# $p$-adic extension of $n$th root of unity.

I have used the following command to define the 5-adic Unramified extension ring in c defined by the polynomial $x^3 + 3x + 3$:

```
Sage: R.<c> = zq(125, prec=20)
```

Now, I want to find all the $n$th root of unity in this ring for $n$ dividing $124$. I dont know, how the $n$-th roots are implemented. Kindly help me with this.

Thank you.

You should provide more details. In particular, what is

`zq`

?`zq`

is`Zq`