A <2,5,7> group "best" list

Here we find, of course, the 3136/3125 system I mentioned before, but I'd also like to draw attention to the last temperament on the list--a
mathematically (if not practically) amazing temperament, associated to the rather amazing 789 et.

686/625

map [[0, 3, 4], [1, 1, 1]]

generators 539.1060370 1200.

badness 489.0718160 rms 31.61840515 g_w 2.491595620

343/320

map [[0, -3, -1], [1, 3, 3]]

generators 274.0898101 1200.

badness 232.0702794 rms 32.11518107 g_w 1.933316912

32768/30625

map [[0, 1, -2], [2, 4, 7]]

generators 407.2232374 600.

badness 643.0205101 rms 15.64725500 g_w 3.450872300

4375/4096

map [[0, 1, -4], [1, 2, 4]]

generators 361.8678362 1200.

badness 454.9331633 rms 17.60304342 g_w 2.956559423

2560/2401

map [[0, -4, -1], [1, 3, 3]]

generators 201.2867627 1200.

badness 392.3271620 rms 21.77086970 g_w 2.621747521

16807/16000

map [[0, 5, 3], [1, 1, 2]]

generators 317.7111025 1200.

badness 450.1531173 rms 13.81938198 g_w 3.193673737

8575/8192

map [[0, 3, -2], [1, 2, 3]]

generators 123.9139044 1200.

badness 328.0735082 rms 12.83254896 g_w 2.945909568

256/245

map [[0, 2, -1], [1, 2, 3]]

generators 204.0189242 1200.

badness 119.7408063 rms 20.32106851 g_w 1.806197400

823543/800000

map [[0, -7, -5], [1, 4, 4]]

generators 287.3935752 1200.

badness 536.0657103 rms 5.685477364 g_w 4.551456166

401408/390625

map [[0, 1, 4], [2, 4, 3]]

generators 392.6597660 600.

badness 470.1905708 rms 4.622664052 g_w 4.667960736

16807/16384

map [[0, 1, 0], [5, 10, 14]]

generators 381.9007604 240.

badness 281.4513766 rms 6.240857928 g_w 3.559478388

128/125

map [[0, 0, -1], [3, 7, 9]]

generators 224.3309516 400.

badness 69.03052049 rms 9.677665952 g_w 1.924967967

1071875/1048576

map [[0, 3, -5], [1, 1, 5]]

generators 527.0889187 1200.

badness 370.6464204 rms 3.843254849 g_w 4.585853840

268435456/262609375

map [[0, -5, 6], [1, 3, 2]]

generators 162.0275880 1200.

badness 708.1906883 rms 2.815872080 g_w 6.312175959

50/49

map [[0, -1, -1], [2, 5, 6]]

generators 222.4301906 600.

badness 35.69105715 rms 12.36574700 g_w 1.423791355

68359375/67108864

map [[0, 1, -10], [1, 2, 6]]

generators 383.2901826 1200.

badness 664.8390958 rms 2.145218464 g_w 6.767293431

4194304/4117715

map [[0, 7, -1], [1, 1, 3]]

generators 226.9760748 1200.

badness 445.7435327 rms 2.988171840 g_w 5.303466469

78125/76832

map [[0, -4, -7], [1, 3, 4]]

generators 204.3976654 1200.

badness 230.3456068 rms 3.358669391 g_w 4.093274712

40960000/40353607

map [[0, -9, -4], [1, 5, 4]]

generators 357.0527370 1200.

badness 439.4738808 rms 2.337786935 g_w 5.728523696

244140625/240945152

map [[0, 1, 2], [6, 12, 13]]

generators 384.4129525 200.

badness 514.3166613 rms 1.551964221 g_w 6.920162556

1977326743/1953125000

map [[0, 11, 12], [1, -3, -3]]

generators 580.6686988 1200.

badness 705.1161663 rms 1.307238490 g_w 8.140203868

2000000000/1977326743

map [[0, -11, -9], [1, 5, 5]]

generators 292.2142738 1200.

badness 544.3754097 rms 1.375242977 g_w 7.342427853

762939453125/755603996672

map [[0, 8, 17], [1, 1, 0]]

generators 198.1639627 1200.

