FAMILY a=1.0 b=0.8 N=4 tau=1 : a''=0.7808688094430303107046406 b''=0.499756038043539454335036  closed-form check |da''|=9.86076e-32
  max |A1-A2| over 360 members: k607=5.91646e-30  k609=1.08468e-30  k610=1.47517e-28  k905=2.76101e-29  k906=3.9443e-31  k907b_dual=1.67633e-30  k907b_dualinv=1.18329e-30
  k406a_S          min|.|=6.56001 at t=2.46964 ; sign changes: 0
  k607_2           min|.|=3.12195 at t=0.671952 ; sign changes: 0
  k609_2           min|.|=0.321785 at t=0.671952 ; sign changes: 0
  k610_2           min|.|=1.56099 at t=0.671952 ; sign changes: 0
  k905_2           min|.|=2.975 at t=1.5708 ; sign changes: 0
  k906_2           min|.|=1.18977 at t=0.0 ; sign changes: 0
  k907_dual_2      min|.|=0.65536 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=0.32768 at t=0.0 ; sign changes: 0
FAMILY a=1.0 b=0.8 N=8 tau=1 : a''=0.9401810974574230251510778 b''=0.7238373408551429819104371
  max |A1-A2| over 360 members: k607=1.97215e-30  k609=4.73317e-30  k610=1.38051e-30  k905=4.57539e-29  k906=2.8399e-29  k907b_dual=1.77494e-30  k907b_dualinv=2.07076e-30
  k406a_S          min|.|=3.1202 at t=2.79253 ; sign changes: 0
  k607_2           min|.|=2.033 at t=0.349066 ; sign changes: 0
  k609_2           min|.|=2.02068 at t=2.79253 ; sign changes: 0
  k610_2           min|.|=1.61214 at t=0.0 ; sign changes: 0
  k905_2           min|.|=8.12588 at t=1.5708 ; sign changes: 0
  k906_2           min|.|=4.93744 at t=2.79253 ; sign changes: 0
  k907_dual_2      min|.|=1.08521 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=0.870283 at t=0.0 ; sign changes: 0
FAMILY a=1.0 b=0.15 N=4 tau=1 : a''=0.9889363528682975254758966 b''=0.02225106793953669267629781  closed-form check |da''|=9.86076e-32
  max |A1-A2| over 360 members: k607=1.06772e-26  k609=1.1762e-29  k610=1.20229e-24  k905=5.63073e-24  k906=3.9443e-31  k907b_dual=4.93038e-31  k907b_dualinv=2.46519e-31
  k406a_S          min|.|=4.09003 at t=2.99324 ; sign changes: 0
  k607_2           min|.|=0.17604 at t=2.99324 ; sign changes: 0
  k609_2           min|.|=4.45151e-5 at t=2.99324 ; sign changes: 0
  k610_2           min|.|=4.77305 at t=0.148353 ; sign changes: 4
     ROOT t=0.14719219795686158634  k610_2=-2.17619e+19 partner k610_1=-2.17619e+19 |diff|=7.60592e+11 minsin=2.19732e-20
     ROOT t=0.15060669072047929459  k610_2=3.21842e+19 partner k610_1=3.21842e+19 |diff|=1.55159e+12 minsin=1.48575e-20
     ROOT t=2.9909859628693139439  k610_2=3.21842e+19 partner k610_1=3.21842e+19 |diff|=1.66456e+12 minsin=1.48575e-20
     ROOT t=2.9944004556329316521  k610_2=-2.17619e+19 partner k610_1=-2.17619e+19 |diff|=7.34496e+11 minsin=2.19732e-20
  k905_2           min|.|=0.77821 at t=2.97579 ; sign changes: 4
     ROOT t=0.13371545128237250205  k905_2=2.87812e-17 partner k905_1=2.87812e-17 |diff|=3.65985e-25
     ROOT t=0.16572951906878582854  k905_2=2.12016e-17 partner k905_1=2.12016e-17 |diff|=3.1607e-25
     ROOT t=2.9758631345210074099  k905_2=2.12016e-17 partner k905_1=2.12016e-17 |diff|=3.17086e-25
