FAMILY a=1.0 b=0.5 N=4 tau=1 : a''=0.8944271909999158785636695 b''=0.2236067977499789696409174  closed-form check |da''|=0.0
  max |A1-A2| over 360 members: k607=5.44314e-29  k609=1.84889e-30  k610=2.80052e-24  k905=4.51228e-28  k906=1.18329e-30  k907b_dual=8.38165e-31  k907b_dualinv=4.43734e-31
  k406a_S          min|.|=5.00001 at t=0.462512 ; sign changes: 0
  k607_2           min|.|=1.6 at t=0.462512 ; sign changes: 0
  k609_2           min|.|=0.0442909 at t=0.462512 ; sign changes: 0
  k610_2           min|.|=0.800594 at t=0.462512 ; sign changes: 4
     ROOT t=0.39301019289013527616  k610_2=2.44291e+19 partner k610_1=2.44291e+19 |diff|=3.37116e+10 minsin=1.29374e-20
     ROOT t=0.54263910224965272798  k610_2=1.29931e+20 partner k610_1=1.29931e+20 |diff|=2.29617e+11 minsin=2.43245e-21
     ROOT t=2.5989535513401405105  k610_2=1.29931e+20 partner k610_1=1.29931e+20 |diff|=3.98126e+11 minsin=2.43245e-21
     ROOT t=2.7485824606996579623  k610_2=2.44291e+19 partner k610_1=2.44291e+19 |diff|=2.06197e+10 minsin=1.29374e-20
  k905_2           min|.|=0.185275 at t=0.698132 ; sign changes: 4
     ROOT t=0.29116820766977336422  k905_2=-3.16395e-19 partner k905_1=-3.16395e-19 |diff|=4.4318e-29
     ROOT t=0.69525422227667645226  k905_2=-1.70285e-19 partner k905_1=-1.70285e-19 |diff|=1.10453e-28
     ROOT t=2.4463384313131167862  k905_2=-1.70285e-19 partner k905_1=-1.70285e-19 |diff|=4.41146e-29
     ROOT t=2.8504244459200198742  k905_2=-3.16395e-19 partner k905_1=-3.16395e-19 |diff|=1.35342e-28
  k906_2           min|.|=0.72644 at t=0.0 ; sign changes: 0
  k907_dual_2      min|.|=0.0625 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=0.03125 at t=1.5708 ; sign changes: 0
FAMILY a=1.0 b=0.5 N=6 tau=1 : a''=0.9428090415820633658677925 b''=0.3726779962499649494015289
  max |A1-A2| over 360 members: k607=2.03132e-29  k609=1.74535e-29  k610=1.91299e-29  k905=1.55879e-27  k906=2.01948e-28  k907b_dual=1.20794e-30  k907b_dualinv=1.18329e-30
  k406a_S          min|.|=2.6162 at t=0.0 ; sign changes: 0
  k607_2           min|.|=0.0 at t=0.0349066 ; sign changes: 32
     ROOT t=0.014591858765487591744  k607_2=1.38051e-30 partner k607_1=2.5638e-30 |diff|=1.18329e-30
     ROOT t=0.018372086757033993176  k607_2=2.95823e-31 partner k607_1=2.85962e-30 |diff|=2.5638e-30
     ROOT t=0.033637902738761562799  k607_2=9.86076e-31 partner k607_1=2.66241e-30 |diff|=1.67633e-30
     ROOT t=0.055647417125466085302  k607_2=-9.86076e-32 partner k607_1=1.67633e-30 |diff|=1.77494e-30
     ROOT t=0.30543261909900767593  k607_2=5.71924e-30 partner k607_1=-7.88861e-31 |diff|=6.5081e-30
     ROOT t=0.30543262117960228147  k607_2=6.90253e-30 partner k607_1=-7.88861e-31 |diff|=7.69139e-30
     ROOT t=0.60813816124177421196  k607_2=4.93038e-31 partner k607_1=9.86076e-32 |diff|=3.9443e-31
     ROOT t=0.61086523819801584798  k607_2=1.2326e-30 partner k607_1=1.25725e-30 |diff|=2.46519e-32
