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 $1-a_{26}$ ?

Kind of inspired by this problem.