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foreach my $close_to_zero (1e-3,
                           1e-4,
...
  print $close_to_zero**$close_to_zero,"\n";
}

0.993116048420934
0.999079389984462
...
0.999999999746716
0.999999999972369
0.999999999997007

 use Math::Complex;

...
                          ){
  print $close_to_zero**$close_to_zero,"\n";
}

1.00689492851834+0.00322274943578533i
1.00091826683245+0.000322665621543586i
...
1.00000000025297+3.38487684801375e-11i
1.0000000000276+3.40790269818147e-12i
1.00000000000299+3.43092854902761e-13i