     ROOT t=3.0078772023074207364  k905_2=2.87812e-17 partner k905_1=2.87812e-17 |diff|=3.04048e-25
  k906_2           min|.|=0.573885 at t=1.5708 ; sign changes: 0
  k907_dual_2      min|.|=0.000151875 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=7.59375e-5 at t=0.0 ; sign changes: 0
FAMILY a=1.0 b=0.15 N=6 tau=1 : a''=0.9914568913905547650183394 b''=0.0740727175539166084660537
  max |A1-A2| over 360 members: k607=7.07608e-28  k609=5.51463e-29  k610=6.40926e-25  k905=5.42029e-25  k906=2.45367e-26  k907b_dual=3.82105e-31  k907b_dualinv=2.95823e-31
  k406a_S          min|.|=1.20962 at t=0.0 ; sign changes: 0
  k607_2           min|.|=5.30031 at t=0.0 ; sign changes: 0
  k609_2           min|.|=0.0814436 at t=1.5708 ; sign changes: 0
  k610_2           min|.|=6.53073 at t=1.7366 ; sign changes: 0
  k905_2           min|.|=19.3044 at t=1.87623 ; sign changes: 6
     ROOT t=0.089266276960483350387  k905_2=-9.1562e-17 partner k905_1=-9.1562e-17 |diff|=2.29471e-25
     ROOT t=0.18517533150278485412  k905_2=2.29622e-17 partner k905_1=2.29622e-17 |diff|=1.48155e-25
     ROOT t=1.2611458719708151448  k905_2=-7.0529e-18 partner k905_1=-7.0529e-18 |diff|=2.37836e-25
     ROOT t=1.8804467816189780937  k905_2=-7.0529e-18 partner k905_1=-7.0529e-18 |diff|=3.16156e-25
     ROOT t=2.9564173220870083843  k905_2=2.29622e-17 partner k905_1=2.29622e-17 |diff|=1.3698e-25
     ROOT t=3.0523263766293098881  k905_2=-9.1562e-17 partner k905_1=-9.1562e-17 |diff|=2.83084e-25
  k906_2           min|.|=110.557 at t=1.5708 ; sign changes: 0
  k907_dual_2      min|.|=0.00053749 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=0.000288901 at t=0.0 ; sign changes: 0
FAMILY a=1.0 b=0.15 N=8 tau=1 : a''=0.9940889188166627882443283 b''=0.1035025531766322085008834
  max |A1-A2| over 360 members: k607=4.96982e-28  k609=1.7986e-28  k610=3.09439e-26  k905=1.32794e-24  k906=1.53885e-25  k907b_dual=4.5606e-31  k907b_dualinv=6.90253e-31
  k406a_S          min|.|=0.774642 at t=2.38237 ; sign changes: 0
  k607_2           min|.|=7.34649 at t=2.38237 ; sign changes: 0
  k609_2           min|.|=0.646662 at t=0.759218 ; sign changes: 0
  k610_2           min|.|=11.0156 at t=0.0 ; sign changes: 0
  k905_2           min|.|=1.34252 at t=1.50098 ; sign changes: 8
     ROOT t=0.0071049368297008945439  k905_2=1.20513e-18 partner k905_1=1.20513e-18 |diff|=5.04983e-25
     ROOT t=0.29078229281874299  k905_2=-1.16461e-18 partner k905_1=-1.16461e-18 |diff|=2.42425e-26
     ROOT t=0.3348138895322498031  k905_2=-2.64144e-18 partner k905_1=-2.64144e-18 |diff|=1.51997e-26
     ROOT t=1.5026615369632083032  k905_2=2.49848e-18 partner k905_1=2.49848e-18 |diff|=1.08461e-25
     ROOT t=1.6389311166265849353  k905_2=2.49848e-18 partner k905_1=2.49848e-18 |diff|=1.48175e-25
     ROOT t=2.8067787640575434354  k905_2=-2.64144e-18 partner k905_1=-2.64144e-18 |diff|=7.05783e-26
     ROOT t=2.8508103607710502485  k905_2=-1.16461e-18 partner k905_1=-1.16461e-18 |diff|=7.59897e-26
     ROOT t=3.1344877167600923439  k905_2=1.20513e-18 partner k905_1=1.20513e-18 |diff|=6.591e-25
