The nth Cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial of largest degree with integer coefficients that is a divisor of x^n − 1, and is not a divisor of x^k − 1 for any k < n.



Task

 Find and print the first 30 cyclotomic polynomials.
 Find and print the order of the first 10 cyclotomic polynomials that have n or -n as a coefficient.


See also
 Wikipedia article, Cyclotomic polynomial, showing ways to calculate them.
 The sequence A013594 with the smallest order of cyclotomic polynomial containing n or -n as a coefficient.
use Math::Polynomial::Cyclotomic:from<Perl5> <cyclo_poly_iterate cyclo_poly>;
 
say 'First 30 cyclotomic polynomials:';
my $iterator = cyclo_poly_iterate(1);
say "Φ($_) = " ~ super $iterator().Str for 1..30;
 
say "\nSmallest cyclotomic polynomial with |n| as a coefficient:";
say "Φ(1) has a coefficient magnitude: 1";
 
my $index = 0;
for 2..9 -> $coefficient {
    loop {
        $index += 5;
        my \Φ = cyclo_poly($index);
        next unless Φ ~~ / $coefficient\* /;
        say "Φ($index) has a coefficient magnitude: $coefficient";
        $index -= 5;
        last;
    }
}
 
sub super ($str) {
    $str.subst( / '^' (\d+) /, { $0.trans([<0123456789>.comb] => [<⁰¹²³⁴⁵⁶⁷⁸⁹>.comb]) }, :g)
}