\in\mathcal{K}}e^{2\pi i\operatorname{tr}\left[%
\frac{1}{2}\mathbf{A}^{\mathrm{T}}\boldsymbol{{\Omega}}\mathbf{A}+\mathbf{A}^{%
\mathrm{T}}[\mathbf{Z}+\mathbf{B}]\right]}\*\prod_{j=1}^{h}\theta\left(\mathbf%
{z}_{j}+\boldsymbol{{\Omega}}\mathbf{a}_{j}+\mathbf{b}_{j}\middle|\boldsymbol{%
{\Omega}}\right),\]