Navarro–Tiep's character-value conjecture for finite quasi-simple groups

Let $p$ be an odd prime, let $G$ be a finite group, and let $\rho\in\operatorname{Irr}_{p'}(G)$ have conductor $p^a m$, where $a\in\mathbb{Z}_{\geq 0}$ and $m\in\mathbb{Z}_{\geq 1}$ is not divisible by $p$. Say that $G$ and $\rho$ have Property 1.3 for $p$ if there is a $p$-element $g\in G$ such that $p$ does not divide $[\mathbb{Q}_{p^a}:\mathbb{Q}(\rho(g))]$. Say that $G$ has Property 1.3 if this holds for every odd prime $p$ and every $\rho\in\operatorname{Irr}_{p'}(G)$. Navarro–Tiep's conjecture. Every finite quasi-simple group has Property 1.3. This conjecture concerns the values of irreducible complex characters of finite quasi-simple groups and would complete the characterization of the corresponding character fields for odd primes. Its status is not resolved in the supplied source.