r2_geom.py -- mpmath 1.3.0, 60 digits; 5 ellipses x 28 (N, tau) families (N = 3..13, all turning numbers), 7 members each

== ellipse a = 1, b = 0.6
  [PASS] N=3 tau=1 lambda/b^2=0.96322503895729 : noise 1.26e-57; constant rows spread <= 5.36e-58; varying rows spread >= 0.0854; closed forms 3.14e-58; gamma = -1.0, 2+gamma = 1.0, k808 = k810 = 25.8076127072299
  [PASS] N=4 tau=1 lambda/b^2=0.73529411764706 : noise 1.0e-58; constant rows spread <= 5.69e-60; varying rows spread >= 0.129; closed forms 6.05e-60; k807 = 0.280276816608997, k809 = 1.44, k110 = 0.560553633217993
  [PASS] N=5 tau=1 lambda/b^2=0.53004279892552 : noise 7.77e-58; constant rows spread <= 5.03e-59; varying rows spread >= 1.88e-5; closed forms 9.0e-59; gamma = 0.630882535379, 2+gamma = 2.6308825, k808 = k810 = 2.46550323461174
  [PASS] N=5 tau=2 lambda/b^2=0.99951894943377 : noise 4.87e-56; constant rows spread <= 2.02e-56; varying rows spread >= 0.0776; closed forms 1.27e-56; gamma = -1.21648419678, 2+gamma = 0.7835158, k808 = k810 = 290.916349086531; A on 48 members in [0.655681, 0.717179]
  [PASS] N=6 tau=1 lambda/b^2=0.390625 : noise 2.51e-58; constant rows spread <= 1.25e-59; varying rows spread >= 0.00509; closed forms 1.76e-59; k807 = 1.2637092590332, k809 = 2.413125, k110 = 1.68494567871094
  [PASS] N=7 tau=1 lambda/b^2=0.29701290940081 : noise 1.0e-58; constant rows spread <= 2.44e-60; varying rows spread >= 1.63e-7; closed forms 3.09e-60; gamma = 1.23681541479, 2+gamma = 3.2368154, k808 = k810 = 1.55963987738811
  [PASS] N=7 tau=2 lambda/b^2=0.85823780744519 : noise 2.78e-58; constant rows spread <= 5.13e-59; varying rows spread >= 2.46e-5; closed forms 3.72e-59; gamma = -0.478887026289, 2+gamma = 1.521113, k808 = k810 = 8.40172533631408; A on 48 members in [1.86682, 1.86685]
  [PASS] N=7 tau=3 lambda/b^2=0.99999405311806 : noise 4.04e-54; constant rows spread <= 1.64e-54; varying rows spread >= 0.0766; closed forms 1.08e-54; gamma = -1.2194747351, 2+gamma = 0.78052526, k808 = k810 = 2626.86439575192; A on 48 members in [0.6559, 0.717379]
  [PASS] N=8 tau=1 lambda/b^2=0.23239650069375 : noise 1.34e-57; constant rows spread <= 3.48e-59; varying rows spread >= 0.000226; closed forms 4.17e-59; k807 = 2.00746811906771, k809 = 2.85401574674215, k110 = 2.36254299149863
  [PASS] N=8 tau=3 lambda/b^2=0.99570577275787 : noise 1.27e-56; constant rows spread <= 1.4e-57; varying rows spread >= 0.0786; closed forms 1.15e-57; k807 = 0.0198294801739196, k809 = 7.19777983054154, k110 = 0.0982432626648653; A on 48 members in [1.30785, 1.43114]
  [PASS] N=9 tau=1 lambda/b^2=0.18633471851671 : noise 2.48e-58; constant rows spread <= 3.54e-60; varying rows spread >= 4.62e-10; closed forms 5.79e-60; gamma = 1.51471113448, 2+gamma = 3.5147111, k808 = k810 = 1.30624720953332
  [PASS] N=9 tau=2 lambda/b^2=0.62370909809094 : noise 1.13e-57; constant rows spread <= 6.18e-59; varying rows spread >= 1.43e-8; closed forms 8.58e-59; gamma = 0.361039135451, 2+gamma = 2.3610391, k808 = k810 = 3.13627346134283; A on 48 members in [2.54388, 2.54388]
  [PASS] N=9 tau=4 lambda/b^2=0.99999992657995 : noise 4.26e-52; constant rows spread <= 1.73e-52; varying rows spread >= 0.0766; closed forms 1.14e-52; gamma = -1.21951173264, 2+gamma = 0.78048827, k808 = k810 = 23642.6561557258; A on 48 members in [0.655903, 0.717382]
  [PASS] N=10 tau=1 lambda/b^2=0.152505749164 : noise 1.87e-57; constant rows spread <= 2.74e-59; varying rows spread >= 6.91e-6; closed forms 3.15e-59; k807 = 2.47090475696618, k809 = 3.08490953343283, k110 = 2.7451212062281
  [PASS] N=10 tau=3 lambda/b^2=0.89774867321608 : noise 6.01e-58; constant rows spread <= 4.54e-59; varying rows spread >= 0.00144; closed forms 4.94e-59; k807 = 0.578464845614814, k809 = 8.3587424869314, k110 = 1.72628843923399; A on 48 members in [2.56001, 2.56333]
  [PASS] N=11 tau=1 lambda/b^2=0.12700201489842 : noise 1.0e-58; constant rows spread <= 6.22e-61; varying rows spread >= 1.18e-12; closed forms 2.6e-61; gamma = 1.66555827678, 2+gamma = 3.6655583, k808 = k810 = 1.19557134160097
  [PASS] N=11 tau=2 lambda/b^2=0.45327435236085 : noise 1.21e-57; constant rows spread <= 3.12e-59; varying rows spread >= 2.53e-11; closed forms 5.57e-59; gamma = 0.837580745026, 2+gamma = 2.8375807, k808 = k810 = 2.08406228049702; A on 48 members in [2.92366, 2.92366]
  [PASS] N=11 tau=3 lambda/b^2=0.8170920172674 : noise 3.53e-58; constant rows spread <= 4.16e-59; varying rows spread >= 4.21e-9; closed forms 2.61e-59; gamma = -0.306234816797, 2+gamma = 1.6937652, k808 = k810 = 6.57256987968035; A on 48 members in [3.01561, 3.01561]
  [PASS] N=11 tau=4 lambda/b^2=0.99114158548113 : noise 4.67e-57; constant rows spread <= 8.58e-58; varying rows spread >= 8.62e-6; closed forms 3.58e-58; gamma = -1.16445178051, 2+gamma = 0.83554822, k808 = k810 = 63.4221791164097; A on 48 members in [2.04714, 2.04717]
