So Many Constraints!

Number Theory Level 5

Let $(a,b)$ are positive integers such that

$\begin{cases} \gcd(a,b)=1, \\ b\le 100, \\ \left(\dfrac{a}{b}-\left[\dfrac{a}{b}\right]\right)\left[\dfrac{a}{b}\right]=2013, \end{cases}$

where $[x]$ Is the Largest Integer Not Greater Than $x$

Find the total number of pairs $(a,b)$ .