Number of conjugacy classes in symplectic group of fixed degree over a finite field is PORC function of field size

Statement
Suppose $$n$$ is an even natural number, i.e., $$n = 2m$$ for some natural number $$m$$. Then, there exists a PORC function $$f$$ of degree $$m = n/2$$ such that, for any prime power $$q$$, the  number of conjugacy classes in the  symplectic group $$Sp(n,q)$$ (i.e., the symplectic group of degree $$n$$ over the finite field of size $$q$$) is $$f(q)$$.

A PORC function is a polynomial on residue classes -- it looks like different polynomial functions on different congruence classes modulo a particular number. In this case, we only need to consider congruence classes modulo $$n$$ to define the PORC function. In fact, for a field size of $$q$$, the polynomial depends only on the value $$\operatorname{gcd}(\operatorname{lcm}(2,m),q - 1)$$.

Related facts

 * Number of conjugacy classes in projective symplectic group of fixed degree over a finite field is PORC function of field size
 * Number of conjugacy classes in general linear group of fixed degree over a finite field is polynomial function of field size
 * Number of conjugacy classes in projective general linear group of fixed degree over a finite field is PORC function of field size
 * Number of conjugacy classes in special linear group of fixed degree over a finite field is PORC function of field size
 * Number of conjugacy classes in projective special linear group of fixed degree over a finite field is PORC function of field size