  [PASS] N=11 tau=5 lambda/b^2=0.99999999909358 : noise 1.97e-51; constant rows spread <= 8.02e-52; varying rows spread >= 0.0766; closed forms 5.27e-52; gamma = -1.21951218941, 2+gamma = 0.78048781, k808 = k810 = 212783.993165624; A on 48 members in [0.655903, 0.717382]
  [PASS] N=12 tau=1 lambda/b^2=0.10733387488043 : noise 1.05e-57; constant rows spread <= 9.94e-60; varying rows spread >= 8.78e-7; closed forms 1.08e-59; k807 = 2.76269071440215, k809 = 3.21926889515454, k110 = 2.9737127564969
  [PASS] N=12 tau=5 lambda/b^2=0.99994648669393 : noise 2.31e-55; constant rows spread <= 2.46e-56; varying rows spread >= 0.0731; closed forms 1.13e-56; k807 = 0.00215004979262645, k809 = 62.7760070779891, k110 = 0.0110142485739103; A on 48 members in [1.31176, 1.43472]
  [PASS] N=13 tau=1 lambda/b^2=0.091865517133573 : noise 2.82e-57; constant rows spread <= 1.72e-59; varying rows spread >= 4.5e-15; closed forms 2.19e-59; gamma = 1.756196484, 2+gamma = 3.7561965, k808 = k810 = 1.13642150889249
  [PASS] N=13 tau=2 lambda/b^2=0.33931688364903 : noise 1.51e-57; constant rows spread <= 2.93e-59; varying rows spread >= 5.91e-14; closed forms 4.43e-59; gamma = 1.13036576907, 2+gamma = 3.1303658, k808 = k810 = 1.67787326146019; A on 48 members in [3.15335, 3.15335]
  [PASS] N=13 tau=3 lambda/b^2=0.65898709043477 : noise 1.12e-57; constant rows spread <= 6.13e-59; varying rows spread >= 3.39e-12; closed forms 6.26e-59; gamma = 0.252461602503, 2+gamma = 2.2524616, k808 = k810 = 3.481944999845; A on 48 members in [3.68614, 3.68614]
  [PASS] N=13 tau=4 lambda/b^2=0.91627465126694 : noise 3.65e-57; constant rows spread <= 3.44e-58; varying rows spread >= 2.32e-9; closed forms 2.49e-58; gamma = -0.750273806413, 2+gamma = 1.2497262, k808 = k810 = 13.5124313611159; A on 48 members in [3.2442, 3.2442]
  [PASS] N=13 tau=5 lambda/b^2=0.99792623490205 : noise 2.53e-57; constant rows spread <= 4.91e-58; varying rows spread >= 1.11e-5; closed forms 2.49e-58; gamma = -1.20649028494, 2+gamma = 0.79350972, k808 = k810 = 138.288104086307; A on 48 members in [2.05615, 2.05617]
  [PASS] N=13 tau=6 lambda/b^2=0.99999999998881 : noise 5.98e-49; constant rows spread <= 2.43e-49; varying rows spread >= 0.0766; closed forms 1.6e-49; gamma = -1.21951219505, 2+gamma = 0.7804878, k808 = k810 = 1915055.94717069; A on 48 members in [0.655903, 0.717382]
  [PASS] a=1 b=0.6: N=4 caustic lambda = a^2b^2/(a^2+b^2); k807 = 4a^4b^4/(a^2+b^2)^2, k809 = 4a^2b^2, k110 = 8a^4b^4/(a^2+b^2)^2 = 4 x (printed 2a^4b^4/(a^2+b^2)^2), k106 = 8a^2b^2 : lambda 7.39e-61, values 2.3e-59
  [PASS] a=1 b=0.6: N=3 lambda = a^2b^2(2 sqrt(a^4-a^2b^2+b^4)-a^2-b^2)/c^4, gamma(lambda) = -1, k808 = 4 kappa : 1.08e-59, 1.71e-58, 1.87e-57
  [PASS] a=1 b=0.6: N=6 k807/k110 = k809/k106 = 3/4; Garcia-Reznik N=6 values of k106, k110; hence k807 = 3a^3b^3(2a+b)^2(a+2b)^2/(a+b)^6, k809 = 3a^2b^2(2a+b)(a+2b)/(a+b)^2 : 1.89e-59

== ellipse a = 1, b = 0.35
  [PASS] N=3 tau=1 lambda/b^2=0.99603214708853 : noise 1.03e-56; constant rows spread <= 8.23e-57; varying rows spread >= 0.407; closed forms 7.39e-58; gamma = -1.0, 2+gamma = 1.0, k808 = k810 = 67.7701424215563
  [PASS] N=4 tau=1 lambda/b^2=0.89086859688196 : noise 2.32e-58; constant rows spread <= 2.77e-59; varying rows spread >= 0.413; closed forms 1.48e-59; k807 = 0.0476386525860487, k809 = 0.49, k110 = 0.0952773051720974
  [PASS] N=5 tau=1 lambda/b^2=0.70805729590707 : noise 1.1e-57; constant rows spread <= 1.19e-58; varying rows spread >= 0.00228; closed forms 7.81e-59; gamma = 0.668464764088, 2+gamma = 2.6684648, k808 = k810 = 2.90303170298372
  [PASS] N=5 tau=2 lambda/b^2=0.99999574233308 : noise 4.81e-54; constant rows spread <= 3.68e-54; varying rows spread >= 0.404; closed forms 9.72e-55; gamma = -1.06517441171, 2+gamma = 0.93482559, k808 = k810 = 2213.70561347009; A on 48 members in [0.237941, 0.372077]
  [PASS] N=6 tau=1 lambda/b^2=0.54869684499314 : noise 1.0e-58; constant rows spread <= 7.86e-61; varying rows spread >= 0.0258; closed forms 5.24e-61; k807 = 0.339122296136485, k809 = 0.805576131687243, k110 = 0.452163061515314
  [PASS] N=7 tau=1 lambda/b^2=0.42918785444784 : noise 2.58e-58; constant rows spread <= 9.42e-60; varying rows spread >= 2.47e-5; closed forms 9.25e-60; gamma = 1.20778114796, 2+gamma = 3.2077811, k808 = k810 = 1.69565055016954
  [PASS] N=7 tau=2 lambda/b^2=0.96262910845656 : noise 7.05e-57; constant rows spread <= 1.63e-57; varying rows spread >= 0.00143; closed forms 4.3e-58; gamma = -0.562370725386, 2+gamma = 1.4376293, k808 = k810 = 15.3247315362079; A on 48 members in [0.881344, 0.882636]
  [PASS] N=7 tau=3 lambda/b^2=0.99999999545897 : noise 2.16e-51; constant rows spread <= 1.66e-51; varying rows spread >= 0.404; closed forms 4.38e-52; gamma = -1.0652462615, 2+gamma = 0.93475374, k808 = k810 = 67789.4144619901; A on 48 members in [0.237942, 0.372078]
