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.
Cyclotomic[#, x] & /@ Range[30] // Column
i = 1;
n = 10;
PrintTemporary[Dynamic[{magnitudes, i}]];
magnitudes = ConstantArray[True, n];
While[Or @@ magnitudes,
 coeff = Abs[CoefficientList[Cyclotomic[i, x], x]];
 coeff = Select[coeff, Between[{1, n}]];
 coeff = DeleteDuplicates[coeff];
 If[Or @@ magnitudes[[coeff]],
  Do[
   If[magnitudes[[c]] == True,
    Print["CyclotomicPolynomial(", i, 
     ") has coefficient with magnitude ", c]
    ]
   ,
   {c, coeff}
   ];
  magnitudes[[coeff]] = False;
  ];
 i++;
 ]