A family of complex Hadamard martrices found by M. Matolcsi et al. [34] in June 2006 reads: $$S_{16}^{(11)}(a,b,c,d,e,f,g,h,i,j,k)=S_{16}\circ{\rm EXP}\left(i R_{S_{16}^{(11)}}(a,...,k)\right),$$ where $$R_{S_{16}^{(11)}}(a,...,k)= \left[\begin{array}{rrrrrrrrrrrrrrrr} \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet\\ \bullet & \bullet & h + i& i& c& c& b& b& k& k& i& i& k& k& i& h + i\\ \bullet & \bullet & \bullet & \bullet & d& d& d& d& \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet\\ \bullet & \bullet & h + i& i& c + j& c + j& b + j& b + j& k& k& i& i& k& k& i& h + i\\ \bullet & \bullet & h& \bullet & \bullet & \bullet & \bullet & \bullet & a& f& e& \bullet & a& f& e& h\\ \bullet & \bullet & i& i& c& c& b& b& a& f& e + i& i& a& f& e + i& i\\ \bullet & \bullet & h& \bullet & d& d& d& d& a& f& e& \bullet & a& f& e& h\\ \bullet & \bullet & i& i& c + j& c + j& b + j& b + j& a& f& e + i& i& a& f& e + i& i\\ \bullet & \bullet & h& g& \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & g& \bullet & \bullet & \bullet & h\\ \bullet & \bullet & i& g + i& c& c& b& b& k& k& i& g + i& k& k& i& i\\ \bullet & \bullet & h& g& d& d& d& d& \bullet & \bullet & \bullet & g& \bullet & \bullet & \bullet & h\\ \bullet & \bullet & i& g + i& c + j& c + j& b + j& b + j& k& k& i& g + i& k& k& i& i\\ \bullet & \bullet & \bullet & g& \bullet & \bullet & \bullet & \bullet & a& f& e& g& a& f& e& \bullet\\ \bullet & \bullet & h + i& g + i& c& c& b& b& a& f& e + i& g + i& a& f& e + i& h + i\\ \bullet & \bullet & \bullet & g& d& d& d& d& a& f& e& g& a& f& e& \bullet\\ \bullet & \bullet & h + i& g + i& c + j& c + j& b + j& b + j& a& f& e + i& g + i& a& f& e + i& h + i \end{array}\right].$$ It is generated by the spectral matrix $S_{16}$ containing $8^{\rm th}$-roots of unity: $${\rm LOG}\left(S_{16}\right)=\pi\frac{2}{8} \left[\begin{array}{rrrrrrrrrrrrrrrr} \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet\\ \bullet & 4& 6& 2& 7& 3& 5& 1& \bullet & 4& 6& 2& \bullet & 4& 6& 2\\ \bullet & \bullet & 4& 4& 6& 6& 2& 2& \bullet & \bullet & 4& 4& \bullet & \bullet & 4& 4\\ \bullet & 4& 2& 6& 5& 1& 7& 3& \bullet & 4& 2& 6& \bullet & 4& 2& 6\\ \bullet & \bullet & \bullet & \bullet & 4& 4& 4& 4& 5& \bullet & \bullet & \bullet & 1& 4& 4& 4\\ \bullet & 4& 6& 2& 3& 7& 1& 5& 5& 4& 6& 2& 1& \bullet & 2& 6\\ \bullet & \bullet & 4& 4& 2& 2& 6& 6& 5& \bullet & 4& 4& 1& 4& \bullet & \bullet\\ \bullet & 4& 2& 6& 1& 5& 3& 7& 5& 4& 2& 6& 1& \bullet & 6& 2\\ \bullet & \bullet & \bullet & 6& \bullet & \bullet & \bullet & \bullet & 4& 4& 4& 2& 4& 4& 4& 4\\ \bullet & 4& 6& \bullet & 7& 3& 5& 1& 4& \bullet & 2& 4& 4& \bullet & 2& 6\\ \bullet & \bullet & 4& 2& 6& 6& 2& 2& 4& 4& \bullet & 6& 4& 4& \bullet & \bullet\\ \bullet & 4& 2& 4& 5& 1& 7& 3& 4& \bullet & 6& \bullet & 4& \bullet & 6& 2\\ \bullet & \bullet & \bullet & 6& 4& 4& 4& 4& 1& 4& 4& 2& 5& \bullet & \bullet & \bullet\\ \bullet & 4& 6& \bullet & 3& 7& 1& 5& 1& \bullet & 2& 4& 5& 4& 6& 2\\ \bullet & \bullet & 4& 2& 2& 2& 6& 6& 1& 4& \bullet & 6& 5& \bullet & 4& 4\\ \bullet & 4& 2& 4& 1& 5& 3& 7& 1& \bullet & 6& \bullet & 5& 4& 2& 6 \end{array}\right].$$