If the sum of all possible rational solutions of the equation $a\times \lfloor 4 a \rfloor\times\{ a \}=58$ can be expressed as $\frac {p}{q}$ where $p, q$ are coprime to each other, then $p=?$

[Here,  $\lfloor x \rfloor$ means the integer part of $x$, and $\{ x \}$ means the fractional part of $x$. Such as, $\lfloor 3.1416 \rfloor=3$, $\lfloor 5 \rfloor=5$, $\{ 3.1416 \}=0.1416$, $\{ 5 \}=0.00$ etc.]