I'm having some trouble understanding how to calculate $r$ and $s$ as specified in the wikipedia page for ECDSA (https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm)
We can see on step 4 of the signature generation algorithm that they calculate the following:
$r = x_1 \text{mod}\ n$, where $n$ is the order of the group.
However, $x_1$ is an element of $F_{p^m}$, which for $m > 1$ it doesn't make sense to compute it's remainder over an integer.
Similarly on the next step they calculate $s = k^{-1} * (z + r d_A)\ \text{mod}\ n$. However, here I also do not understand what operation they are refering to when they write $z + r d_A$, since $z$ is a number and $rd_A$ is a curve point.
Surely I must be missing something very obvious but I cant figure out what. For $r$ it occurs to me that you could just take the modulus over the corresponding field element to $n$, since all the elements of $F_p$ are also in $F_{p^n}$.
For calculating $z + rd_A$ I'm at a loss though, how do you calculate the sum of an Integer and an element of $F_q$?