r2_check.py (verification run 2); Python 3.13.5; parts 4; back end python; PB = 320
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N2000:  N = 2000;  Sigma* = 1/2 (computed);  nu = 7/10000000, x0 = 1/100, X = 20004997/20000000, rho = 363553/500000000000
  [4] coefficients of a positive multiple of P: degree 2001, up to 46553 bits   (time: 13.6 s)
      back end plain Python integers: 12 intervals between x0 and X, sign changes: 0 0 0 0 0 1 1 1 0 1 1 0
      cut points: 1/2, 4/5, 9/10, 19/20, 49/50, 99/100, 124/125, 199/200, 249/250, 997/1000, 499/500
      every interval has 0 or 1 sign changes: True;  number of roots of P in (x0, X): 5   PASS   (time: 156.5 s)
  N2000: ALL EXECUTED PARTS PASS   (total 170.2 s)
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1 parameter points: ALL PASS