  k906_2           min|.|=565.427 at t=0.759218 ; sign changes: 0
  k907_dual_2      min|.|=0.000813376 at t=1.5708 ; sign changes: 0
  k907_dualinv_2   min|.|=0.000482626 at t=1.5708 ; sign changes: 0
FAMILY a=1.0 b=0.2 N=10 tau=1 : a''=0.9935859145812564839998473 b''=0.1649635403786906806260761
  max |A1-A2| over 360 members: k607=1.3174e-28  k609=9.38744e-29  k610=1.72761e-28  k905=2.79093e-25  k906=4.55394e-26  k907b_dual=7.64209e-31  k907b_dualinv=1.08468e-30
  k406a_S          min|.|=0.599902 at t=0.0 ; sign changes: 0
  k607_2           min|.|=5.92723 at t=0.0 ; sign changes: 0
  k609_2           min|.|=1.59746 at t=1.5708 ; sign changes: 0
  k610_2           min|.|=7.40335 at t=1.5708 ; sign changes: 0
  k905_2           min|.|=1176.74 at t=0.0 ; sign changes: 0
  k906_2           min|.|=538.875 at t=1.5708 ; sign changes: 0
  k907_dual_2      min|.|=0.00337339 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=0.00227991 at t=0.0 ; sign changes: 0
FAMILY a=1.0 b=0.5 N=8 tau=3 : a''=0.8662089773271802624198854 b''=0.01783234146710660982479333
  max |A1-A2| over 360 members: k607=4.13118e-23  k609=7.38787e-31  k610=2.08537e-16  k905=4.22766e-26  k906=6.16245e-27  k907b_dual=2.94837e-29  k907b_dualinv=1.09743e-29
  k406a_S          min|.|=814.071 at t=0.0 ; sign changes: 0
  k607_2           min|.|=459.325 at t=0.523599 ; sign changes: 0
  k609_2           min|.|=5.13224e-6 at t=0.523599 ; sign changes: 0
  k610_2           min|.|=33.9485 at t=0.0 ; sign changes: 4
     ROOT t=0.52286393589161168669  k610_2=-1.95214e+20 partner k610_1=-1.95214e+20 |diff|=1.71458e+13 minsin=7.60932e-21
     ROOT t=0.52359932146486996999  k610_2=1.84077e+20 partner k610_1=1.84077e+20 |diff|=1.5659e+13 minsin=8.0697e-21
     ROOT t=2.6179933321249232685  k610_2=1.84077e+20 partner k610_1=1.84077e+20 |diff|=1.65326e+13 minsin=8.0697e-21
     ROOT t=2.6187287176981815518  k610_2=-1.95214e+20 partner k610_1=-1.95214e+20 |diff|=1.71461e+13 minsin=7.60932e-21
  k905_2           min|.|=16.0741 at t=0.523599 ; sign changes: 0
  k906_2           min|.|=0.00113669 at t=0.0 ; sign changes: 8
     ROOT t=0.032769881930811485461  k906_2=6.16403e-20 partner k906_1=6.16403e-20 |diff|=2.40855e-28
     ROOT t=0.038763078774542840582  k906_2=-9.90162e-21 partner k906_1=-9.90162e-21 |diff|=2.42963e-28
     ROOT t=0.48800097202499175774  k906_2=-3.81513e-22 partner k906_1=-3.81512e-22 |diff|=2.49132e-28
     ROOT t=0.56074922447696954088  k906_2=-5.26036e-22 partner k906_1=-5.26037e-22 |diff|=2.61766e-28
     ROOT t=2.5808434291128236976  k906_2=-5.26036e-22 partner k906_1=-5.26036e-22 |diff|=2.81697e-28
     ROOT t=2.6535916815648014807  k906_2=-3.81513e-22 partner k906_1=-3.81513e-22 |diff|=2.20191e-28
     ROOT t=3.1028295748152503979  k906_2=-9.90162e-21 partner k906_1=-9.90162e-21 |diff|=3.40936e-27
     ROOT t=3.108822771658981753  k906_2=6.16403e-20 partner k906_1=6.16403e-20 |diff|=3.4132e-27
  k907_dual_2      min|.|=0.0669609 at t=1.5708 ; sign changes: 0
  k907_dualinv_2   min|.|=0.00223046 at t=1.5708 ; sign changes: 0
