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