A complex Hadamard matrix found by P. Diţă $$D_{10\Sigma}^{(7)}(a,b,c,d,e,f,g)=H_{10\Sigma}\circ{\rm EXP}\left(i R_{10}^{(7)}(a,b,c,d,e,f,g)\right)$$ stemming from $$H_{10\Sigma}=\left[\begin{array}{rrrrrrrrrr} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\ 1 & 1 & 1 & w & w^2 & -1 & -1 & 1 & w^2 & w\\ 1 & 1 & 1 & w^2 & w & -1 & 1 & -1 & w & w^2\\ 1 & w & w^2 & 1 & 1 & -1 & w^2 & w & -1 & 1\\ 1 & w^2 & w & 1 & 1 & -1 & w & w^2 & 1 & -1\\ 1 & w^2 & w & 1 &-1 & 1 &-w &-w^2 &-1 &-1\\ 1 &-1 & 1 & w & w^2 & 1 & -1 &-1 & -w^2 & -w\\ 1 & 1 &-1 & w^2 & w & 1 & -1 &-1 & -w & -w^2\\ 1 & w & w^2 & -1 & 1 & 1 & -w^2 & -w & -1 & -1\\ 1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1 & 1 \end{array}\right],$$ where
$$\begin{aligned} R_{10}^{(7)} & (a,b,c,d,e,f,g)= \\ & \left[\begin{array}{rrrrrrrrrr} \bullet &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet\\ \bullet &2a+c+d&a+b+c&a+b+c&a+b+c&2a+c+d&\bullet&a-b+d&a-b+d&a-b+d\\ \bullet&a+b+c&2a+c+e&a+b+c&a+b+c&2a+c+e&a-b+e&\bullet&a-b+e&a-b+e\\ \bullet&a+b+c&a+b+c&2a+c+f&a+b+c&2a+c+f&a-b+f&a-b+f&\bullet&a-b+f\\ \bullet&a+b+c&a+b+c&a+b+c&2a+c+g&2a+c+g&a-b+g&a-b+g&a-b+g&\bullet\\ \bullet&a+b+c&a+b+c&a+b+c&2a+c+g&2a+c+g&a-b+g&a-b+g&a-b+g&\bullet\\ \bullet &2a+c+d&a+b+c&a+b+c&a+b+c&2a+c+d&\bullet&a-b+d&a-b+d&a-b+d\\ \bullet&a+b+c&2a+c+e&a+b+c&a+b+c&2a+c+e&a-b+e&\bullet&a-b+e&a-b+e\\ \bullet&a+b+c&a+b+c&2a+c+f&a+b+c&2a+c+f&a-b+f&a-b+f&\bullet&a-b+f\\ \bullet &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet &\bullet \end{array}\right]. \end{aligned}$$
Additional parameter $\Sigma \in\{A,B\}$ stands for $w_+$ or $w_-$, respectively, where $w_{\mp}$ is the root of the equation $w^2+w+1=0$.