Second independent verification run: Coxeter data from explicit root systems (exact arithmetic)
columns: type | rank | #roots | graph ok | N | l(w0)=N | w0=-1 | w0 central | diagram perm | c | classes=odd comps | letters/class=pos roots/class | zeta | [zeta] (long,short) | d | -2 solvable | lattice lambda(zeta)=0 | agrees with Table 1
A1                    | 1 |   2 | True |   1 | True | True | True | id | 1 | True | True | Delta | (1,) | 1 | True | None | True
A2                    | 2 |   6 | True |   3 | True | False | False | 10 | 1 | True | True | Delta^2 | (6,) | 6 | False | None | True
A3                    | 3 |  12 | True |   6 | True | False | False | 210 | 1 | True | True | Delta^2 | (12,) | 12 | False | None | True
A4                    | 4 |  20 | True |  10 | True | False | False | 3210 | 1 | True | True | Delta^2 | (20,) | 20 | False | None | True
A5                    | 5 |  30 | True |  15 | True | False | False | 43210 | 1 | True | True | Delta^2 | (30,) | 30 | False | None | True
A6                    | 6 |  42 | True |  21 | True | False | False | 543210 | 1 | True | True | Delta^2 | (42,) | 42 | False | None | True
A7                    | 7 |  56 | True |  28 | True | False | False | 6543210 | 1 | True | True | Delta^2 | (56,) | 56 | False | None | True
A8                    | 8 |  72 | True |  36 | True | False | False | 76543210 | 1 | True | True | Delta^2 | (72,) | 72 | False | None | True
A9                    | 9 |  90 | True |  45 | True | False | False | 876543210 | 1 | True | True | Delta^2 | (90,) | 90 | False | None | True
B2                    | 2 |   8 | True |   4 | True | True | True | id | 2 | True | True | Delta | (2, 2) | 4 | True | (1, -1) | True
B3                    | 3 |  18 | True |   9 | True | True | True | id | 2 | True | True | Delta | (6, 3) | 9 | False | (1, -2) | True
B4                    | 4 |  32 | True |  16 | True | True | True | id | 2 | True | True | Delta | (12, 4) | 16 | False | (1, -3) | True
B5                    | 5 |  50 | True |  25 | True | True | True | id | 2 | True | True | Delta | (20, 5) | 25 | False | (1, -4) | True
B6                    | 6 |  72 | True |  36 | True | True | True | id | 2 | True | True | Delta | (30, 6) | 36 | False | (1, -5) | True
B7                    | 7 |  98 | True |  49 | True | True | True | id | 2 | True | True | Delta | (42, 7) | 49 | False | (1, -6) | True
B8                    | 8 | 128 | True |  64 | True | True | True | id | 2 | True | True | Delta | (56, 8) | 64 | False | (1, -7) | True
B9                    | 9 | 162 | True |  81 | True | True | True | id | 2 | True | True | Delta | (72, 9) | 81 | False | (1, -8) | True
D4                    | 4 |  24 | True |  12 | True | True | True | id | 1 | True | True | Delta | (12,) | 12 | False | None | True
D5                    | 5 |  40 | True |  20 | True | False | False | 01243 | 1 | True | True | Delta^2 | (40,) | 40 | False | None | True
D6                    | 6 |  60 | True |  30 | True | True | True | id | 1 | True | True | Delta | (30,) | 30 | False | None | True
D7                    | 7 |  84 | True |  42 | True | False | False | 0123465 | 1 | True | True | Delta^2 | (84,) | 84 | False | None | True
D8                    | 8 | 112 | True |  56 | True | True | True | id | 1 | True | True | Delta | (56,) | 56 | False | None | True
D9                    | 9 | 144 | True |  72 | True | False | False | 012345687 | 1 | True | True | Delta^2 | (144,) | 144 | False | None | True
E6                    | 6 |  72 | True |  36 | True | False | False | 013254 | 1 | True | True | Delta^2 | (72,) | 72 | False | None | True
