Here,
is a completely multiplicative arithmetic function, which is periodic
modulo a positive integer q (called the modulus of 
).
Also, 
if and only if
gcd(n,q)>1. Moreover, must be primitive which means
that there does exist anothe character 
to a smaller modulus 
such that 
for all n with gcd(n,q)=1.
A character is even if 
and odd if 
Trivial zeros of 
are at 0 and the negative even integers if
is even and at the negative odd integers if is odd.
Special values are at the positive even integers and the negative
odd integers for even and positive odd and negative even integers
if is odd.