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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