badness 748.4465765 rms .8028678840 g_w 9.768748008

40353607/40000000

map [[0, 9, 7], [1, 0, 1]]

generators 309.6535849 1200.

badness 275.9060105 rms 1.316290184 g_w 5.940228799

97656250000/96889010407

map [[0, 13, 14], [1, -4, -4]]

generators 583.5195442 1200.

badness 623.8314928 rms .7137704924 g_w 9.560990833

69206436005/68719476736

map [[0, 12, -1], [1, 0, 3]]

generators 232.1473890 1200.

badness 478.2656671 rms .6898731204 g_w 8.850476649

1638400000000000/1628413597910449

map [[0, 18, 11], [1, 1, 2]]

generators 88.12377826 1200.

badness 726.3196762 rms .4762208496 g_w 11.51082544

823543/819200

map [[0, -7, -2], [1, 3, 3]]

generators 116.2911944 1200.

badness 97.72611226 rms 1.036476664 g_w 4.551456166

8589934592/8544921875

map [[0, 1, -13], [1, 2, 7]]

generators 386.9847164 1200.

badness 311.5353743 rms .4754474072 g_w 8.685636061

19073486328125/18990246039772

map [[0, -15, -19], [1, 8, 10]]

generators 454.2650388 1200.

badness 540.6271280 rms .3086102069 g_w 12.05486958

3136/3125

map [[0, 2, 5], [1, 2, 2]]

generators 193.7971982 1200.

badness 23.18483462 rms .9868326492 g_w 2.864091121

65712362363534280139543/65536000000000000000000

map [[0, 3, 2], [9, 10, 18]]

generators 484.3391018 133.3333333

badness 727.8282850 rms .1381631578 g_w 17.39985221

186759498717153574912/186264514923095703125

map [[0, -19, -29], [1, 9, 13]]

generators 421.7657192 1200.

badness 669.4337469 rms .1273318109 g_w 17.38829083

7450580596923828125/7430984482854797312

map [[0, 4, 9], [3, 1, -5]]

generators 596.5348276 400.

badness 510.7162100 rms .1375962522 g_w 15.48309146

80000000000000000/79792266297612001

map [[0, -5, -4], [4, 19, 19]]

generators 582.7533331 300.

badness 406.7075158 rms .1736411704 g_w 13.28035949

591363588909912109375/590295810358705651712

map [[0, -13, 14], [1, 4, 1]]

generators 154.9079648 1200.

badness 354.5227097 rms .9459396236e-1 g_w 15.53317425

2100875/2097152

map [[0, 5, -3], [1, 2, 3]]

generators 77.19380915 1200.

badness 33.21811689 rms .3101843093 g_w 4.748812924

134217728/133984375

map [[0, -3, 8], [1, 3, 1]]

generators 271.1304136 1200.

badness 56.35222399 rms .2162902226 g_w 6.386918744

37778931862957161709568/37714514598846435546875

map [[0, 11, -19], [1, -3, 12]]

generators 580.5834970 1200.

badness 404.7327302 rms .7947342068e-1 g_w 17.20476745

22539340290692258087863249/22517998136852480000000000

map [[0, -3, -1], [10, 29, 30]]

generators 231.2326670 120.

badness 316.7381823 rms .4383199824e-1 g_w 19.33316912

3909821048582988049/3906250000000000000

map [[0, -22, -21], [1, 13, 13]]

generators 582.4387327 1200.

badness 189.2472322 rms .5198637212e-1 g_w 15.38319960

23303567338232644370432/23283064365386962890625

map [[0, 7, 16], [2, 0, -5]]

generators 398.0518660 600.

badness 239.3677518 rms .3878099806e-1 g_w 18.34350066

59604644775390625/59553411580724992

map [[0, -17, -24], [1, 6, 8]]

generators 259.6315753 1200.

badness 155.9226447 rms .4924199004e-1 g_w 14.68445611

1342177280000000000000/1341068619663964900807

map [[0, 25, 13], [1, -5, -1]]

generators 351.4524874 1200.

badness 187.4404574 rms .4671147988e-1 g_w 15.89082956

281484423828125/281474976710656

map [[0, 8, -11], [1, 0, 6]]

generators 348.2888153 1200.

badness 3.206369973 rms .2486103265e-2 g_w 10.88507660