θ4⁡(z|τ)=θ3⁡(z+12⁢π|τ)=-ⅈ⁢M⁢θ1⁡(z+12⁢π⁢τ|τ)=ⅈ⁢M⁢θ2⁡(z+12⁢π+12⁢π⁢τ|τ).