  [PASS] N=8 tau=1 lambda/b^2=0.34173377386232 : noise 1.97e-57; constant rows spread <= 7.42e-59; varying rows spread >= 0.00468; closed forms 5.53e-59; k807 = 0.596437893220814, k809 = 0.945661623734147, k110 = 0.711184092496499
  [PASS] N=8 tau=3 lambda/b^2=0.9998696621697 : noise 3.23e-55; constant rows spread <= 6.37e-56; varying rows spread >= 0.404; closed forms 6.04e-57; k807 = 0.00088538382040703, k809 = 7.74116041304806, k110 = 0.00377984064030303; A on 48 members in [0.47584, 0.744104]
  [PASS] N=9 tau=1 lambda/b^2=0.27718173865089 : noise 2.51e-57; constant rows spread <= 7.04e-59; varying rows spread >= 2.6e-7; closed forms 5.71e-59; gamma = 1.46435744868, 2+gamma = 3.4643574, k808 = k810 = 1.38173260483446
  [PASS] N=9 tau=2 lambda/b^2=0.80012599778331 : noise 2.12e-57; constant rows spread <= 2.07e-58; varying rows spread >= 7.5e-6; closed forms 9.11e-59; gamma = 0.401776646285, 2+gamma = 2.4017766, k808 = k810 = 3.92238000482248; A on 48 members in [1.31168, 1.31169]
  [PASS] N=9 tau=4 lambda/b^2=0.99999999999516 : noise 4.58e-48; constant rows spread <= 3.51e-48; varying rows spread >= 0.404; closed forms 9.27e-49; gamma = -1.06524633813, 2+gamma = 0.93475366, k808 = k810 = 2075739.36125537; A on 48 members in [0.237942, 0.372078]
  [PASS] N=10 tau=1 lambda/b^2=0.22868986260125 : noise 5.85e-58; constant rows spread <= 1.46e-59; varying rows spread >= 0.000424; closed forms 1.03e-59; k807 = 0.76858765731023, k809 = 1.02519052560177, k110 = 0.866265802615377
  [PASS] N=10 tau=3 lambda/b^2=0.97850642402498 : noise 1.94e-58; constant rows spread <= 5.31e-60; varying rows spread >= 0.0209; closed forms 3.11e-60; k807 = 0.0607103189181476, k809 = 3.20926478568914, k110 = 0.194091660213429; A on 48 members in [1.1729, 1.20314]
  [PASS] N=11 tau=1 lambda/b^2=0.19155868729904 : noise 2.67e-57; constant rows spread <= 4.58e-59; varying rows spread >= 2.81e-9; closed forms 3.68e-59; gamma = 1.61559979711, 2+gamma = 3.6155998, k808 = k810 = 1.24512138097087
  [PASS] N=11 tau=2 lambda/b^2=0.62330879702694 : noise 5.07e-58; constant rows spread <= 2.11e-59; varying rows spread >= 4.68e-8; closed forms 1.49e-59; gamma = 0.857071685761, 2+gamma = 2.8570717, k808 = k810 = 2.37352412468401; A on 48 members in [1.57754, 1.57754]
  [PASS] N=11 tau=3 lambda/b^2=0.94222933047959 : noise 4.54e-57; constant rows spread <= 8.95e-58; varying rows spread >= 5.01e-6; closed forms 2.14e-58; gamma = -0.364437308645, 2+gamma = 1.6355627, k808 = k810 = 10.8186058081261; A on 48 members in [1.45061, 1.45062]
  [PASS] N=11 tau=4 lambda/b^2=0.99959244121387 : noise 2.38e-55; constant rows spread <= 8.66e-56; varying rows spread >= 0.00142; closed forms 1.33e-56; gamma = -1.05838040409, 2+gamma = 0.9416196, k808 = k810 = 224.62260335211; A on 48 members in [0.902219, 0.903479]
  [PASS] N=11 tau=5 lambda/b^2=0.99999999999999 : noise 2.26e-45; constant rows spread <= 1.73e-45; varying rows spread >= 0.404; closed forms 4.56e-46; gamma = -1.06524633822, 2+gamma = 0.93475366, k808 = k810 = 63559976.3120182; A on 48 members in [0.237942, 0.372078]
  [PASS] N=12 tau=1 lambda/b^2=0.16260104809706 : noise 3.91e-58; constant rows spread <= 7.69e-60; varying rows spread >= 4.78e-5; closed forms 3.98e-60; k807 = 0.881774938142838, k809 = 1.0743930825838, k110 = 0.961340965155783
  [PASS] N=12 tau=5 lambda/b^2=0.99999986095179 : noise 3.72e-53; constant rows spread <= 7.12e-54; varying rows spread >= 0.404; closed forms 6.53e-55; k807 = 2.88553798049535e-5, k809 = 236.490809085247, k110 = 0.000123477696725313; A on 48 members in [0.475884, 0.744155]
  [PASS] N=13 tau=1 lambda/b^2=0.13963570234535 : noise 1.74e-57; constant rows spread <= 2.09e-59; varying rows spread >= 5.6e-11; closed forms 1.61e-59; gamma = 1.71222464365, 2+gamma = 3.7122246, k808 = k810 = 1.17173950228857
  [PASS] N=13 tau=2 lambda/b^2=0.48431121379832 : noise 2.79e-57; constant rows spread <= 6.82e-59; varying rows spread >= 4.86e-10; closed forms 6.44e-59; gamma = 1.11390427428, 2+gamma = 3.1139043, k808 = k810 = 1.84434350183092; A on 48 members in [1.74351, 1.74351]
  [PASS] N=13 tau=3 lambda/b^2=0.83119349389099 : noise 2.83e-57; constant rows spread <= 2.79e-58; varying rows spread >= 2.44e-8; closed forms 8.49e-59; gamma = 0.286252155209, 2+gamma = 2.2862522, k808 = k810 = 4.49324266051106; A on 48 members in [1.87978, 1.87978]
  [PASS] N=13 tau=4 lambda/b^2=0.98462711578239 : noise 2.54e-56; constant rows spread <= 2.54e-57; varying rows spread >= 5.14e-6; closed forms 6.54e-58; gamma = -0.830372088199, 2+gamma = 1.1696279, k808 = k810 = 29.4134192066061; A on 48 members in [1.49072, 1.49073]
  [PASS] N=13 tau=5 lambda/b^2=0.99995833131137 : noise 1.59e-54; constant rows spread <= 7.94e-55; varying rows spread >= 0.00143; closed forms 6.15e-56; gamma = -1.06454259387, 2+gamma = 0.93545741, k808 = k810 = 707.141347067241; A on 48 members in [0.902425, 0.903684]
