$F_3^{(0)}$

All complex $3\times 3$ Hadamard matrices are equivalent to the Fourier matrix $$F_3=F_3^{(0)}=\left[\begin{array}{lll} 1& 1 & 1\\ 1& w & w^2\\ 1& w^2 & w \end{array}\right]:\quad w=\exp(2\pi i/3)$$ which is an isolated point [32], [62].