FAMILY a=1.0 b=0.8 N=10 tau=3 : a''=0.7051481305775573687708493 b''=0.3704509226024737119399598
  max |A1-A2| over 360 members: k607=8.04638e-29  k609=1.82424e-30  k610=3.10895e-24  k905=1.12807e-28  k906=4.93038e-30  k907b_dual=4.14152e-30  k907b_dualinv=1.57772e-30
  k406a_S          min|.|=33.1394 at t=1.5708 ; sign changes: 0
  k607_2           min|.|=13.8417 at t=0.0 ; sign changes: 0
  k609_2           min|.|=0.17632 at t=1.5708 ; sign changes: 0
  k610_2           min|.|=1.87743 at t=0.0 ; sign changes: 10
     ROOT t=0.086920098802161099159  k610_2=6.09236e+19 partner k610_1=6.09236e+19 |diff|=2.89354e+10 minsin=6.85683e-21
     ROOT t=0.37698033459204032784  k610_2=-1.4869e+21 partner k610_1=-1.4869e+21 |diff|=1.6502e+13 minsin=2.80949e-22
     ROOT t=0.59397400251304971113  k610_2=-4.61916e+20 partner k610_1=-4.61916e+20 |diff|=2.22961e+12 minsin=9.04369e-22
     ROOT t=1.0060297146089819593  k610_2=-3.11933e+20 partner k610_1=-3.11933e+20 |diff|=8.06963e+10 minsin=1.33921e-21
     ROOT t=1.3152655699843283252  k610_2=-5.71264e+20 partner k610_1=-5.71264e+20 |diff|=3.24779e+12 minsin=7.31259e-22
     ROOT t=1.8263270836054649133  k610_2=-5.71264e+20 partner k610_1=-5.71264e+20 |diff|=1.0826e+11 minsin=7.31259e-22
     ROOT t=2.1355629389808112792  k610_2=-3.11933e+20 partner k610_1=-3.11933e+20 |diff|=1.29114e+12 minsin=1.33921e-21
     ROOT t=2.5476186510767435273  k610_2=-4.61916e+20 partner k610_1=-4.61916e+20 |diff|=1.06172e+11 minsin=9.04369e-22
     ROOT t=2.7646123189977529106  k610_2=-1.4869e+21 partner k610_1=-1.4869e+21 |diff|=4.10716e+13 minsin=2.80949e-22
     ROOT t=3.0546725547876321393  k610_2=6.09236e+19 partner k610_1=6.09236e+19 |diff|=3.07824e+9 minsin=6.85683e-21
  k905_2           min|.|=2.77012 at t=0.0 ; sign changes: 0
  k906_2           min|.|=1.17529 at t=1.5708 ; sign changes: 0
  k907_dual_2      min|.|=1.48395 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=0.539268 at t=0.0 ; sign changes: 0
FAMILY a=1.0 b=0.65 N=12 tau=5 : a''=0.7599733493020829898801336 b''=0.007713083003953279597380722
  max |A1-A2| over 360 members: k607=1.87056e-20  k609=1.88934e-30  k610=1.81384e-22  k905=3.74173e-26  k906=1.41329e-27  k907b_dual=2.73538e-28  k907b_dualinv=7.72999e-29
  k406a_S          min|.|=106813.0 at t=1.5708 ; sign changes: 0
  k607_2           min|.|=7647.71 at t=2.43473 ; sign changes: 0
  k609_2           min|.|=1.281e-6 at t=2.43473 ; sign changes: 0
  k610_2           min|.|=66.2202 at t=1.5708 ; sign changes: 0
  k905_2           min|.|=12.1332 at t=2.43473 ; sign changes: 0
  k906_2           min|.|=3.65687e-5 at t=1.5708 ; sign changes: 4
     ROOT t=0.69502066522844967629  k906_2=2.91283e-21 partner k906_1=2.91283e-21 |diff|=3.39808e-28
     ROOT t=0.72021323465818862738  k906_2=3.0419e-23 partner k906_1=3.04184e-23 |diff|=5.81335e-28
     ROOT t=2.4213794189316046111  k906_2=3.04222e-23 partner k906_1=3.04218e-23 |diff|=4.32277e-28
     ROOT t=2.4465719883613435622  k906_2=2.91283e-21 partner k906_1=2.91283e-21 |diff|=4.09499e-28
