  We investigate averages of long Dirichlet polynomials twisted by Kronecker
symbols and we compare our result with the recipe of [CFKRS]. We are able to
compute these averages in the case that the length of the polynomial is a power
less than 2 of the basic scaling parameter on the assumption of the Lindel\"of
Hypothesis for $L$-functions of quadratic characters, and we show that the
answer is consistent with this recipe. This corresponds, in terms of the
recipe, to verifying 0- and 1-swap terms.