  [PASS] N=13 tau=6 lambda/b^2=1.0 : noise 4.6e-42; constant rows spread <= 3.52e-42; varying rows spread >= 0.404; closed forms 9.31e-43; gamma = -1.06524633822, 2+gamma = 0.93475366, k808 = k810 = 1946232105.95815; A on 48 members in [0.237942, 0.372078]
  [PASS] a=1 b=0.35: N=4 caustic lambda = a^2b^2/(a^2+b^2); k807 = 4a^4b^4/(a^2+b^2)^2, k809 = 4a^2b^2, k110 = 8a^4b^4/(a^2+b^2)^2 = 4 x (printed 2a^4b^4/(a^2+b^2)^2), k106 = 8a^2b^2 : lambda 5.54e-61, values 1.47e-58
  [PASS] a=1 b=0.35: N=3 lambda = a^2b^2(2 sqrt(a^4-a^2b^2+b^4)-a^2-b^2)/c^4, gamma(lambda) = -1, k808 = 4 kappa : 4.58e-60, 5.96e-58, 1.75e-56
  [PASS] a=1 b=0.35: N=6 k807/k110 = k809/k106 = 3/4; Garcia-Reznik N=6 values of k106, k110; hence k807 = 3a^3b^3(2a+b)^2(a+2b)^2/(a+b)^6, k809 = 3a^2b^2(2a+b)(a+2b)/(a+b)^2 : 1.38e-60

== ellipse a = 3, b = 2
  [PASS] N=3 tau=1 lambda/b^2=0.94337976665279 : noise 4.21e-58; constant rows spread <= 1.63e-58; varying rows spread >= 0.0395; closed forms 1.51e-58; gamma = -1.0, 2+gamma = 1.0, k808 = k810 = 22.0592495318652
  [PASS] N=4 tau=1 lambda/b^2=0.69230769230769 : noise 4.19e-58; constant rows spread <= 4.79e-59; varying rows spread >= 0.0853; closed forms 8.8e-59; k807 = 30.6745562130178, k809 = 144.0, k110 = 61.3491124260355
  [PASS] N=5 tau=1 lambda/b^2=0.49172266873827 : noise 2.9e-58; constant rows spread <= 1.61e-59; varying rows spread >= 9.05e-6; closed forms 3.75e-59; gamma = 0.626199152619, 2+gamma = 2.6261992, k808 = k810 = 2.41673779809495
  [PASS] N=5 tau=2 lambda/b^2=0.99868299590384 : noise 2.19e-56; constant rows spread <= 7.34e-57; varying rows spread >= 0.0322; closed forms 4.48e-57; gamma = -1.27870845136, 2+gamma = 0.72129155, k808 = k810 = 204.910008256579; A on 48 members in [7.12456, 7.46723]
  [PASS] N=6 tau=1 lambda/b^2=0.36 : noise 7.6e-58; constant rows spread <= 3.4e-59; varying rows spread >= 0.00254; closed forms 5.99e-59; k807 = 130.056192, k809 = 241.92, k110 = 173.408256
  [PASS] N=7 tau=1 lambda/b^2=0.27276214582079 : noise 8.68e-58; constant rows spread <= 2.38e-59; varying rows spread >= 3.06e-8; closed forms 4.24e-59; gamma = 1.24050584662, 2+gamma = 3.2405058, k808 = k810 = 1.5440833660312
  [PASS] N=7 tau=2 lambda/b^2=0.82037298999396 : noise 1.0e-58; constant rows spread <= 1.06e-59; varying rows spread >= 3.87e-6; closed forms 1.1e-59; gamma = -0.466964050044, 2+gamma = 1.5330359, k808 = k810 = 7.72327890248075; A on 48 members in [19.2747, 19.2748]
  [PASS] N=7 tau=3 lambda/b^2=0.99997186003389 : noise 1.3e-54; constant rows spread <= 4.13e-55; varying rows spread >= 0.0398; closed forms 2.85e-55; gamma = -1.28556440154, 2+gamma = 0.7144356, k808 = k810 = 1416.01053454373; A on 48 members in [7.13081, 7.47307]
  [PASS] N=8 tau=1 lambda/b^2=0.21296843950232 : noise 1.27e-57; constant rows spread <= 2.82e-59; varying rows spread >= 9.98e-5; closed forms 4.16e-59; k807 = 204.032388684784, k809 = 286.346399178279, k110 = 239.726617393332
  [PASS] N=8 tau=3 lambda/b^2=0.99112013708085 : noise 7.02e-57; constant rows spread <= 6.6e-58; varying rows spread >= 0.0288; closed forms 9.46e-58; k807 = 2.8247075977489, k809 = 568.545816287641, k110 = 14.8440446640404; A on 48 members in [14.1757, 14.8658]
  [PASS] N=9 tau=1 lambda/b^2=0.17052088968716 : noise 2.0e-57; constant rows spread <= 2.81e-59; varying rows spread >= 5.17e-11; closed forms 4.65e-59; gamma = 1.52103461874, 2+gamma = 3.5210346, k808 = k810 = 1.29748082338837
  [PASS] N=9 tau=2 lambda/b^2=0.58195157180905 : noise 4.71e-58; constant rows spread <= 2.12e-59; varying rows spread >= 2.04e-9; closed forms 4.1e-59; gamma = 0.356020323364, 2+gamma = 2.3560203, k808 = k810 = 3.0496822558571; A on 48 members in [25.8489, 25.8489]
  [PASS] N=9 tau=4 lambda/b^2=0.99999940093564 : noise 1.9e-53; constant rows spread <= 6.05e-54; varying rows spread >= 0.04; closed forms 4.17e-54; gamma = -1.28571109478, 2+gamma = 0.71428891, k808 = k810 = 9707.01041010515; A on 48 members in [7.13094, 7.4732]
  [PASS] N=10 tau=1 lambda/b^2=0.13942940403729 : noise 2.84e-57; constant rows spread <= 3.47e-59; varying rows spread >= 2.96e-6; closed forms 4.9e-59; k807 = 249.748680172388, k809 = 309.385056806616, k110 = 276.971879748115
  [PASS] N=10 tau=3 lambda/b^2=0.86422003842543 : noise 1.23e-58; constant rows spread <= 9.58e-60; varying rows spread >= 0.000415; closed forms 1.36e-59; k807 = 69.1468634697351, k809 = 826.846789903042, k110 = 204.186125591815; A on 48 members in [26.5661, 26.5781]
  [PASS] N=11 tau=1 lambda/b^2=0.11603231689347 : noise 2.11e-57; constant rows spread <= 1.76e-59; varying rows spread >= 9.94e-14; closed forms 2.8e-59; gamma = 1.6717422882, 2+gamma = 3.6717423, k808 = k810 = 1.18978077171218