     ROOT t=0.67958278328518121616  k607_2=1.38051e-30 partner k607_1=1.73796e-30 |diff|=3.57453e-31
     ROOT t=0.6806874630478449573  k607_2=1.72563e-30 partner k607_1=2.58845e-30 |diff|=8.62817e-31
     ROOT t=0.69590516470778830374  k607_2=-2.46519e-31 partner k607_1=1.3312e-30 |diff|=1.57772e-30
     ROOT t=0.69813596185547608158  k607_2=1.38051e-30 partner k607_1=2.40356e-30 |diff|=1.02305e-30
     ROOT t=0.72427688528478434793  k607_2=2.46519e-31 partner k607_1=2.07076e-30 |diff|=1.82424e-30
     ROOT t=0.73309062114876908298  k607_2=1.82424e-30 partner k607_1=3.2787e-30 |diff|=1.45446e-30
     ROOT t=0.74939435143308471856  k607_2=9.86076e-32 partner k607_1=1.82424e-30 |diff|=1.72563e-30
     ROOT t=0.75062906837291803168  k607_2=8.87469e-31 partner k607_1=2.83497e-30 |diff|=1.9475e-30
     ROOT t=0.76276230841295992701  k607_2=2.46519e-31 partner k607_1=1.45446e-30 |diff|=1.20794e-30
     ROOT t=0.76863839473331951642  k607_2=-3.9443e-31 partner k607_1=7.64209e-31 |diff|=1.15864e-30
     ROOT t=0.7853289039784103461  k607_2=9.86076e-31 partner k607_1=1.9968e-30 |diff|=1.01073e-30
     ROOT t=0.79966631542242729103  k607_2=9.86076e-32 partner k607_1=1.77494e-30 |diff|=1.67633e-30
     ROOT t=0.86366085415899091487  k607_2=2.46519e-31 partner k607_1=2.24332e-30 |diff|=1.9968e-30
     ROOT t=0.86588102258917968419  k607_2=6.16298e-31 partner k607_1=1.30655e-30 |diff|=6.90253e-31
     ROOT t=0.90316101468704926568  k607_2=9.86076e-31 partner k607_1=2.41589e-30 |diff|=1.42981e-30
     ROOT t=0.91042300819769130155  k607_2=-2.95823e-31 partner k607_1=1.3312e-30 |diff|=1.62703e-30
     ROOT t=0.95119591969314533066  k607_2=3.9443e-31 partner k607_1=1.67633e-30 |diff|=1.2819e-30
     ROOT t=0.95352385642969025331  k607_2=8.38165e-31 partner k607_1=1.67633e-30 |diff|=8.38165e-31
     ROOT t=2.1293016874330820838  k607_2=7.88861e-31 partner k607_1=-3.74709e-30 |diff|=4.53595e-30
     ROOT t=2.1293016874330820839  k607_2=1.08468e-30 partner k607_1=-3.69779e-30 |diff|=4.78247e-30
     ROOT t=2.1467549799525174219  k607_2=9.36772e-31 partner k607_1=-3.69779e-30 |diff|=4.63456e-30
     ROOT t=2.146756045217969369  k607_2=6.40949e-31 partner k607_1=-3.20475e-30 |diff|=3.8457e-30
     ROOT t=2.1895800925909824779  k607_2=-9.86076e-32 partner k607_1=-2.76101e-30 |diff|=2.66241e-30
     ROOT t=3.0329450301527643721  k607_2=-9.86076e-32 partner k607_1=1.57772e-30 |diff|=1.67633e-30
  k609_2           min|.|=0.943099 at t=1.5708 ; sign changes: 0
  k610_2           min|.|=1.00497 at t=0.0 ; sign changes: 0
  k905_2           min|.|=19.5656 at t=0.0 ; sign changes: 0
  k906_2           min|.|=9.09045 at t=1.5708 ; sign changes: 0
  k907_dual_2      min|.|=0.116462 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=0.0727887 at t=0.0 ; sign changes: 0
FAMILY a=1.0 b=0.5 N=8 tau=1 : a''=0.9659512983419707876533162 b''=0.4278573486204707651246957
