diagonalize {{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,-i√3/2,0,0,0},{0,0,0,i√3/2,0,0,0,0},{0,0,0,0,0,0,-i√3/2,0},{0,0,0,0,0,i√3/2,0,0},{0,0,0,0,0,0,0,0}}