Table 1: normalised balance psi at the test points
  N1000
    x = 1/100                  psi = +1.0000e+00
    x = 197/200                psi = -2.2705e-05
    x = 1977/2000              psi = +1.4758e-05
    x = 9913/10000             psi = -1.6624e-05
    x = 9931/10000             psi = +2.1897e-05
    x = 10006777/10000000      psi = -1.0000e+00
  N2000
    x = 1/100                  psi = +1.0000e+00
    x = 1237/1250              psi = -5.9069e-05
    x = 9929/10000             psi = +8.5065e-05
    x = 4977/5000              psi = -1.3431e-04
    x = 997/1000               psi = +5.1067e-04
    x = 20004997/20000000      psi = -1.0000e+00

Table of all points: N, b, nu1, lambda = N^2 nu1/phi, beta, S_T, largest |psi| at the four interior test points
  N1000    N=1000  b=1/100     nu1=13/4000000                 lambda=3.25000  beta=1.7172350000e-06  S_T=0.990677700000000  |psi| at the interior test points: 1.48e-05 .. 2.27e-05
  N2000    N=2000  b=1/100     nu1=7/10000000                 lambda=2.80000  beta=3.6355300000e-07  S_T=0.990249850000000  |psi| at the interior test points: 5.91e-05 .. 5.11e-04
  N651-B   N= 651  b=1/5000    nu1=102451/12108600000         lambda=3.58579  beta=4.4951633453e-06  S_T=1.001062064552234  |psi| at the interior test points: 1.54e-12 .. 2.74e-12
  N652-B   N= 652  b=1/2000    nu1=17923/2125520000           lambda=3.58460  beta=4.4810086583e-06  S_T=1.000759357680286  |psi| at the interior test points: 2.21e-11 .. 9.15e-11
  N655-B   N= 655  b=1/1000    nu1=35807/4290250000           lambda=3.58070  beta=4.4366600525e-06  S_T=1.000251064899138  |psi| at the interior test points: 5.43e-10 .. 6.04e-10
  N660-B   N= 660  b=1/1000    nu1=7147/871200000             lambda=3.57350  beta=4.3594820549e-06  S_T=1.000236969109472  |psi| at the interior test points: 3.83e-09 .. 6.95e-09
  N700-B   N= 700  b=1/100     nu1=141/19600000               lambda=3.52500  beta=3.8494838602e-06  S_T=0.991137518398440  |psi| at the interior test points: 1.08e-07 .. 1.00e-06
  N652-A   N= 652  b=1/100000  nu1=843117449/100000000000000  lambda=3.58413  beta=4.4781260545e-06  S_T=1.001249059066115  |psi| at the interior test points: 5.48e-11 .. 5.69e-11
  N653-A   N= 653  b=1/100000  nu1=84019273/10000000000000    lambda=3.58266  beta=4.4622958793e-06  S_T=1.001246181901763  |psi| at the interior test points: 1.91e-10 .. 2.02e-10
  N655-A   N= 655  b=1/1000    nu1=8346141/1000000000000      lambda=3.58070  beta=4.4366641161e-06  S_T=1.000251066022913  |psi| at the interior test points: 5.44e-10 .. 6.02e-10
  N660-A   N= 660  b=1/1000    nu1=6409/781250000             lambda=3.57345  beta=4.3594224939e-06  S_T=1.000236952091663  |psi| at the interior test points: 4.24e-09 .. 4.70e-09
  N680-A   N= 680  b=1/1000    nu1=7667/1000000000            lambda=3.54522  beta=4.0691500470e-06  S_T=1.000183091843000  |psi| at the interior test points: 6.61e-08 .. 1.29e-07
  N690-A   N= 690  b=1/1000    nu1=3709/500000000             lambda=3.53171  beta=3.9346028595e-06  S_T=1.000157679206200  |psi| at the interior test points: 1.34e-07 .. 2.49e-07
