There exist at least two equivalence classes of $11\times 11$ complex Hadamard matrices represented by circulant Hadamard matrices inequivalent to the Fourier matrix $F_{11}^{(0)}$ [62]. Their dephased forms read: $$C_{11A}^{(0)}=\left[\begin{array}{lllllllllll} 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1\\ 1&\varepsilon^{-1}& \varepsilon&\varepsilon^{-1}& 1& 1& \varepsilon& 1& 1&\varepsilon^{-1}& \varepsilon\\ 1&\varepsilon^{-2}&\varepsilon^{-1}&\varepsilon^{-1}&\varepsilon^{-2}&\varepsilon^{-1}& 1& 1&\varepsilon^{-1}&\varepsilon^{-2}&\varepsilon^{-1}\\ 1& 1& 1&\varepsilon^{-1}& 1&\varepsilon^{-1}& \varepsilon& \varepsilon& \varepsilon&\varepsilon^{-1}& 1\\ 1&\varepsilon^{-1}& \varepsilon&\varepsilon^{-1}&\varepsilon^{-1}& 1& 1& \varepsilon& \varepsilon& 1& 1\\ 1&\varepsilon^{-1}& 1& 1&\varepsilon^{-1}&\varepsilon^{-1}& \varepsilon& 1& \varepsilon& 1& \varepsilon\\ 1&\varepsilon^{-2}&\varepsilon^{-1}&\varepsilon^{-2}&\varepsilon^{-1}&\varepsilon^{-2}&\varepsilon^{-1}& 1&\varepsilon^{-1}&\varepsilon^{-1}& 1\\ 1&\varepsilon^{-1}&\varepsilon^{-1}&\varepsilon^{-2}&\varepsilon^{-2}&\varepsilon^{-1}&\varepsilon^{-1}&\varepsilon^{-1}& 1&\varepsilon^{-2}& 1\\ 1&\varepsilon^{-1}& 1&\varepsilon^{-2}&\varepsilon^{-2}&\varepsilon^{-2}& 1&\varepsilon^{-1}&\varepsilon^{-1}&\varepsilon^{-1}&\varepsilon^{-1}\\ 1& 1& \varepsilon& 1&\varepsilon^{-1}&\varepsilon^{-1}& 1& \varepsilon& 1&\varepsilon^{-1}& \varepsilon\\ 1&\varepsilon^{-2}& 1&\varepsilon^{-1}&\varepsilon^{-1}&\varepsilon^{-2}&\varepsilon^{-1}&\varepsilon^{-1}& 1&\varepsilon^{-2}&\varepsilon^{-1}\end{array}\right]:\quad \varepsilon=-\frac{5}{6}+i\frac{\sqrt{11}}{6}$$
and $C_{11B}^{(0)}=\left(C_{11A}^{(0)}\right)^{\rm T}$.