Hello

Let $p$ be a prime number. According to Davenport (Multiplicative Number Theory, page 137) Schur proved (Indeed he proved much more, but let consider the simplest case) $$ \max_{t}\left|\sum_{n\leq t}\left(\frac{n}{p}\right)\right|>\frac{\sqrt{p}}{2\pi}. $$ What can we say about $t$ which we obtain the maximum? In other words, can we find $t\gg p^{\frac{1}{2}+\varepsilon}$ such that $$ \left|\sum_{n\leq t}\left(\frac{n}{p}\right)\right|>\frac{\sqrt{p}}{2\pi}. $$