For figure "eight" there is a list of finite sheeted covering discussed in Hatcher's book "Algebraic topology". I was thinking about the following question:

Let $S$ be a finite subset with $|S|>1$ of $\mathbb{C}$, then what are the $n(\geq 2)$ sheeted coverings for $\mathbb{C}-S$?

It is known to me that, for $|S|=1$, finite $n$ sheeted covering for $\mathbb{C}-S$ is itself given by $z\to z^n$.

Thanks in advance!

For figure "eight" there is a list of finite sheeted covering discussed in Hatcher's book "Algebraic topology". I was thinking about the following question:

Let $S$ be a finite subset with $|S|>1$ of $\mathbb{C}$ and $n\ge 2$, then what are the $n$-sheeted coverings for $\mathbb{C}-S$?

It is known to me that, for $|S|=1$, finite $n$-sheeted covering for $\mathbb{C}-S$ is itself given by $z\to z^n$.

Thanks in advance!