Motivic Serre invariants modulo the square of $\mathbb{L}-1$

Motivic Serre invariants defined by Loeser and Sebag are elements of the Grothendieck ring of varities modulo $\mathbb{L}-1$. In this paper, we show that we can lift these invariants to modulo the square of $\mathbb{L}-1$ after tensoring the Grothendieck ring with $\mathbb{Q}$, under certain assumptions.