Ultramagic squares

A magic square is said to be an ultramagic square, if it has the following properties:

Let us take a look at the following magic square of order n=4. You can easily see that this square is pandiagonal, as all rows, columns and diagonals sum to S=65.

11522189
23196512
102132416
14212073
17841125
25114817
37202114
162413210
12561923
91822151

Now we transform this magic square into its complement and we can see that a rotation with an angle of 180° will produce the original square again. So it is selfcomplement and hence ultramagic.