This image was made in Tinkerplots, so it was easy to go from a 10 x 10 table to a 50 x 50 table (removing the numbers and just keeping the colours, and shrinking each cell down a bit):
If you take the values in this 50 x 50 table mod 9, you'll get this nice quilt - repeating in 9 x 9 blocks.
If you choose your mod value to line up with the width of the table (take the values mod 50) you get this:
The light blue along the bottom and the right side are all zeros - anything that is a multiple of 50, as the bottom and the far right side are, will have a remainder of 0 when you divide them by 50.
If you take the values mod 2500, then you get something that looks like the rainbow we started with - except for one square (maybe you can spot it, or figure out where it will be).
Here's a 75x75 table, mod 75, in shades of blue.