Self Powers

The series, $1^{1} + 2^{2} + 3^{3} + \dots + 10^{10} = 10405071317$ .

Find the last ten digits of the series, $1^{1} + 2^{2} + 3^{3} + \dots + 1000^{1000}$ .

Write-up coming later

The complete problem is available here. An approach, code, and answer will be added later.