Irregular Star Polygons (noch nicht übersetzt)

Define an $n$-star polygon as an $n$-gon whose vertices are $n$ equally spaced points on a circle. Two $n$-star polygons differing by a rotation/reflection are considered different.

For example, there are twelve $5$-star polygons shown below.

For an $n$-star polygon $S$, let $I(S)$ be the number of its self intersection points.
Let $T(n)$ be the sum of $I(S)$ over all $n$-star polygons $S$.
For the example above $T(5) = 20$ because in total there are $20$ self intersection points.

Some star polygons may have intersection points made from more than two lines. These are only counted once. For example, $S$, shown below is one of the sixty $6$-star polygons. This one has $I(S) = 4$.

You are also given that $T(8) = 14640$.

Find $\displaystyle \sum_{n = 3}^{60}T(n)$. Give your answer modulo $(10^9 + 7)$.