$\hat{h}({\bm k}, {\bm p}, t=0) = \hat{h}_0({\bm k}, {\bm p})$ denotes some arbitrary initial condition; below we demonstrate that the long-time statistical properties of the suspension are insensitive to $\hat{h}_0({\bm k}, {\bm p})$. In Eq., we have also introduced an important dimensionless parameter $\Delta = n/n_{crit}$, where $n_{crit} = 5\lambda/(B\kappa)$ is the mean-field onset of collective motion in pusher suspensions, $\kappa>0$. For pushers, $\Delta$ measures the dimensionless distance from the onset, with $\Delta=1$ corresponding to the instability. Eq. is a linear integral equation for $\hat{h}({\bm k}, {\bm p}, s)$ and its solution is straightforward. Substituting Eq. into Eqs.-, gives $$\begin{aligned}
&I^{(0)}({\bm k},s) \nonumber \\
&\qquad\qquad= \frac{1}{1-\frac{\lambda}{4\pi}f_0} \int d{\bm p} \frac{\hat{h}_0({\bm k}, {\bm p}) + \hat{\xi}({\bm k}, {\bm p},s)}{\sigma({\bm k},{\bm p}, s)},
\label{I0sol}\end{aligned}$$ $$\begin{aligned}
&I^{(2)}({\bm k},s) = \frac{\lambda}{4\pi} f_1 I^{(0)}({\bm k},s) \nonumber \\
& \qquad\qquad + \int d{\bm p} (\hat{\bm k}\cdot {\bm p})^2\frac{\hat{h}_0({\bm k}, {\bm p}) + \hat{\xi}({\bm k}, {\bm p},s)}{\sigma({\bm k},{\bm p}, s)},
\label{I1sol}\end{aligned}$$ $$\begin{aligned}
&I^{(1)}({\bm k},{\bm p}, s) = \frac{1}{1+\frac{15 \lambda}{8\pi} \Delta A(k\epsilon) (f_2 - f_1)} \Bigg[ \nonumber \\
& \quad \int d{\bm p}' (\hat{\bm k}\cdot {\bm p}')({\bm p}\cdot {\bm p}') \frac{\hat{h}_0({\bm k}, {\bm p}') + \hat{\xi}({\bm k}, {\bm p}',s)}{\sigma({\bm k},{\bm p}', s)} \nonumber \\
& \quad + (\hat{\bm 