  [PASS] N=11 tau=2 lambda/b^2=0.41888106179515 : noise 1.31e-57; constant rows spread <= 3.15e-59; varying rows spread >= 1.78e-12; closed forms 6.69e-59; gamma = 0.835125135892, 2+gamma = 2.8351251, k808 = k810 = 2.05157891193015; A on 48 members in [29.5194, 29.5194]
  [PASS] N=11 tau=3 lambda/b^2=0.77640752252284 : noise 3.87e-58; constant rows spread <= 3.81e-59; varying rows spread >= 2.87e-10; closed forms 3.52e-59; gamma = -0.298489682266, 2+gamma = 1.7015103, k808 = k810 = 6.14326672192488; A on 48 members in [31.0136, 31.0136]
  [PASS] N=11 tau=4 lambda/b^2=0.98336789999807 : noise 6.14e-58; constant rows spread <= 8.95e-59; varying rows spread >= 2.24e-6; closed forms 6.68e-59; gamma = -1.19856508502, 2+gamma = 0.80143491, k808 = k810 = 51.5803402651621; A on 48 members in [21.6605, 21.6605]
  [PASS] N=11 tau=5 lambda/b^2=0.99999998724813 : noise 1.58e-51; constant rows spread <= 5.03e-52; varying rows spread >= 0.04; closed forms 3.47e-52; gamma = -1.28571421779, 2+gamma = 0.71428578, k808 = k810 = 66533.036251992; A on 48 members in [7.13095, 7.4732]
  [PASS] N=12 tau=1 lambda/b^2=0.098012494599908 : noise 3.9e-57; constant rows spread <= 2.97e-59; varying rows spread >= 2.49e-7; closed forms 3.96e-59; k807 = 278.378809612648, k809 = 322.684737523728, k110 = 299.174558884237
  [PASS] N=12 tau=5 lambda/b^2=0.99980723723104 : noise 9.29e-56; constant rows spread <= 8.24e-57; varying rows spread >= 0.0381; closed forms 5.36e-57; k807 = 0.394194667898539, k809 = 3680.38394025747, k110 = 2.2043221274472; A on 48 members in [14.26, 14.9447]
  [PASS] N=13 tau=1 lambda/b^2=0.083854347411153 : noise 6.03e-57; constant rows spread <= 3.11e-59; varying rows spread >= 2.74e-16; closed forms 4.88e-59; gamma = 1.7615771385, 2+gamma = 3.7615771, k808 = k810 = 1.13228352385339
  [PASS] N=13 tau=2 lambda/b^2=0.31208696078761 : noise 5.49e-58; constant rows spread <= 1.05e-59; varying rows spread >= 2.32e-15; closed forms 1.73e-59; gamma = 1.13245850223, 2+gamma = 3.1324585, k808 = k810 = 1.65894508809119; A on 48 members in [31.7386, 31.7386]
  [PASS] N=13 tau=3 lambda/b^2=0.61643725420676 : noise 1.0e-58; constant rows spread <= 1.79e-60; varying rows spread >= 2.26e-13; closed forms 6.46e-61; gamma = 0.24830280818, 2+gamma = 2.2483028, k808 = k810 = 3.37140035119158; A on 48 members in [37.5189, 37.5189]
  [PASS] N=13 tau=4 lambda/b^2=0.88555648454951 : noise 1.59e-58; constant rows spread <= 1.38e-59; varying rows spread >= 2.03e-10; closed forms 1.46e-59; gamma = -0.736548689837, 2+gamma = 1.2634513, k808 = k810 = 12.0176448241967; A on 48 members in [33.74, 33.74]
  [PASS] N=13 tau=5 lambda/b^2=0.99528545350913 : noise 3.49e-57; constant rows spread <= 5.21e-58; varying rows spread >= 1.84e-6; closed forms 2.57e-58; gamma = -1.26071983138, 2+gamma = 0.73928017, k808 = k810 = 105.52364062957; A on 48 members in [21.8303, 21.8303]
  [PASS] N=13 tau=6 lambda/b^2=0.99999999972856 : noise 3.73e-50; constant rows spread <= 1.19e-50; varying rows spread >= 0.04; closed forms 8.19e-51; gamma = -1.28571428427, 2+gamma = 0.71428572, k808 = k810 = 456024.239536209; A on 48 members in [7.13095, 7.4732]
  [PASS] a=3 b=2: N=4 caustic lambda = a^2b^2/(a^2+b^2); k807 = 4a^4b^4/(a^2+b^2)^2, k809 = 4a^2b^2, k110 = 8a^4b^4/(a^2+b^2)^2 = 4 x (printed 2a^4b^4/(a^2+b^2)^2), k106 = 8a^2b^2 : lambda 1.16e-58, values 2.12e-58
  [PASS] a=3 b=2: N=3 lambda = a^2b^2(2 sqrt(a^4-a^2b^2+b^4)-a^2-b^2)/c^4, gamma(lambda) = -1, k808 = 4 kappa : 6.63e-59, 7.97e-59, 7.24e-58
  [PASS] a=3 b=2: N=6 k807/k110 = k809/k106 = 3/4; Garcia-Reznik N=6 values of k106, k110; hence k807 = 3a^3b^3(2a+b)^2(a+2b)^2/(a+b)^6, k809 = 3a^2b^2(2a+b)(a+2b)/(a+b)^2 : 6.01e-59

== ellipse a = 1.3, b = 1.25
  [PASS] N=3 tau=1 lambda/b^2=0.77850425415782 : noise 1.07e-58; constant rows spread <= 7.26e-60; varying rows spread >= 6.07e-5; closed forms 1.18e-58; gamma = -1.0, 2+gamma = 1.0, k808 = k810 = 16.0553846806775
  [PASS] N=4 tau=1 lambda/b^2=0.5196003074558 : noise 2.17e-58; constant rows spread <= 3.78e-60; varying rows spread >= 0.000863; closed forms 9.99e-59; k807 = 2.63656718269693, k809 = 10.5625, k110 = 5.27313436539385
  [PASS] N=5 tau=1 lambda/b^2=0.35913272669255 : noise 1.79e-58; constant rows spread <= 1.6e-60; varying rows spread >= 1.99e-10; closed forms 3.62e-59; gamma = 0.618111516534, 2+gamma = 2.6181115, k808 = k810 = 2.33513532054781
  [PASS] N=5 tau=2 lambda/b^2=0.93546464904393 : noise 6.18e-58; constant rows spread <= 9.68e-59; varying rows spread >= 2.02e-6; closed forms 6.41e-58; gamma = -1.60872137246, 2+gamma = 0.39127863, k808 = k810 = 109.47897498746; A on 48 members in [2.37933, 2.37934]
  [PASS] N=6 tau=1 lambda/b^2=0.25990003844675 : noise 5.87e-58; constant rows spread <= 3.73e-60; varying rows spread >= 2.37e-6; closed forms 6.32e-59; k807 = 10.0214120717825, k809 = 17.8234573241061, k110 = 13.3618827623766
