Inspired by Nihar

Algebra Level 5

\[\large x^{26} + 4x^{25} + 9x^{24} + 16x^{23} + ... + 676x + 729=0 \]

If \(a_{1}\), \(a_{2}\), \(a_{3}\)..., \(a_{25}\), and \(a_{26}\) are the roots of the equation above whose coefficients are of the form \(n^{2}\), what is the constant of the monic polynomial whose roots are \(1-a_{1}\), \(1-a_{2}\), \(1-a_{3}\), ... \(1-a_{25}\), and \(1-a_{26}\)?