$F_7$ is an isolated $7\times 7$ complex Hadamard (Fourier) matrix:
$$F_7=F_7^{(0)} = \left[\begin{array}{lllllll} 1& 1& 1& 1& 1& 1& 1\\ 1& w& w^2& w^3& w^4& w^5& w^6\\ 1& w^2& w^4& w^6& w& w^3& w^5\\ 1& w^3& w^6& w^2& w^5& w& w^4\\ 1& w^4& w& w^5& w^2& w^6& w^3\\ 1& w^5& w^3& w& w^6& w^4& w^2\\ 1& w^6& w^5& w^4& w^3& w^2& w\end{array}\right]:\quad w=\exp(2\pi i/7).$$