$a \in \mathbb Z$, thinking of $t$ as the fractional part of $-\mu/s$.

\[lem:CAP1\] Let $\Gamma$ be a strongly regular graph with parameters $(v,k,\lambda,\mu)$ and eigenvalues $k > r \geqslant s$. Then $$\begin{aligned}
        C_\Gamma(-\mu/s - t, 2-k/s - t) &= (t-1)((v - 2k + \lambda)t - (2s-r)(r+1)); \label{eqn:SRG-Pol} \\
        C_\Gamma(-\mu/s - t, 1-k/s - t) &= t( (v - 2k + \lambda)(t-1) + r(r+1)). \label{eqn:SRGPol}
                    \end{aligned}$$ Moreover, if $\Gamma$ is co-connected then these polynomials have positive leading coefficients.

The equalities follow from direct calculation (see Appendix \[sec:comp\]), using the equalities in Proposition \[pro:SRG\]. By Proposition \[pro:SRGbound\] if $\Gamma$ is co-connected then the polynomials have positive leading coefficients.

Note that Lemma \[lem:CAP0\] is a special case of Lemma \[lem:CAP1\], for $t=0$.

\[cor:meetDelsarte1\] Let $\Gamma$ be a type-II strongly regular graph with parameters $(v,k,\lambda,\mu)$ and eigenvalues $k > r \geqslant s$. Then $$C_\Gamma(\lfloor -\mu/s \rfloor, \lfloor 2-k/s \rfloor) < 0.$$

If $\Gamma$ is disconnected then we have $\mu = 0$ and $2-k/s = \lambda + 3$. Whence $C_\Gamma(\lfloor -\mu/s \rfloor, \lfloor 2-k/s \rfloor) = C_\Gamma(0, \lambda+3) = -(\lambda + 3)(\lambda + 2) < 0$, as required. Hence we can assume that $\Gamma$ is connected.

Let $t = {\operatorname{frac} \left ( -\mu/s \right 