The complex numbers z and w satisfy z^{13}=w, w^{11}=z, and the imaginary part of z is \sin \left(\frac{m \pi}{n}\right) for relatively prime positive integers m and n with m<n. Find n.
The complex numbers z and w satisfy z^{13}=w, w^{11}=z, and the imaginary part of z is \sin \left(\frac{m \pi}{n}\right) for relatively prime positive integers m and n with m<n. Find n.