  [PASS] N=7 tau=1 lambda/b^2=0.19572147839586 : noise 1.0e-58; constant rows spread <= 7.17e-61; varying rows spread >= 2.45e-15; closed forms 2.36e-60; gamma = 1.24691789578, 2+gamma = 3.2469179, k808 = k810 = 1.51785995108709
  [PASS] N=7 tau=2 lambda/b^2=0.63501279485954 : noise 1.04e-58; constant rows spread <= 2.44e-60; varying rows spread >= 4.2e-13; closed forms 3.58e-59; gamma = -0.445257574279, 2+gamma = 1.5547424, k808 = k810 = 6.62739602032071; A on 48 members in [5.54155, 5.54155]
  [PASS] N=7 tau=3 lambda/b^2=0.97806023889236 : noise 6.57e-58; constant rows spread <= 2.11e-58; varying rows spread >= 6.7e-7; closed forms 5.86e-58; gamma = -1.77432457767, 2+gamma = 0.22567542, k808 = k810 = 386.758208820178; A on 48 members in [2.45062, 2.45062]
  [PASS] N=8 tau=1 lambda/b^2=0.1522601228092 : noise 7.97e-58; constant rows spread <= 2.49e-60; varying rows spread >= 1.09e-8; closed forms 3.33e-59; k807 = 15.3866292324749, k809 = 21.123845484349, k110 = 18.0270500513878
  [PASS] N=8 tau=3 lambda/b^2=0.88456512352602 : noise 4.51e-58; constant rows spread <= 2.56e-59; varying rows spread >= 1.15e-5; closed forms 2.44e-58; k807 = 0.449023794820857, k809 = 21.3528518074461, k110 = 3.04978543824759; A on 48 members in [4.58595, 4.58599]
  [PASS] N=9 tau=1 lambda/b^2=0.12162420602793 : noise 2.62e-57; constant rows spread <= 4.12e-60; varying rows spread >= 3.62e-20; closed forms 7.46e-59; gamma = 1.53198374285, 2+gamma = 3.5319837, k808 = k810 = 1.28263862496744
  [PASS] N=9 tau=2 lambda/b^2=0.42944591372233 : noise 8.64e-58; constant rows spread <= 5.46e-60; varying rows spread >= 1.4e-18; closed forms 1.26e-58; gamma = 0.347379039878, 2+gamma = 2.347379, k808 = k810 = 2.90527059340823; A on 48 members in [7.19946, 7.19946]
  [PASS] N=9 tau=4 lambda/b^2=0.99243236780571 : noise 5.19e-58; constant rows spread <= 2.61e-58; varying rows spread >= 3.49e-7; closed forms 3.93e-58; gamma = -1.8302440054, 2+gamma = 0.16975599, k808 = k810 = 943.375484250372; A on 48 members in [2.47448, 2.47448]
  [PASS] N=10 tau=1 lambda/b^2=0.099286023255089 : noise 2.75e-57; constant rows spread <= 3.98e-60; varying rows spread >= 3.97e-11; closed forms 5.61e-59; k807 = 18.6566650572452, k809 = 22.806753466092, k110 = 20.6269074893075
  [PASS] N=10 tau=3 lambda/b^2=0.67981532061006 : noise 1.0e-58; constant rows spread <= 1.57e-60; varying rows spread >= 4.74e-9; closed forms 2.46e-59; k807 = 7.10298307090137, k809 = 59.7191390892754, k110 = 20.5632045363538; A on 48 members in [7.72171, 7.72171]
  [PASS] N=11 tau=1 lambda/b^2=0.082528188076817 : noise 8.72e-58; constant rows spread <= 1.19e-60; varying rows spread >= 7.87e-25; closed forms 1.36e-59; gamma = 1.68240494597, 2+gamma = 3.6824049, k808 = k810 = 1.17995940846738
  [PASS] N=11 tau=2 lambda/b^2=0.30385335753252 : noise 8.73e-58; constant rows spread <= 3.35e-60; varying rows spread >= 1.4e-23; closed forms 6.23e-59; gamma = 0.830870890814, 2+gamma = 2.8308709, k808 = k810 = 1.99711847388763; A on 48 members in [8.12854, 8.12854]
  [PASS] N=11 tau=3 lambda/b^2=0.59343364531345 : noise 4.35e-58; constant rows spread <= 5.37e-60; varying rows spread >= 3.54e-21; closed forms 8.73e-59; gamma = -0.284763607443, 2+gamma = 1.7152364, k808 = k810 = 5.44401995202606; A on 48 members in [8.842, 8.842]
  [PASS] N=11 tau=4 lambda/b^2=0.85799649625456 : noise 7.83e-58; constant rows spread <= 2.57e-59; varying rows spread >= 7.83e-17; closed forms 2.85e-58; gamma = -1.30800556861, 2+gamma = 0.69199443, k808 = k810 = 33.7366455823914; A on 48 members in [6.74213, 6.74213]
  [PASS] N=11 tau=5 lambda/b^2=0.99744715689232 : noise 3.46e-57; constant rows spread <= 2.24e-57; varying rows spread >= 2.8e-7; closed forms 2.25e-57; gamma = -1.8497609645, 2+gamma = 0.15023904, k808 = k810 = 1889.13974345013; A on 48 members in [2.48278, 2.48279]
  [PASS] N=12 tau=1 lambda/b^2=0.06965051151542 : noise 3.58e-57; constant rows spread <= 3.03e-60; varying rows spread >= 2.17e-13; closed forms 4.2e-59; k807 = 20.6857287788211, k809 = 23.7647114964005, k110 = 22.1714654320576
  [PASS] N=12 tau=5 lambda/b^2=0.9626355057652 : noise 9.96e-58; constant rows spread <= 1.51e-58; varying rows spread >= 1.17e-6; closed forms 4.79e-58; k807 = 0.107684221535537, k809 = 26.2024729197743, k110 = 1.5078356303581; A on 48 members in [4.84981, 4.84981]
  [PASS] N=13 tau=1 lambda/b^2=0.059549328455104 : noise 7.04e-57; constant rows spread <= 3.87e-60; varying rows spread >= 1.4e-29; closed forms 6.39e-59; gamma = 1.77082368165, 2+gamma = 3.7708237, k808 = k810 = 1.12525999792359
  [PASS] N=13 tau=2 lambda/b^2=0.22452747256883 : noise 1.64e-57; constant rows spread <= 3.92e-60; varying rows spread >= 1.49e-28; closed forms 6.74e-59; gamma = 1.13609450243, 2+gamma = 3.1360945, k808 = k810 = 1.6270923151275; A on 48 members in [8.69185, 8.69185]
