Part A: type | rank | N | l(w0) | w0=-1 | w0 central | pi | c | letters per class | pos. roots per class | [zeta] | d | lambda(zeta)=-2 solvable | generator of {lambda(zeta)=0} | agrees with Table 1
A1 | 1 | 1 | 1 | True | True | [0] | 1 | [1] | [1] | [1] | 1 | True | None | True
A2 | 2 | 3 | 3 | False | False | [1, 0] | 1 | [3] | [3] | [6] | 6 | False | None | True
A3 | 3 | 6 | 6 | False | False | [2, 1, 0] | 1 | [6] | [6] | [12] | 12 | False | None | True
A4 | 4 | 10 | 10 | False | False | [3, 2, 1, 0] | 1 | [10] | [10] | [20] | 20 | False | None | True
A5 | 5 | 15 | 15 | False | False | [4, 3, 2, 1, 0] | 1 | [15] | [15] | [30] | 30 | False | None | True
A6 | 6 | 21 | 21 | False | False | [5, 4, 3, 2, 1, 0] | 1 | [21] | [21] | [42] | 42 | False | None | True
A7 | 7 | 28 | 28 | False | False | [6, 5, 4, 3, 2, 1, 0] | 1 | [28] | [28] | [56] | 56 | False | None | True
A8 | 8 | 36 | 36 | False | False | [7, 6, 5, 4, 3, 2, 1, 0] | 1 | [36] | [36] | [72] | 72 | False | None | True
B2 | 2 | 4 | 4 | True | True | [0, 1] | 2 | [2, 2] | [2, 2] | [2, 2] | 4 | True | (1, -1) | True
B3 | 3 | 9 | 9 | True | True | [0, 1, 2] | 2 | [6, 3] | [6, 3] | [6, 3] | 9 | False | (1, -2) | True
B4 | 4 | 16 | 16 | True | True | [0, 1, 2, 3] | 2 | [12, 4] | [12, 4] | [12, 4] | 16 | False | (1, -3) | True
B5 | 5 | 25 | 25 | True | True | [0, 1, 2, 3, 4] | 2 | [20, 5] | [20, 5] | [20, 5] | 25 | False | (1, -4) | True
B6 | 6 | 36 | 36 | True | True | [0, 1, 2, 3, 4, 5] | 2 | [30, 6] | [30, 6] | [30, 6] | 36 | False | (1, -5) | True
B7 | 7 | 49 | 49 | True | True | [0, 1, 2, 3, 4, 5, 6] | 2 | [42, 7] | [42, 7] | [42, 7] | 49 | False | (1, -6) | True
B8 | 8 | 64 | 64 | True | True | [0, 1, 2, 3, 4, 5, 6, 7] | 2 | [56, 8] | [56, 8] | [56, 8] | 64 | False | (1, -7) | True
D4 | 4 | 12 | 12 | True | True | [0, 1, 2, 3] | 1 | [12] | [12] | [12] | 12 | False | None | True
D5 | 5 | 20 | 20 | False | False | [0, 1, 2, 4, 3] | 1 | [20] | [20] | [40] | 40 | False | None | True
D6 | 6 | 30 | 30 | True | True | [0, 1, 2, 3, 4, 5] | 1 | [30] | [30] | [30] | 30 | False | None | True
D7 | 7 | 42 | 42 | False | False | [0, 1, 2, 3, 4, 6, 5] | 1 | [42] | [42] | [84] | 84 | False | None | True
D8 | 8 | 56 | 56 | True | True | [0, 1, 2, 3, 4, 5, 6, 7] | 1 | [56] | [56] | [56] | 56 | False | None | True
E6 | 6 | 36 | 36 | False | False | [5, 1, 4, 3, 2, 0] | 1 | [36] | [36] | [72] | 72 | False | None | True
E7 | 7 | 63 | 63 | True | True | [0, 1, 2, 3, 4, 5, 6] | 1 | [63] | [63] | [63] | 63 | False | None | True
E8 | 8 | 120 | 120 | True | True | [0, 1, 2, 3, 4, 5, 6, 7] | 1 | [120] | [120] | [120] | 120 | False | None | True
