numerical (mpmath, 50 digits); relative widths of the windows of X and of rho in which the five roots persist
N1000    N=1000  X-window: (X - X_lo)/X = 3.49e-7, (X_hi - X)/X = 3.15e-7, relative width 6.64e-7 ;  rho-window: (rho - rho_lo)/rho = 3.41e-5, (rho_hi - rho)/rho = 2.98e-5, relative width 6.38e-5
         steady states S = 0.9730787590153, 0.9769764841247, 0.98013172134375, 0.98243342914786, 0.98371530910428 ;  (S_5 - S_1)/S_1 = 0.0109
N2000    N=2000  X-window: (X - X_lo)/X = 1.28e-6, (X_hi - X)/X = 1.28e-6, relative width 2.56e-6 ;  rho-window: (rho - rho_lo)/rho = 0.000119, (rho_hi - rho)/rho = 0.000181, relative width 0.0003
         steady states S = 0.97782286123299, 0.98131744100382, 0.98453089949262, 0.98634681409667, 0.98771627444645 ;  (S_5 - S_1)/S_1 = 0.0101
N651-B   N= 651  X-window: (X - X_lo)/X = 5.01e-14, (X_hi - X)/X = 5.01e-14, relative width 1.0e-13 ;  rho-window: (rho - rho_lo)/rho = 3.09e-12, (rho_hi - rho)/rho = 3.11e-12, relative width 6.2e-12
         steady states S = 0.98477200387301, 0.98487039218968, 0.98501974979333, 0.98521925181001, 0.98530596840636 ;  (S_5 - S_1)/S_1 = 0.000542
N652-B   N= 652  X-window: (X - X_lo)/X = 7.13e-13, (X_hi - X)/X = 7.13e-13, relative width 1.43e-12 ;  rho-window: (rho - rho_lo)/rho = 4.49e-11, (rho_hi - rho)/rho = 4.42e-11, relative width 8.91e-11
         steady states S = 0.98430085122062, 0.98447654469859, 0.98474318242257, 0.98498368398438, 0.98527329763139 ;  (S_5 - S_1)/S_1 = 0.000988
N655-B   N= 655  X-window: (X - X_lo)/X = 1.76e-11, (X_hi - X)/X = 1.76e-11, relative width 3.52e-11 ;  rho-window: (rho - rho_lo)/rho = 1.11e-9, (rho_hi - rho)/rho = 1.09e-9, relative width 2.19e-9
         steady states S = 0.98345856626368, 0.98379871388993, 0.98432086092781, 0.98482522591917, 0.98513568303244 ;  (S_5 - S_1)/S_1 = 0.00171
N660-B   N= 660  X-window: (X - X_lo)/X = 1.24e-10, (X_hi - X)/X = 1.24e-10, relative width 2.48e-10 ;  rho-window: (rho - rho_lo)/rho = 8.04e-9, (rho_hi - rho)/rho = 7.66e-9, relative width 1.57e-8
         steady states S = 0.98304069181174, 0.98370168590589, 0.984437783975, 0.98516777748393, 0.98560649355139 ;  (S_5 - S_1)/S_1 = 0.00261
N700-B   N= 700  X-window: (X - X_lo)/X = 3.72e-9, (X_hi - X)/X = 3.72e-9, relative width 7.43e-9 ;  rho-window: (rho - rho_lo)/rho = 2.17e-7, (rho_hi - rho)/rho = 2.35e-7, relative width 4.51e-7
         steady states S = 0.97355193568223, 0.97456645853917, 0.97603608327071, 0.97722034437693, 0.97889246195333 ;  (S_5 - S_1)/S_1 = 0.00549
N652-A   N= 652  X-window: (X - X_lo)/X = 1.77e-12, (X_hi - X)/X = 1.77e-12, relative width 3.54e-12 ;  rho-window: (rho - rho_lo)/rho = 1.1e-10, (rho_hi - rho)/rho = 1.1e-10, relative width 2.2e-10
         steady states S = 0.98470986909093, 0.98491907519604, 0.98524933394395, 0.98557199622012, 0.98576807688878 ;  (S_5 - S_1)/S_1 = 0.00107
N653-A   N= 653  X-window: (X - X_lo)/X = 6.18e-12, (X_hi - X)/X = 6.18e-12, relative width 1.24e-11 ;  rho-window: (rho - rho_lo)/rho = 3.88e-10, (rho_hi - rho)/rho = 3.82e-10, relative width 7.7e-10
         steady states S = 0.98457262557957, 0.98484589104661, 0.98526949155551, 0.98568216483432, 0.98593249003474 ;  (S_5 - S_1)/S_1 = 0.00138
N655-A   N= 655  X-window: (X - X_lo)/X = 1.73e-11, (X_hi - X)/X = 1.73e-11, relative width 3.47e-11 ;  rho-window: (rho - rho_lo)/rho = 1.11e-9, (rho_hi - rho)/rho = 1.09e-9, relative width 2.2e-9
         steady states S = 0.98345128922965, 0.9838046891863, 0.98432454857589, 0.98482757175026, 0.98513092532664 ;  (S_5 - S_1)/S_1 = 0.00171
N660-A   N= 660  X-window: (X - X_lo)/X = 1.37e-10, (X_hi - X)/X = 1.37e-10, relative width 2.75e-10 ;  rho-window: (rho - rho_lo)/rho = 8.6e-9, (rho_hi - rho)/rho = 8.48e-9, relative width 1.71e-8
         steady states S = 0.98310476021621, 0.98363103720473, 0.98442171046048, 0.98517423798655, 0.98562310055069 ;  (S_5 - S_1)/S_1 = 0.00256
N680-A   N= 680  X-window: (X - X_lo)/X = 2.28e-9, (X_hi - X)/X = 2.28e-9, relative width 4.56e-9 ;  rho-window: (rho - rho_lo)/rho = 1.32e-7, (rho_hi - rho)/rho = 1.42e-7, relative width 2.74e-7
         steady states S = 0.98246221073897, 0.98339845472161, 0.98478696021482, 0.98601815081316, 0.98689950366977 ;  (S_5 - S_1)/S_1 = 0.00452
N690-A   N= 690  X-window: (X - X_lo)/X = 4.67e-9, (X_hi - X)/X = 4.67e-9, relative width 9.33e-9 ;  rho-window: (rho - rho_lo)/rho = 2.68e-7, (rho_hi - rho)/rho = 2.92e-7, relative width 5.6e-7
         steady states S = 0.98227762574027, 0.98337059409464, 0.98497176775348, 0.98638397969726, 0.98733506958935 ;  (S_5 - S_1)/S_1 = 0.00515
N700-A   N= 700  X-window: (X - X_lo)/X = 7.56e-9, (X_hi - X)/X = 7.56e-9, relative width 1.51e-8 ;  rho-window: (rho - rho_lo)/rho = 4.33e-7, (rho_hi - rho)/rho = 4.77e-7, relative width 9.1e-7
         steady states S = 0.98216710778479, 0.98337951093175, 0.98513128326627, 0.98663775671358, 0.98777987342903 ;  (S_5 - S_1)/S_1 = 0.00571
N4000-A  N=4000  X-window: (X - X_lo)/X = 1.99e-6, (X_hi - X)/X = 1.99e-6, relative width 3.99e-6 ;  rho-window: (rho - rho_lo)/rho = 0.000266, (rho_hi - rho)/rho = 0.000508, relative width 0.000774
         steady states S = 0.98080930979541, 0.98445597761528, 0.98718126254118, 0.98837612041388, 0.98890275849969 ;  (S_5 - S_1)/S_1 = 0.00825