E7                    | 7 | 126 | True |  63 | True | True | True | id | 1 | True | True | Delta | (63,) | 63 | False | None | True
E8                    | 8 | 240 | True | 120 | True | True | True | id | 1 | True | True | Delta | (120,) | 120 | False | None | True
F4                    | 4 |  48 | True |  24 | True | True | True | id | 2 | True | True | Delta | (12, 12) | 24 | False | (1, -1) | True
G2(crystallographic)  | 2 |  12 | True |   6 | True | True | True | id | 2 | True | True | Delta | (3, 3) | 6 | False | (1, -1) | True
H3                    | 3 |  30 | True |  15 | True | True | True | id | 1 | True | True | Delta | (15,) | 15 | False | None | True
H4                    | 4 | 120 | True |  60 | True | True | True | id | 1 | True | True | Delta | (60,) | 60 | False | None | True
I2(3)                 | 2 |   6 | True |   3 | True | False | False | 10 | 1 | True | True | Delta^2 | (6,) | 6 | False | None | True
I2(4)                 | 2 |   8 | True |   4 | True | True | True | id | 2 | True | True | Delta | (2, 2) | 4 | True | (1, -1) | True
I2(5)                 | 2 |  10 | True |   5 | True | False | False | 10 | 1 | True | True | Delta^2 | (10,) | 10 | False | None | True
I2(6)                 | 2 |  12 | True |   6 | True | True | True | id | 2 | True | True | Delta | (3, 3) | 6 | False | (1, -1) | True
I2(7)                 | 2 |  14 | True |   7 | True | False | False | 10 | 1 | True | True | Delta^2 | (14,) | 14 | False | None | True
I2(8)                 | 2 |  16 | True |   8 | True | True | True | id | 2 | True | True | Delta | (4, 4) | 8 | False | (1, -1) | True
I2(9)                 | 2 |  18 | True |   9 | True | False | False | 10 | 1 | True | True | Delta^2 | (18,) | 18 | False | None | True
I2(10)                | 2 |  20 | True |  10 | True | True | True | id | 2 | True | True | Delta | (5, 5) | 10 | False | (1, -1) | True
I2(11)                | 2 |  22 | True |  11 | True | False | False | 10 | 1 | True | True | Delta^2 | (22,) | 22 | False | None | True
I2(12)                | 2 |  24 | True |  12 | True | True | True | id | 2 | True | True | Delta | (6, 6) | 12 | False | (1, -1) | True
I2(13)                | 2 |  26 | True |  13 | True | False | False | 10 | 1 | True | True | Delta^2 | (26,) | 26 | False | None | True
I2(14)                | 2 |  28 | True |  14 | True | True | True | id | 2 | True | True | Delta | (7, 7) | 14 | False | (1, -1) | True
I2(15)                | 2 |  30 | True |  15 | True | False | False | 10 | 1 | True | True | Delta^2 | (30,) | 30 | False | None | True
I2(16)                | 2 |  32 | True |  16 | True | True | True | id | 2 | True | True | Delta | (8, 8) | 16 | False | (1, -1) | True
I2(17)                | 2 |  34 | True |  17 | True | False | False | 10 | 1 | True | True | Delta^2 | (34,) | 34 | False | None | True
I2(18)                | 2 |  36 | True |  18 | True | True | True | id | 2 | True | True | Delta | (9, 9) | 18 | False | (1, -1) | True
I2(19)                | 2 |  38 | True |  19 | True | False | False | 10 | 1 | True | True | Delta^2 | (38,) | 38 | False | None | True
I2(20)                | 2 |  40 | True |  20 | True | True | True | id | 2 | True | True | Delta | (10, 10) | 20 | False | (1, -1) | True

types for which lambda(zeta) = -2 is solvable: A1, B2, I2(4)
B_n: lattice lambda(zeta) = 0 generated by (1, -(n-1)) (order: class of s_1..s_{n-1}, class of s_n): True
I2(2k), G2, F4: lattice lambda(zeta) = 0 generated by (1, -1): True
minimum of d over the types of rank >= 2: 4
ALL CHECKS PASSED: True
