\[\theta\left(\left[[\mathbf{C}\boldsymbol{{\Omega}}+\mathbf{D}]^{-1}\right]^{%
\mathrm{T}}\mathbf{z}\middle|[\mathbf{A}\boldsymbol{{\Omega}}+\mathbf{B}][%
\mathbf{C}\boldsymbol{{\Omega}}+\mathbf{D}]^{-1}\right)=\xi(\boldsymbol{{%
\Gamma}})\sqrt{\det[\mathbf{C}\boldsymbol{{\Omega}}+\mathbf{D}]}e^{\pi i%
\mathbf{z}\cdot\left[[\mathbf{C}\boldsymbol{{\Omega}}+\mathbf{D}]^{-1}\mathbf{%
C}\right]\cdot\mathbf{z}}\theta\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}%
\right).\]