Trigonometric functions of for prime have an especially complicated Galois-minimal representation.
In particular, the case requires approximately 500 MB of space using the
Wolfram Language command `Developer`TrigToRadicals`[`Cos`[`Pi`/23]].
However, they can be expressed concisely as algebraic numbers. For example, letting
denote the th
root of the polynomial using the ordering of the Wolfram
Language's `Root`
function,
is given by

and by