Divisor function and Dircihlet

Jul 2013
6
0
So I have constructed a table of all the non principal Dirichlet characters mod 16. Here is said table:

Now, for each real-valued nonprincipal character ? mod 16, I want to veryify that:

A(225) ? 1.

A(n) =
\(\displaystyle \Sigma\) ?(d)
d|n

Can anyone help?

Thanks

Here is the table mod 16 fwiw:

X(n) mod 16
n 1 3 5 7 9 11 13 15
X1(n) 1 1 1 1 1 1 1 1
X2(n) 1 i -i -1 -1 -i i 1
X3(n) 1 -1 -1 1 1 -1 -1 1
X4(n) 1 -i i -1 -1 i -i 1
X5(n) 1 1 -1 -1 1 1 -1 -1
X6(n) 1 i i 1 -1 -i -i -1
X7(n) 1 -1 1 -1 1 -1 1 -1
X8(n) 1 -i -i 1 -1 i i -1