The eigenvalues of the complement are $$\{v-k-1,-{\theta}-1,-\tau-1\}.$$ The characterizing equations for the complement of $X$, written in terms of the parameters of $X$, are: $$\begin{aligned}
ce^{i(n-k-1)t} \sqrt{n} & = 1 + xk + y(n-k-1) \label{eqn:flatsrgc1} \\
ce^{i(-{\theta}-1) t} \sqrt{n} & = 1 + x{\theta}+ y(-{\theta}-1) \label{eqn:flatsrgc2} \\
ce^{i(-\tau-1) t} \sqrt{n} & = 1 + x\tau + y(-\tau-1)\label{eqn:flatsrgc3} .\end{aligned}$$

Regular symmetric Hadamard matrices
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We first consider uniform mixing on strongly regular graphs with parameters given in (i) or (ii) of Theorem \[thm:chan\]. If a graph $X$ with adjacency matrix $A$ has these parameters or the complementary parameters, then $J-2A$ or $J-2A-2I$, respectively, is a regular symmetric Hadamard matrix [@brouwer84].

Suppose $X$ is a primitive strongly regular graph such that $X$ or $\overline{X}$ has parameters given in (i) or (ii) of Theorem \[thm:chan\]. Then $X$ admits uniform mixing if and only if one of the following holds:

1.  The parameters of $X$ or $\overline{X}$ are given in (i) and $\theta$ is even.

2.  The parameters of $X$ or $\overline{X}$ are given in (ii) and $\theta$ is odd.

[*Proof.* ]{}First suppose that $X$ is a graph with parameters $(4{\theta}^2,2{\theta}^2- {\theta}, {\theta}^2-{\theta},{\theta}^2-{\theta})$. Chan shows that $x = -1$ and $y = 1$. The 