check_spectrum.py: point N1000, N = 1000, PREC = 448 bits; points file spectrum_points_N1000.json (sha256 67351ab2b591305f79e85ff58608881522c11a937c5be149367d4e2c2dfede10)
state 1: x in an interval of length 1.48e-64 inside (1/100, 197/200); S = 0.973078759015299...; largest width of a C_j interval 7.15e-65   (0.3 s)
   250 points done (3 s)
   500 points done (5 s)
   750 points done (7 s)
   1000 points done (10 s)
   1003 points from 0 down to -5, decreasing: True; undecided signs: 0; signs alternate: True; sign of chi at p_0: +1;  exact eigenvalue -(nu1 + kappa') = -39/4000000
   state 1: all 1002 eigenvalues are real, simple and negative (hyperbolic sink)   (10 s)
state 2: x in an interval of length 1.36e-64 inside (197/200, 1977/2000); S = 0.976976484124700...; largest width of a C_j interval 6.44e-65   (0.3 s)
   250 points done (3 s)
   500 points done (5 s)
   750 points done (7 s)
   1000 points done (10 s)
   1003 points from 1 down to -5, decreasing: True; undecided signs: 0; signs alternate: True; sign of chi at p_0: +1;  exact eigenvalue -(nu1 + kappa') = -39/4000000
   state 2: exactly one eigenvalue lies in (0, 1), the other 1001 are real, simple and negative (saddle, one unstable direction)   (10 s)
state 3: x in an interval of length 1.09e-64 inside (1977/2000, 9913/10000); S = 0.980131721343748...; largest width of a C_j interval 4.98e-65   (0.2 s)
   250 points done (3 s)
   500 points done (5 s)
   750 points done (7 s)
   1000 points done (10 s)
   1003 points from 0 down to -5, decreasing: True; undecided signs: 0; signs alternate: True; sign of chi at p_0: +1;  exact eigenvalue -(nu1 + kappa') = -39/4000000
   state 3: all 1002 eigenvalues are real, simple and negative (hyperbolic sink)   (10 s)
state 4: x in an interval of length 1.40e-64 inside (9913/10000, 9931/10000); S = 0.982433429147861...; largest width of a C_j interval 6.09e-65   (0.3 s)
   250 points done (3 s)
   500 points done (5 s)
   750 points done (7 s)
   1000 points done (10 s)
   1003 points from 1 down to -5, decreasing: True; undecided signs: 0; signs alternate: True; sign of chi at p_0: +1;  exact eigenvalue -(nu1 + kappa') = -39/4000000
   state 4: exactly one eigenvalue lies in (0, 1), the other 1001 are real, simple and negative (saddle, one unstable direction)   (10 s)
state 5: x in an interval of length 1.47e-64 inside (9931/10000, 10006777/10000000); S = 0.983715309104275...; largest width of a C_j interval 6.12e-65   (0.3 s)
   250 points done (3 s)
   500 points done (5 s)
   750 points done (7 s)
   1000 points done (10 s)
   1003 points from 0 down to -5, decreasing: True; undecided signs: 0; signs alternate: True; sign of chi at p_0: +1;  exact eigenvalue -(nu1 + kappa') = -39/4000000
   state 5: all 1002 eigenvalues are real, simple and negative (hyperbolic sink)   (10 s)
total 49 s:  ALL FIVE STATES CERTIFIED
