In the expression |a:sxy,b:SXY|, "a" and "b" are numbers for fundamental
matrices which are listed in the following part. The numbers (x,y)
and (X,Y) mean the displacements of the elements. Therefore,
the matrix element 
for a:xy is given by
such that 
is one of
fundamental matrix.
s and S mean symmetrical transformations summarized in the following table.
For example, the matrix element for a:3xy is an
element
of a fundamental matrix.
The above symmetrical transformations cover 
of symmetries.
These results are calculated by the
awk script.
Prof. Suzuki's "ultra-super" magic squares are also decomposed,
which leads to only two fundamental digit-matrices
(here).