  max |A1-A2| over 360 members: k607=5.47272e-30  k609=1.04524e-29  k610=5.91646e-30  k905=8.96146e-28  k906=2.33503e-28  k907b_dual=7.14905e-31  k907b_dualinv=1.40516e-30
  k406a_S          min|.|=2.02772 at t=0.261799 ; sign changes: 0
  k607_2           min|.|=0.376087 at t=2.87979 ; sign changes: 0
  k609_2           min|.|=1.76908 at t=0.261799 ; sign changes: 0
  k610_2           min|.|=0.933965 at t=1.5708 ; sign changes: 0
  k905_2           min|.|=41.7282 at t=1.5708 ; sign changes: 0
  k906_2           min|.|=19.8675 at t=2.87979 ; sign changes: 0
  k907_dual_2      min|.|=0.144215 at t=1.5708 ; sign changes: 0
  k907_dualinv_2   min|.|=0.103358 at t=1.5708 ; sign changes: 0
FAMILY a=1.0 b=0.8 N=6 tau=1 : a''=0.8958064164776166212404277 b''=0.6651835354264785127997353
  max |A1-A2| over 360 members: k607=3.54987e-30  k609=4.33873e-30  k610=2.76101e-30  k905=4.33873e-29  k906=1.34106e-29  k907b_dual=1.67633e-30  k907b_dualinv=1.57772e-30
  k406a_S          min|.|=3.76059 at t=0.0 ; sign changes: 0
  k607_2           min|.|=2.24499 at t=0.0 ; sign changes: 0
  k609_2           min|.|=1.37882 at t=1.5708 ; sign changes: 0
  k610_2           min|.|=1.49443 at t=1.5708 ; sign changes: 0
  k905_2           min|.|=7.21625 at t=0.0 ; sign changes: 0
  k906_2           min|.|=3.24758 at t=1.5708 ; sign changes: 0
  k907_dual_2      min|.|=0.953607 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=0.667525 at t=0.0 ; sign changes: 0
FAMILY a=1.7 b=0.3 N=4 tau=1 : a''=1.674132049990492531019023 b''=0.0521356001727142991390048  closed-form check |da''|=1.97215e-31
  max |A1-A2| over 360 members: k607=1.5199e-26  k609=2.80015e-29  k610=2.19467e-25  k905=5.92315e-25  k906=9.63889e-30  k907b_dual=8.87469e-31  k907b_dualinv=4.43734e-31
  k406a_S          min|.|=11.92 at t=2.96706 ; sign changes: 0
  k607_2           min|.|=0.698255 at t=0.174533 ; sign changes: 0
  k609_2           min|.|=0.000337934 at t=2.96706 ; sign changes: 0
  k610_2           min|.|=0.566865 at t=0.174533 ; sign changes: 4
     ROOT t=0.17190061857777436749  k610_2=3.72681e+19 partner k610_1=3.72681e+19 |diff|=4.45103e+11 minsin=3.64579e-20
     ROOT t=0.17748660478923784295  k610_2=8.06561e+19 partner k610_1=8.06561e+19 |diff|=2.16759e+12 minsin=1.68458e-20
     ROOT t=2.9641060488005553955  k610_2=8.06561e+19 partner k610_1=8.06561e+19 |diff|=2.07814e+12 minsin=1.68458e-20
     ROOT t=2.969692035012018871  k610_2=3.72681e+19 partner k610_1=3.72681e+19 |diff|=4.58412e+11 minsin=3.64579e-20
  k905_2           min|.|=4.63421 at t=2.94088 ; sign changes: 4
     ROOT t=0.15380889753607077373  k905_2=1.15972e-18 partner k905_1=1.15972e-18 |diff|=4.28687e-26
     ROOT t=0.19823390080229409485  k905_2=6.68075e-18 partner k905_1=6.68075e-18 |diff|=4.53708e-26
     ROOT t=2.9433587527874991436  k905_2=6.68075e-18 partner k905_1=6.68075e-18 |diff|=4.98832e-26