  N700-A   N= 700  b=1/1000    nu1=359/50000000               lambda=3.51820  beta=3.8060947980e-06  S_T=1.000133090435600  |psi| at the interior test points: 2.17e-07 .. 5.42e-07
  N4000-A  N=4000  b=1/100     nu1=811/5000000000             lambda=2.59520  beta=8.3423706550e-08  S_T=0.990099841185900  |psi| at the interior test points: 1.31e-04 .. 7.23e-04

Figure 1: psi for the point N1000 on 0.9810 <= x <= 0.9955 (step 1/10000); TikZ coordinates (x - 0.981)*1000, psi*10^5
(0.0,10.700) -- (0.1,9.968) -- (0.2,9.258) -- (0.3,8.570) -- (0.4,7.905) -- (0.5,7.262) -- (0.6,6.641) -- (0.7,6.043) -- (0.8,5.466) -- (0.9,4.912) -- (1.0,4.379) -- (1.1,3.869) -- (1.2,3.380) -- (1.3,2.913) -- (1.4,2.467) -- (1.5,2.043) -- (1.6,1.640) -- (1.7,1.258) -- (1.8,0.897) -- (1.9,0.557) -- (2.0,0.237) -- (2.1,-0.062) -- (2.2,-0.341) -- (2.3,-0.600) -- (2.4,-0.840) -- (2.5,-1.060) -- (2.6,-1.261) -- (2.7,-1.443) -- (2.8,-1.607) -- (2.9,-1.753) -- (3.0,-1.881) -- (3.1,-1.991) -- (3.2,-2.085) -- (3.3,-2.161) -- (3.4,-2.222) -- (3.5,-2.267) -- (3.6,-2.296) -- (3.7,-2.311) -- (3.8,-2.311) -- (3.9,-2.297) -- (4.0,-2.271) -- (4.1,-2.231) -- (4.2,-2.179) -- (4.3,-2.116) -- (4.4,-2.042) -- (4.5,-1.958) -- (4.6,-1.864) -- (4.7,-1.761) -- (4.8,-1.651) -- (4.9,-1.532) -- (5.0,-1.407) -- (5.1,-1.276) -- (5.2,-1.140) -- (5.3,-1.000) -- (5.4,-0.856) -- (5.5,-0.709) -- (5.6,-0.561) -- (5.7,-0.411) -- (5.8,-0.262) -- (5.9,-0.113) -- (6.0,0.034) -- (6.1,0.179) -- (6.2,0.321) -- (6.3,0.458) -- (6.4,0.590) -- (6.5,0.716) -- (6.6,0.835) -- (6.7,0.947) -- (6.8,1.050) -- (6.9,1.144) -- (7.0,1.228) -- (7.1,1.302) -- (7.2,1.364) -- (7.3,1.414) -- (7.4,1.451) -- (7.5,1.476) -- (7.6,1.487) -- (7.7,1.484) -- (7.8,1.467) -- (7.9,1.436) -- (8.0,1.391) -- (8.1,1.332) -- (8.2,1.258) -- (8.3,1.170) -- (8.4,1.070) -- (8.5,0.956) -- (8.6,0.830) -- (8.7,0.693) -- (8.8,0.546) -- (8.9,0.389) -- (9.0,0.225) -- (9.1,0.055) -- (9.2,-0.120) -- (9.3,-0.297) -- (9.4,-0.474) -- (9.5,-0.649) -- (9.6,-0.820) -- (9.7,-0.984) -- (9.8,-1.139) -- (9.9,-1.280) -- (10.0,-1.407) -- (10.1,-1.515) -- (10.2,-1.601) -- (10.3,-1.662) -- (10.4,-1.697) -- (10.5,-1.700) -- (10.6,-1.671) -- (10.7,-1.607) -- (10.8,-1.506) -- (10.9,-1.367) -- (11.0,-1.189) -- (11.1,-0.973) -- (11.2,-0.719) -- (11.3,-0.431) -- (11.4,-0.112) -- (11.5,0.231) -- (11.6,0.592) -- (11.7,0.960) -- (11.8,1.321) -- (11.9,1.660) -- (12.0,1.958) -- (12.1,2.190) -- (12.2,2.327) -- (12.3,2.336) -- (12.4,2.177) -- (12.5,1.803) -- (12.6,1.159) -- (12.7,0.183) -- (12.8,-1.198) -- (12.9,-3.068) -- (13.0,-5.522) -- (13.1,-8.667) -- (13.2,-12.629) -- (13.3,-17.545) -- (13.4,-23.572) -- (13.5,-30.889) -- (13.6,-39.693) -- (13.7,-50.207) -- (13.8,-62.679) -- (13.9,-77.388) -- (14.0,-94.640) -- (14.1,-114.779) -- (14.2,-138.184) -- (14.3,-165.276) -- (14.4,-196.519) -- (14.5,-232.426)
values of psi*10^5 at the four interior test points: 197/200: -2.271, 1977/2000: 1.476, 9913/10000: -1.662, 9931/10000: 2.190
