  We study the Kronecker symbol $\left(\frac st\right)$ for the sequence of the
convergents $s/t$ of a purely periodic continued fraction expansion. Whereas
the corresponding sequence of Jacobi symbols is always periodic, it turns out
that the sequence of Kronecker symbols may be aperiodic. Our main result
describes the period length in the periodic case in terms of the period length
of the sequence of Jacobi symbols and gives a necessary and sufficient
condition for the occurrence of the aperiodic case.