  [PASS] N=13 tau=3 lambda/b^2=0.45702608849515 : noise 6.03e-58; constant rows spread <= 3.32e-60; varying rows spread >= 1.09e-26; closed forms 6.74e-59; gamma = 0.241141886525, 2+gamma = 2.2411419, k808 = k810 = 3.18744409608162; A on 48 members in [10.4823, 10.4823]
  [PASS] N=13 tau=4 lambda/b^2=0.70340785491844 : noise 7.75e-58; constant rows spread <= 8.92e-60; varying rows spread >= 1.12e-23; closed forms 1.65e-58; gamma = -0.7094939822, 2+gamma = 1.290506, k808 = k810 = 9.6249220695026; A on 48 members in [9.86815, 9.86815]
  [PASS] N=13 tau=5 lambda/b^2=0.90544479016894 : noise 1.43e-58; constant rows spread <= 7.51e-60; varying rows spread >= 4.16e-18; closed forms 5.24e-59; gamma = -1.49212145124, 2+gamma = 0.50787855, k808 = k810 = 63.4662712134983; A on 48 members in [6.9857, 6.9857]
  [PASS] N=13 tau=6 lambda/b^2=0.99915629930651 : noise 2.27e-56; constant rows spread <= 1.55e-56; varying rows spread >= 2.04e-7; closed forms 1.31e-56; gamma = -1.85641337385, 2+gamma = 0.14358663, k808 = k810 = 3473.81269215386; A on 48 members in [2.48561, 2.48561]
  [PASS] a=1.3 b=1.25: N=4 caustic lambda = a^2b^2/(a^2+b^2); k807 = 4a^4b^4/(a^2+b^2)^2, k809 = 4a^2b^2, k110 = 8a^4b^4/(a^2+b^2)^2 = 4 x (printed 2a^4b^4/(a^2+b^2)^2), k106 = 8a^2b^2 : lambda 4.05e-59, values 1.0e-58
  [PASS] a=1.3 b=1.25: N=3 lambda = a^2b^2(2 sqrt(a^4-a^2b^2+b^4)-a^2-b^2)/c^4, gamma(lambda) = -1, k808 = 4 kappa : 5.31e-59, 5.9e-59, 2.62e-58
  [PASS] a=1.3 b=1.25: N=6 k807/k110 = k809/k106 = 3/4; Garcia-Reznik N=6 values of k106, k110; hence k807 = 3a^3b^3(2a+b)^2(a+2b)^2/(a+b)^6, k809 = 3a^2b^2(2a+b)(a+2b)/(a+b)^2 : 4.91e-59

== ellipse a = 2.5, b = 0.55
  [PASS] N=3 tau=1 lambda/b^2=0.99940047227327 : noise 5.61e-56; constant rows spread <= 6.44e-56; varying rows spread >= 0.579; closed forms 1.13e-56; gamma = -1.0, 2+gamma = 1.0, k808 = k810 = 167.46402172622
  [PASS] N=4 tau=1 lambda/b^2=0.95383441434567 : noise 4.28e-57; constant rows spread <= 2.75e-58; varying rows spread >= 0.621; closed forms 1.13e-58; k807 = 0.333009577938643, k809 = 7.5625, k110 = 0.666019155877287
  [PASS] N=5 tau=1 lambda/b^2=0.82164305219366 : noise 1.53e-57; constant rows spread <= 1.73e-58; varying rows spread >= 0.011; closed forms 6.77e-59; gamma = 0.713145802151, 2+gamma = 2.7131458, k808 = k810 = 3.56248994570232
  [PASS] N=5 tau=2 lambda/b^2=0.9999999077034 : noise 3.78e-52; constant rows spread <= 3.45e-52; varying rows spread >= 0.58; closed forms 9.94e-53; gamma = -1.0247963016, 2+gamma = 0.9752037, k808 = k810 = 13840.2706444417; A on 48 members in [0.602108, 1.40861]
  [PASS] N=6 tau=1 lambda/b^2=0.67186240257995 : noise 1.0e-58; constant rows spread <= 1.21e-59; varying rows spread >= 0.0948; closed forms 3.56e-60; k807 = 3.86741948445214, k809 = 12.1821083042193, k110 = 5.15655931260286
  [PASS] N=7 tau=1 lambda/b^2=0.54352947726421 : noise 1.86e-57; constant rows spread <= 8.68e-59; varying rows spread >= 0.000213; closed forms 6.49e-59; gamma = 1.1745392843, 2+gamma = 3.1745393, k808 = k810 = 1.89000021786804
  [PASS] N=7 tau=2 lambda/b^2=0.98894481748894 : noise 1.81e-56; constant rows spread <= 3.72e-57; varying rows spread >= 0.00924; closed forms 9.43e-58; gamma = -0.643703473854, 2+gamma = 1.3562965, k808 = k810 = 28.7457141386913; A on 48 members in [2.84688, 2.87402]
  [PASS] N=7 tau=3 lambda/b^2=0.9999999999858 : noise 7.0e-49; constant rows spread <= 6.39e-49; varying rows spread >= 0.58; closed forms 1.84e-49; gamma = -1.02480016337, 2+gamma = 0.97519984, k808 = k810 = 1115976.12322598; A on 48 members in [0.602108, 1.40861]
  [PASS] N=8 tau=1 lambda/b^2=0.44234510157482 : noise 1.02e-58; constant rows spread <= 6.4e-60; varying rows spread >= 0.0137; closed forms 2.91e-61; k807 = 7.71460181897054, k809 = 14.136666084448, k110 = 9.34128417519645
  [PASS] N=8 tau=3 lambda/b^2=0.99999255803009 : noise 1.57e-54; constant rows spread <= 3.62e-55; varying rows spread >= 0.58; closed forms 9.22e-57; k807 = 0.00218564785519406, k809 = 308.629676291062, k110 = 0.00896206138553199; A on 48 members in [1.20421, 2.81722]
  [PASS] N=9 tau=1 lambda/b^2=0.36416201229119 : noise 2.11e-58; constant rows spread <= 7.68e-60; varying rows spread >= 5.67e-6; closed forms 4.47e-60; gamma = 1.40516838444, 2+gamma = 3.4051684, k808 = k810 = 1.48631071954829
  [PASS] N=9 tau=2 lambda/b^2=0.89451124550301 : noise 3.7e-57; constant rows spread <= 4.34e-58; varying rows spread >= 8.51e-5; closed forms 8.34e-59; gamma = 0.451617168026, 2+gamma = 2.4516172, k808 = k810 = 5.13588256028476; A on 48 members in [4.4876, 4.48814]
  [PASS] N=9 tau=4 lambda/b^2=1.0 : noise 4.26e-45; constant rows spread <= 3.89e-45; varying rows spread >= 0.58; closed forms 1.12e-45; gamma = -1.02480016397, 2+gamma = 0.97519984, k808 = k810 = 89983639.1538176; A on 48 members in [0.602108, 1.40861]
