Symmetric complexity of 7-limit commas

Here is the list of 7-limit commas with relative error < 0.06 and
epimericity < 0.5, sorted by what shell they belong to--or in other
words, symmetric lattice error. Two commas belonging to the same shell
can be geometrically isomorphic, and will be if two other invariants
are equal. I've mentioned how this leads to isomorphisms of planar
temperaments, but it also leads to automorphisms of the associated
linear temperaments. Linear temperaments with such automorphisms include:

Beep: 49/48 ^ 36/35 shell 3
Tripletone: 126/125 ^ 64/63 shell 7
Blackwood: 64/63 ^ 28/27 shell 7
Dominant seventh 256/245 ^ 64/63 shell 7
Diminished (torsional): (126/125 ^ 360/343)/2
"Number 59": 28/27 ^ 126/125 shell 7
"Number 92": 1728/1715 ^ 875/864 shell 10
Kleismic (torsional): (875/864 ^ 1029/1000)/2 shell 10
Supermajor seconds: 1029/1024 ^ 81/80 shell 13
Jamesbond: 81/80 ^ 135/128 shell 13
<5 -4 -10 -18 -30 -12| 3136/3125 ^ 3125/3087 shell 19
<9 15 19 3 5 2| 3125/3087 ^ 250/243 shell 19
<6 10 25 2 23 30| 250/243 ^ 3136/3125 shell 19

3: {36/35, 49/48}
4: {50/49}
7: {28/27, 360/343, 64/63, 126/125, 256/245}
9: {200/189, 392/375, 128/125, 225/224}
10: {1029/1000, 875/864, 1728/1715}
11: {2401/2400, 525/512}
13: {81/80, 135/128, 686/675, 1029/1024}
15: {405/392, 6144/6125}
16: {648/625}
17: {245/243}
19: {250/243, 3125/3087, 4000/3969, 3136/3125}
21: {3125/3072}
23: {2430/2401}
25: {256/243}
27: {16875/16807}
28: {2048/2025}
31: {15625/15552}
35: {4375/4374}
37: {5120/5103}
38: {65625/65536}
42: {10976/10935}
45: {250047/250000}
47: {420175/419904}
49: {703125/702464}
57: {19683/19600}
73: {32805/32768}
149: {78125000/78121827}