To help with coloring the comic, you might want to use the following two Sage ideas. The first cell lets you type in an integer and check its primality; the second allows you to check whether a number leaves a fraction when divided by (say) 19 or reduces to an integer.

Next, let's test some conductor ideas. In the cell below, which should automatically evaluate for you, Sage will automatically list all the nonnegative numbers up to \(n\) that can be written as \(n=ax+by\) for nonnegative integers \(x\) and \(y\). The default values are the \(a=3,b=4\) combination we ended with last time.

Notice that with the one tried above we definitely are getting the same answers. Also notice that the algorithm I used in the code is very naive - I just listed all possible combinations under a certain size.

It would be interesting to use this to try to verify patterns you may have noticed about the precise size of the conductor, and when it exists.