  [PASS] N=10 tau=1 lambda/b^2=0.30363460210533 : noise 5.57e-58; constant rows spread <= 1.63e-59; varying rows spread >= 0.00265; closed forms 9.04e-60; k807 = 10.5425035490256, k809 = 15.3651317798119, k110 = 12.0916705189226
  [PASS] N=10 tau=3 lambda/b^2=0.99464780065107 : noise 3.1e-56; constant rows spread <= 1.11e-57; varying rows spread >= 0.0735; closed forms 1.43e-58; k807 = 0.30761332355545, k809 = 60.3809886025955, k110 = 1.04441614606188; A on 48 members in [3.65794, 4.00015]
  [PASS] N=11 tau=1 lambda/b^2=0.2563074867133 : noise 2.79e-57; constant rows spread <= 6.94e-59; varying rows spread >= 1.52e-7; closed forms 4.67e-59; gamma = 1.55508372621, 2+gamma = 3.5550837, k808 = k810 = 1.31287710282206
  [PASS] N=11 tau=2 lambda/b^2=0.74533886748405 : noise 1.74e-57; constant rows spread <= 9.99e-59; varying rows spread >= 2.35e-6; closed forms 3.85e-59; gamma = 0.87972394437, 2+gamma = 2.8797239, k808 = k810 = 2.80353539714439; A on 48 members in [5.6342, 5.63421]
  [PASS] N=11 tau=3 lambda/b^2=0.98032462866202 : noise 6.96e-57; constant rows spread <= 1.11e-57; varying rows spread >= 0.000131; closed forms 2.91e-58; gamma = -0.428120853241, 2+gamma = 1.5718791, k808 = k810 = 18.5880981842608; A on 48 members in [4.742, 4.74251]
  [PASS] N=11 tau=4 lambda/b^2=0.99996785070513 : noise 3.32e-55; constant rows spread <= 1.36e-55; varying rows spread >= 0.00914; closed forms 6.21e-56; gamma = -1.0234556378, 2+gamma = 0.97654436, k808 = k810 = 740.550563131151; A on 48 members in [2.86612, 2.8932]
  [PASS] N=11 tau=5 lambda/b^2=1.0 : noise 9.23e-41; constant rows spread <= 8.43e-41; varying rows spread >= 0.58; closed forms 2.43e-41; gamma = -1.02480016397, 2+gamma = 0.97519984, k808 = k810 = 7255581138.44662; A on 48 members in [0.602108, 1.40861]
  [PASS] N=12 tau=1 lambda/b^2=0.2188344464036 : noise 2.54e-57; constant rows spread <= 5.82e-59; varying rows spread >= 0.000273; closed forms 3.4e-59; k807 = 12.5048364161733, k809 = 16.1792852418003, k110 = 13.8519008696138
  [PASS] N=12 tau=5 lambda/b^2=0.99999999885534 : noise 5.54e-50; constant rows spread <= 1.26e-50; varying rows spread >= 0.58; closed forms 3.78e-52; k807 = 2.70981823981388e-5, k809 = 24877.6054475125, k110 = 0.000111149243738004; A on 48 members in [1.20422, 2.81723]
  [PASS] N=13 tau=1 lambda/b^2=0.18877643719791 : noise 4.1e-57; constant rows spread <= 6.9e-59; varying rows spread >= 3.77e-9; closed forms 4.64e-59; gamma = 1.65766715973, 2+gamma = 3.6576672, k808 = k810 = 1.21977204485122
  [PASS] N=13 tau=2 lambda/b^2=0.60424321245552 : noise 6.23e-58; constant rows spread <= 2.01e-59; varying rows spread >= 3.9e-8; closed forms 1.57e-59; gamma = 1.09508140156, 2+gamma = 3.0950814, k808 = k810 = 2.08506210249908; A on 48 members in [6.39865, 6.39865]
  [PASS] N=13 tau=3 lambda/b^2=0.91637573726904 : noise 6.77e-57; constant rows spread <= 7.88e-58; varying rows spread >= 1.47e-6; closed forms 8.19e-59; gamma = 0.327843680747, 2+gamma = 2.3278437, k808 = k810 = 6.07842668234471; A on 48 members in [6.37483, 6.37484]
  [PASS] N=13 tau=4 lambda/b^2=0.99654187386221 : noise 9.75e-56; constant rows spread <= 1.31e-56; varying rows spread >= 9.02e-5; closed forms 9.11e-58; gamma = -0.889180636654, 2+gamma = 1.1108194, k808 = k810 = 62.7669069687811; A on 48 members in [4.78921, 4.78971]
  [PASS] N=13 tau=5 lambda/b^2=0.99999827737824 : noise 2.01e-53; constant rows spread <= 1.06e-53; varying rows spread >= 0.00914; closed forms 7.93e-55; gamma = -1.0247280791, 2+gamma = 0.97527192, k808 = k810 = 3203.40663609204; A on 48 members in [2.86617, 2.89325]
  [PASS] N=13 tau=6 lambda/b^2=1.0 : noise 1.93e-37; constant rows spread <= 1.76e-37; varying rows spread >= 0.58; closed forms 5.07e-38; gamma = -1.02480016397, 2+gamma = 0.97519984, k808 = k810 = 585033658914.252; A on 48 members in [0.602108, 1.40861]
  [PASS] a=2.5 b=0.55: N=4 caustic lambda = a^2b^2/(a^2+b^2); k807 = 4a^4b^4/(a^2+b^2)^2, k809 = 4a^2b^2, k110 = 8a^4b^4/(a^2+b^2)^2 = 4 x (printed 2a^4b^4/(a^2+b^2)^2), k106 = 8a^2b^2 : lambda 1.03e-59, values 2.81e-57
  [PASS] a=2.5 b=0.55: N=3 lambda = a^2b^2(2 sqrt(a^4-a^2b^2+b^4)-a^2-b^2)/c^4, gamma(lambda) = -1, k808 = 4 kappa : 1.14e-59, 1.53e-57, 1.11e-55
  [PASS] a=2.5 b=0.55: N=6 k807/k110 = k809/k106 = 3/4; Garcia-Reznik N=6 values of k106, k110; hence k807 = 3a^3b^3(2a+b)^2(a+2b)^2/(a+b)^6, k809 = 3a^2b^2(2a+b)(a+2b)/(a+b)^2 : 1.04e-59

summary: 140 families x 7 members; largest closure defect 1.93e-37, largest residual (reflection law, tangency, inversion = midpoints) 1.38e-37, largest relative spread of a constant row 1.76e-37, smallest relative spread of one of the five rows in the wrong parity 1.4e-29, largest deviation from the closed forms 5.07e-38
TOTAL checks: 155, failures: 0
running time: 42 s
