New isolated complex Hadamard matrix found by W. Bruzda [175].
$$Y_9^{(0)}=\left[\begin{array}{lllllllll} 1& 1& 1& 1& 1& 1& 1& 1& 1\\ 1& a& d& a^*& c^*& b^*& c& b& d^*\\ 1& b& c& b^*& a& d^*& a^*& d& c^*\\ 1& c& b^*& c^*& d& a& d^*& a^*& b\\ 1& b^*& c^*& b& a^*& d& a& d^*& c\\ 1& d& a^*& d^*& b& c^*& b^*& c& a\\ 1& a^*& d^*& a& c& b& c^*& b^*& d\\ 1& c^*& b& c& d^*& a^*& d& a& b^*\\ 1& d^*& a& d& b^*& c& b& c^*& a^* \end{array}\right],$$where $x^*=1/x$ and
$$ \begin{aligned} a&=\sqrt{\gamma_1^2-1}-\gamma_1,\\ b&=\sqrt{\gamma_2^2-1}-\gamma_2,\\ c&=\sqrt{\gamma_3^2-1}+\gamma_3,\\ d&=\sqrt{\gamma_4^2-1}+\gamma_4 \end{aligned} $$with
$$ \begin{aligned} \gamma_1&=\frac{1}{4}\sqrt{1-\zeta_2-\zeta_2^*}-\frac{1}{4},\\ \gamma_2&=\frac{\sqrt{2}}{2}\sqrt{1-\zeta_1-\zeta_1^*}+\frac{1}{2},\\ \gamma_3&=\frac{\sqrt{2}}{2}\sqrt{1-\zeta_1-\zeta_1^*}-\frac{1}{2},\\ \gamma_4&=\frac{1}{4}\sqrt{1-\zeta_2-\zeta_2^*}+\frac{1}{4}\\ \end{aligned} $$and
$$ \begin{aligned} \zeta_1&=\frac{\omega}{2^{4/3}}\left(43-3 i \sqrt{771}\right)^{1/3}\\ \zeta_2&=2^{5/3}w^2\left(43+3 i \sqrt{771}\right)^{1/3} : \omega = \exp\{i\pi 5 / 3\}. \end{aligned} $$Matrix $Y_9^{(0)}$ can be expressed equivalently in the form:
$$Y_9^{(0)}=\left[\begin{array}{l|ll|ll|ll|ll} 1& 1& 1& 1& 1& 1& 1& 1& 1\\ \hline 1& a& a^*& b& b^*& c& c^*& d& d^*\\ 1& a^*& a& b^*& b& c^*& c& d^*& d\\ \hline 1& b& b^*& d& d^*& a^*& a& c& c^*\\ 1& b^*& b& d^*& d& a& a^*& c^*& c\\ \hline 1& c& c^*& a^*& a& d^*& d& b^*& b\\ 1& c^*& c& a& a^*& d& d^*& b& b^*\\ \hline 1& d& d^*& c& c^*& b^*& b& a^*& a\\ 1& d^*& d& c^*& c& b& b^*& a& a^* \end{array}\right].$$