In Mathematica 7, the command
Table[DirichletCharacter[4, 2, n], {n, 0, 8}]
should return a list of values of the character with modulus 4 and index 2, evaluated at 0, 1, 2, .... Instead, it returns the decidedly non-multiplicative:
{0,1,0,-1,0,-1,0,-1,0}