Sum of roots over each other

Level pending

Given that \(p\) and \(q\) are prime numbers and they are the roots of the quadratic equation

\[x^2-61x+m=0\]

where \(m\) is a constant. Then, \(\frac{p}{q}+\frac{q}{p}=\frac{a}{b}\), where \(a\) and \(b\) are positive coprime integers. What are the last 3 digits of \(a+b\)?

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