Modular multiplicative inverse graphs

A number

*b*is called a modular multiplicative inverse of*a*modulo*M*if*(a b) mod M = 1*. The above image was created by mapping the numbers*0 .. M - 1*for*M = 1 .. 264*onto the unit circle and connecting each number with its inverse. Euler totient function (A000010) counts the numbers less or equal to M and coprime with it and hence having an inverse. Inverses of themselves are marked with radial strokes (A060594 gives their total number).The number of rows, 12, was chosen intentionally. Numbers with many factors (such as in rows 6 and 12) have few lines, and prime numbers > 3 having the most lines can only be found in rows 1, 5, 7, 11.