F4 | 4 | 24 | 24 | True | True | [0, 1, 2, 3] | 2 | [12, 12] | [12, 12] | [12, 12] | 24 | False | (1, -1) | True
G2 | 2 | 6 | 6 | True | True | [0, 1] | 2 | [3, 3] | [3, 3] | [3, 3] | 6 | False | (1, -1) | True
H3 | 3 | 15 | 15 | True | True | [0, 1, 2] | 1 | [15] | [15] | [15] | 15 | False | None | True
H4 | 4 | 60 | 60 | True | True | [0, 1, 2, 3] | 1 | [60] | [60] | [60] | 60 | False | None | True
I2(3) | 2 | 3 | 3 | False | False | [1, 0] | 1 | [3] | [3] | [6] | 6 | False | None | True
I2(4) | 2 | 4 | 4 | True | True | [0, 1] | 2 | [2, 2] | [2, 2] | [2, 2] | 4 | True | (1, -1) | True
I2(5) | 2 | 5 | 5 | False | False | [1, 0] | 1 | [5] | [5] | [10] | 10 | False | None | True
I2(6) | 2 | 6 | 6 | True | True | [0, 1] | 2 | [3, 3] | [3, 3] | [3, 3] | 6 | False | (1, -1) | True
I2(7) | 2 | 7 | 7 | False | False | [1, 0] | 1 | [7] | [7] | [14] | 14 | False | None | True
I2(8) | 2 | 8 | 8 | True | True | [0, 1] | 2 | [4, 4] | [4, 4] | [4, 4] | 8 | False | (1, -1) | True
I2(9) | 2 | 9 | 9 | False | False | [1, 0] | 1 | [9] | [9] | [18] | 18 | False | None | True
I2(10) | 2 | 10 | 10 | True | True | [0, 1] | 2 | [5, 5] | [5, 5] | [5, 5] | 10 | False | (1, -1) | True
I2(11) | 2 | 11 | 11 | False | False | [1, 0] | 1 | [11] | [11] | [22] | 22 | False | None | True
I2(12) | 2 | 12 | 12 | True | True | [0, 1] | 2 | [6, 6] | [6, 6] | [6, 6] | 12 | False | (1, -1) | True
I2(13) | 2 | 13 | 13 | False | False | [1, 0] | 1 | [13] | [13] | [26] | 26 | False | None | True
I2(14) | 2 | 14 | 14 | True | True | [0, 1] | 2 | [7, 7] | [7, 7] | [7, 7] | 14 | False | (1, -1) | True
I2(15) | 2 | 15 | 15 | False | False | [1, 0] | 1 | [15] | [15] | [30] | 30 | False | None | True
I2(16) | 2 | 16 | 16 | True | True | [0, 1] | 2 | [8, 8] | [8, 8] | [8, 8] | 16 | False | (1, -1) | True
I2(17) | 2 | 17 | 17 | False | False | [1, 0] | 1 | [17] | [17] | [34] | 34 | False | None | True
I2(18) | 2 | 18 | 18 | True | True | [0, 1] | 2 | [9, 9] | [9, 9] | [9, 9] | 18 | False | (1, -1) | True
I2(19) | 2 | 19 | 19 | False | False | [1, 0] | 1 | [19] | [19] | [38] | 38 | False | None | True
I2(20) | 2 | 20 | 20 | True | True | [0, 1] | 2 | [10, 10] | [10, 10] | [10, 10] | 20 | False | (1, -1) | True
d >= 3 for every type of rank >= 2: True
lambda(zeta) = -2 solvable exactly for A1, B2 = I2(4): True
B_n: generator of {lambda(zeta) = 0} is (1, -(n-1)): True
Part B (Lemma 5.2), free group identities for even m:
  m = 4: True
  m = 6: True
  m = 8: True
  m = 10: True
  m = 12: True
  m = 14: True
  m = 16: True
  m = 18: True
  m = 20: True
ALL CHECKS PASSED: True