  k907_dual_2      min|.|=0.263612 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=0.000327289 at t=1.5708 ; sign changes: 0
FAMILY a=1.0 b=0.65 N=16 tau=1 : a''=0.9878722921807301299112946 b''=0.6311827513948791901320424
  max |A1-A2| over 360 members: k607=3.9443e-30  k609=1.34106e-29  k610=2.85962e-30  k905=3.187e-28  k906=2.58746e-28  k907b_dual=1.57772e-30  k907b_dualinv=4.68386e-30
  k406a_S          min|.|=2.01215 at t=0.488692 ; sign changes: 0
  k607_2           min|.|=0.7143 at t=2.6529 ; sign changes: 0
  k609_2           min|.|=2.80756 at t=0.488692 ; sign changes: 0
  k610_2           min|.|=0.606456 at t=1.5708 ; sign changes: 0
  k905_2           min|.|=21.3768 at t=0.0 ; sign changes: 0
  k906_2           min|.|=17.782 at t=0.488692 ; sign changes: 0
  k907_dual_2      min|.|=0.528092 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=0.485495 at t=0.0 ; sign changes: 0
FAMILY a=1.0 b=0.3 N=6 tau=1 : a''=0.9730085108210397960192602 b''=0.1916913199134940255930564
  max |A1-A2| over 360 members: k607=5.6798e-29  k609=2.20881e-29  k610=2.70548e-26  k905=8.1158e-27  k906=1.14543e-27  k907b_dual=6.16298e-31  k907b_dualinv=4.19082e-31
  k406a_S          min|.|=1.8523 at t=0.0 ; sign changes: 0
  k607_2           min|.|=2.2151 at t=0.0 ; sign changes: 0
  k609_2           min|.|=0.41267 at t=1.5708 ; sign changes: 0
  k610_2           min|.|=3.32937 at t=1.16937 ; sign changes: 0
  k905_2           min|.|=0.932938 at t=2.13803 ; sign changes: 6
     ROOT t=0.084066586664322547688  k905_2=-3.14694e-18 partner k905_1=-3.14694e-18 |diff|=2.55044e-27
     ROOT t=0.45913368556412174033  k905_2=-7.48528e-19 partner k905_1=-7.48528e-19 |diff|=1.2704e-27
     ROOT t=1.0067900964279322353  k905_2=1.5362e-19 partner k905_1=1.5362e-19 |diff|=2.26396e-27
     ROOT t=2.1348025571618610032  k905_2=1.5362e-19 partner k905_1=1.5362e-19 |diff|=6.71197e-28
     ROOT t=2.6824589680256714981  k905_2=-7.48528e-19 partner k905_1=-7.48528e-19 |diff|=3.29926e-28
     ROOT t=3.0575260669254706908  k905_2=-3.14694e-18 partner k905_1=-3.14694e-18 |diff|=1.44431e-27
  k906_2           min|.|=26.656 at t=1.5708 ; sign changes: 0
  k907_dual_2      min|.|=0.011904 at t=0.0 ; sign changes: 0
  k907_dualinv_2   min|.|=0.00684482 at t=0.0 ; sign changes: 0
FAMILY a=1.0 b=0.3 N=12 tau=1 : a''=0.9918440643083882665764392 b''=0.2715780696296780010970849
  max |A1-A2| over 360 members: k607=2.91879e-29  k609=4.73317e-29  k610=3.03711e-29  k905=3.28166e-26  k906=1.40354e-26  k907b_dual=1.00457e-30  k907b_dualinv=2.24332e-30
  k406a_S          min|.|=0.690074 at t=2.00713 ; sign changes: 0
  k607_2           min|.|=3.45472 at t=1.13446 ; sign changes: 0
  k609_2           min|.|=2.27838 at t=2.00713 ; sign changes: 0
  k610_2           min|.|=3.97928 at t=0.0 ; sign changes: 0
  k905_2           min|.|=385.481 at t=0.0 ; sign changes: 0
  k906_2           min|.|=217.725 at t=2.00713 ; sign changes: 0
  k907_dual_2      min|.|=0.0203575 at t=1.5708 ; sign changes: 0
  k907_dualinv_2   min|.|=0.0157032 at t=1.5708 ; sign changes: 0
