Hi! So i have made a table of all the nonprincipal Dirichlet characters mod 16. Is the following table correct?

n 1 3 5 7 9 11 13 15 X _{1}(n)1 1 1 1 1 1 1 1 X _{2}(n)1 i -i -1 -1 -i i 1 X _{3}(n)1 -1 -1 1 1 -1 -1 1 X _{4}(n)1 -i i -1 -1 i -i 1 X _{5}(n)1 1 -1 -1 1 1 -1 -1 X _{6}(n)1 i i 1 -1 -i -i -1 X _{7}(n)1 -1 1 -1 1 -1 1 -1 X _{8}(n)1 -i -i 1 -1 i i -1

I now want to verify from this table that for each real-valued nonprincipal character X mod 16, that: L(1,X) does not = 0. Any ideas on how to do this?

Thanks

Lexi