\[\theta_{1}\left(z\middle|\tau\right)=-\theta_{2}\left(z+\tfrac{1}{2}\pi\middle%
|\tau\right)=-iM\theta_{4}\left(z+\tfrac{1}{2}\pi\tau\middle|\tau\right)=-iM%
\theta_{3}\left(z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau\middle|\tau\right),\]