I have studied Analytic number theory with Apostol's text book
In page 142, proof of Theorem 6.19, the following is written:
Since Dirichlet Character $\chi$ is real-valued the only possible values for $\chi$(n) are 0 , 1 and -1.
But in the table modulus 5, $\chi_{3}(2) = i$
Is the book wrong ?