The Fourier matrix $F_{13}$ is an isolated $13\times 13$ complex Hadamard matrix: $$F_{13} = F_{13}^{(0)}=\left[\begin{array}{lllllllllllll} 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1\\ 1& w& w^2& w^3& w^4& w^5& w^6& w^7& w^8& w^9&w^{10}&w^{11}&w^{12}\\ 1& w^2& w^4& w^6& w^8&w^{10}&w^{12}& w& w^3& w^5& w^7& w^9&w^{11}\\ 1& w^3& w^6& w^9&w^{12}& w^2& w^5& w^8&w^{11}& w& w^4& w^7&w^{10}\\ 1& w^4& w^8&w^{12}& w^3& w^7&w^{11}& w^2& w^6&w^{10}& w& w^5& w^9\\ 1& w^5&w^{10}& w^2& w^7&w^{12}& w^4& w^9& w& w^6&w^{11}& w^3& w^8\\ 1& w^6&w^{12}& w^5&w^{11}& w^4&w^{10}& w^3& w^9& w^2& w^8& w& w^7\\ 1& w^7& w& w^8& w^2& w^9& w^3&w^{10}& w^4&w^{11}& w^5&w^{12}& w^6\\ 1& w^8& w^3&w^{11}& w^6& w& w^9& w^4&w^{12}& w^7& w^2&w^{10}& w^5\\ 1& w^9& w^5& w&w^{10}& w^6& w^2&w^{11}& w^7& w^3&w^{12}& w^8& w^4\\ 1&w^{10}& w^7& w^4& w&w^{11}& w^8& w^5& w^2&w^{12}& w^9& w^6& w^3\\ 1&w^{11}& w^9& w^7& w^5& w^3& w&w^{12}&w^{10}& w^8& w^6& w^4& w^2\\ 1&w^{12}&w^{11}&w^{10}& w^9& w^8& w^7& w^6& w^5& w^4& w^3& w^2& w \end{array}\right] : \quad w=\exp\frac{2i\pi}{13}.$$