Characteristics

• The polynomial has roots along a spiral centered in 1/(a-1), where the distances of the j-th zero from the center of the spiral approach exponentially 0.
• For n=20, a=i/1000 the condition number of the roots ranges from to . The closest roots have about 60 common digits. In this way a working precision of 198 digits is needed for separating the closest roots. The numerators and the denominators of the coefficients have at most 132 digits.
• Large values of n, say n=500,1000,2000, constitute an interesting test for polynomial root-finders.