Is there a standard notation for a) the primitive root of unity of some root of unity (or its inverse), and b) the quotient of the two?
e.g. let $f:\dfrac{n}{2^p}\mapsto \exp\left(\dfrac{2\pi i\cdot n}{2^p}\right)$ map the dyadic rationals modulo $1$ to the $2^n$th roots of unity.
If $\left\lvert \dfrac{n}{2^p}\right\rvert_2$ is the 2-adic valuation and $\dfrac{n}{2^p}\cdot\left\lvert \dfrac{n}{2^p}\right\rvert_2$ finds $n$ then is there a standard notation for the function that finds the equivalent values in $\Bbb{C}$?
Is there some standard notation for writing such things and if so, what is it; and are there associated notations I should know?