An isolated complex Hadamard matrix found by D. McNulty and S. Weigert [108] reads: $$S_{10}=S_{10}^{(0)}=\frac{1}{\sqrt{10}}\left[\begin{array}{rrrrrrrrrr} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\ 1 & w & w^2 & w^3 & w^4 & w^4 & 1 & w & w^2 & w^3\\ 1 & w^2 & w^4 & w & w^3 & w & w^3 & 1 & w^2 & w^4\\ 1 & w^3 & w & w^4 & w^2 & w & w^4 & w^2 & 1 & w^3\\ 1 & w^4 & w^3 & w^2 & w & w^4 & w^3 & w^2 & w & 1\\ 1 & w^3 & w^2 & w^2 & w^3 & 1 & w & w^4 & w^4 & w\\ 1 & w^2 & 1 & w^4 & w^4 & w^3 & w^2 & w^3 & w & w\\ 1 & w & w^3 & w & 1 & w^2 & w^4 & w^3 & w^4 & w^2\\ 1 & 1 & w & w^3 & w & w^2 & w^2 & w^4 & w^3 & w^4\\ 1 & w^4 & w^4 & 1 & w^2 & w^3 & w & w & w^3 & w^2\\ \end{array}\right] : \quad w=\exp\frac{2i\pi}{5}.$$