It's as easy as 1, 3, 5

Number Theory Level 3

Given that the remainder after dividing \((10{ n }^{ 2 }+13)\) by 4 is 3, where \( n\) is a positive integer.

Let \(m\) denote the sum of all such integers \(n\) less than 1000. Find the remainder when \(m\) is divided by 4.