HMMT 2022 U22

The function $f(x)$ is of the form $a x^{2}+b x+c$ for some integers $a, b$, and $c$. Given that

$$\begin{aligned} \{f(177883), f(348710), & f(796921), f(858522)\} \\ = & \{1324754875645,1782225466694,1984194627862,4388794883485\} \end{aligned}$$

compute $a$.