  The average number of primitive quadratic Dirichlet characters of modulus n
tends to a constant as n->infty. The same is true for primitive cubic
characters. It is therefore surprising that, as n->infty, the average number of
primitive quartic characters of modulus n grows with ln(n), and that the
average number of primitive octic characters of modulus n grows with ln(n)^2.
Leading coefficients in the asymptotic expressions are also computed.