     ROOT t=2.9877837560537224647  k905_2=1.15972e-18 partner k905_1=1.15972e-18 |diff|=4.9047e-26
  k906_2           min|.|=0.202734 at t=0.0 ; sign changes: 0
  k907_dual_2      min|.|=0.000989212 at t=1.5708 ; sign changes: 0
  k907_dualinv_2   min|.|=0.000494606 at t=0.0 ; sign changes: 0
FAMILY a=1.7 b=0.3 N=6 tau=1 : a''=1.680766194329240979933035 b''=0.1580348062927910762057755
  max |A1-A2| over 360 members: k607=5.97957e-28  k609=4.99941e-29  k610=1.20107e-23  k905=4.1147e-26  k906=2.39183e-27  k907b_dual=6.16298e-31  k907b_dualinv=5.91646e-31
  k406a_S          min|.|=3.84975 at t=0.0 ; sign changes: 0
  k607_2           min|.|=13.1344 at t=0.0 ; sign changes: 0
  k609_2           min|.|=0.356832 at t=1.5708 ; sign changes: 0
  k610_2           min|.|=26.7756 at t=1.76278 ; sign changes: 4
     ROOT t=1.3699171214004921528  k610_2=4.93266e+18 partner k610_1=4.93266e+18 |diff|=5.4769e+10 minsin=3.50776e-21
     ROOT t=1.3703054638187323167  k610_2=-1.91162e-16 partner k610_1=-1.91162e-16 |diff|=3.35805e-25 minsin=0.000617497
     ROOT t=1.7712871897710609218  k610_2=-1.91162e-16 partner k610_1=-1.91162e-16 |diff|=9.41644e-25 minsin=0.000617497
     ROOT t=1.7716755321893010857  k610_2=4.93266e+18 partner k610_1=4.93266e+18 |diff|=3.95826e+10 minsin=3.50776e-21
  k905_2           min|.|=1.37133 at t=3.0456 ; sign changes: 6
     ROOT t=0.096212547997124492534  k905_2=4.8637e-19 partner k905_1=4.8637e-19 |diff|=9.56639e-27
     ROOT t=0.22345068331928975123  k905_2=9.7695e-18 partner k905_1=9.7695e-18 |diff|=7.48783e-28
     ROOT t=1.2243599966612510698  k905_2=-1.94507e-18 partner k905_1=-1.94507e-18 |diff|=1.67977e-26
     ROOT t=1.9172326569285421686  k905_2=-1.94507e-18 partner k905_1=-1.94507e-18 |diff|=1.3726e-26
     ROOT t=2.9181419702705034872  k905_2=9.7695e-18 partner k905_1=9.7695e-18 |diff|=1.66851e-27
     ROOT t=3.0453801055926687459  k905_2=4.8637e-19 partner k905_1=4.8637e-19 |diff|=9.6908e-27
  k906_2           min|.|=27.4739 at t=1.5708 ; sign changes: 0
  k907_dual_2      min|.|=0.00321345 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=0.00174849 at t=0.0 ; sign changes: 0
FAMILY a=1.7 b=0.3 N=8 tau=1 : a''=1.686986848833783764257978 b''=0.2143003223005969671200755
  max |A1-A2| over 360 members: k607=5.93223e-28  k609=2.79257e-28  k610=1.0697e-27  k905=1.57671e-25  k906=1.80744e-26  k907b_dual=1.13399e-30  k907b_dualinv=1.70098e-30
  k406a_S          min|.|=2.52711 at t=0.794125 ; sign changes: 0
  k607_2           min|.|=17.8541 at t=0.794125 ; sign changes: 0
  k609_2           min|.|=2.26732 at t=2.34747 ; sign changes: 0
  k610_2           min|.|=26.0665 at t=1.5708 ; sign changes: 0
  k905_2           min|.|=111.237 at t=1.5708 ; sign changes: 0
  k906_2           min|.|=125.369 at t=2.34747 ; sign changes: 0
  k907_dual_2      min|.|=0.00473271 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=0.00286096 at t=0.0 ; sign changes: 0
