(* list of possible bases b3 for F-theory compactifications
   with dual smooth heterotic descriptions as described in
   Anderson and Taylor arXiv:1404.nnnn.  Bases described are P^1
   bundles over toric base surfaces B2.

Format of list:

{{base B2, twists}, ...}

Base B2 given in terms of toric fan {v_1 ={0, 1}, v_2 ={1, 0}, ...}

twists is a list of possible twists and gauge groups in the form

twists = {{t, g1, g2}, ...}

t = {t_3, t_4, ...} (linear transformations used to set t_1 = t_2 = 0)

g1 = {n, group}, g2 indicate gauge group on Sigma_-, Sigma_+, in
numerical and text format

Possibilities are
0 x (no gauge group)
1 SU(2)
2 SU(3)
3 G_2
4 SO(8)
5 F_4
6 E_6
7 E_7
8 E_8

 *)

structures =
{{{{0, 1}, {1, 0}, {-1, -1}}, {{{0}, {0, "x"}, {0, "x"}}, 
   {{1}, {0, "x"}, {0, "x"}}, {{2}, {0, "x"}, {0, "x"}}, 
   {{3}, {0, "x"}, {0, "x"}}, {{4}, {1, "SU(2)"}, {0, "x"}}, 
   {{5}, {3, "G_2"}, {0, "x"}}, {{6}, {4, "SO(8)"}, {0, "x"}}, 
   {{7}, {5, "F_4"}, {0, "x"}}, {{8}, {5, "F_4"}, {0, "x"}}, 
   {{9}, {6, "E_6"}, {0, "x"}}, {{10}, {7, "E_7"}, {0, "x"}}, 
   {{11}, {7, "E_7"}, {0, "x"}}, {{12}, {7, "E_7"}, {0, "x"}}, 
   {{18}, {8, "E_8"}, {0, "x"}}}}, {{{0, 1}, {1, 0}, {0, -1}, {-1, 0}}, 
  {{{-8, 1}, {0, "x"}, {7, "E_7"}}, {{-8, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-8, 3}, {1, "SU(2)"}, {7, "E_7"}}, {{-8, 4}, {3, "G_2"}, {7, "E_7"}}, 
   {{-8, 5}, {5, "F_4"}, {7, "E_7"}}, {{-8, 6}, {5, "F_4"}, {7, "E_7"}}, 
   {{-8, 7}, {7, "E_7"}, {7, "E_7"}}, {{-8, 8}, {7, "E_7"}, {7, "E_7"}}, 
   {{-7, 1}, {0, "x"}, {7, "E_7"}}, {{-7, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-7, 3}, {1, "SU(2)"}, {7, "E_7"}}, {{-7, 4}, {3, "G_2"}, {7, "E_7"}}, 
   {{-7, 5}, {5, "F_4"}, {7, "E_7"}}, {{-7, 6}, {5, "F_4"}, {7, "E_7"}}, 
   {{-7, 7}, {7, "E_7"}, {7, "E_7"}}, {{-6, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, 2}, {0, "x"}, {5, "F_4"}}, {{-6, 3}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{-6, 4}, {3, "G_2"}, {5, "F_4"}}, {{-6, 5}, {5, "F_4"}, {5, "F_4"}}, 
   {{-6, 6}, {5, "F_4"}, {5, "F_4"}}, {{-5, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, 2}, {0, "x"}, {5, "F_4"}}, {{-5, 3}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{-5, 4}, {3, "G_2"}, {5, "F_4"}}, {{-5, 5}, {5, "F_4"}, {5, "F_4"}}, 
   {{-4, 1}, {0, "x"}, {3, "G_2"}}, {{-4, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, 3}, {1, "SU(2)"}, {3, "G_2"}}, {{-4, 4}, {3, "G_2"}, {3, "G_2"}}, 
   {{-3, 1}, {0, "x"}, {1, "SU(2)"}}, {{-3, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, 3}, {1, "SU(2)"}, {1, "SU(2)"}}, {{-2, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, 2}, {0, "x"}, {0, "x"}}, {{-1, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 0}, {0, "x"}, {0, "x"}}, {{1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1}, {0, "x"}, {0, "x"}}, {{2, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 1}, {0, "x"}, {0, "x"}}, {{2, 2}, {0, "x"}, {0, "x"}}, 
   {{3, 0}, {1, "SU(2)"}, {0, "x"}}, {{3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 2}, {1, "SU(2)"}, {0, "x"}}, {{3, 3}, {2, "SU(3)"}, {0, "x"}}, 
   {{4, 0}, {3, "G_2"}, {0, "x"}}, {{4, 1}, {3, "G_2"}, {0, "x"}}, 
   {{4, 2}, {3, "G_2"}, {0, "x"}}, {{4, 3}, {3, "G_2"}, {0, "x"}}, 
   {{4, 4}, {4, "SO(8)"}, {0, "x"}}, {{5, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 1}, {5, "F_4"}, {0, "x"}}, {{5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{5, 3}, {5, "F_4"}, {0, "x"}}, {{5, 4}, {5, "F_4"}, {0, "x"}}, 
   {{5, 5}, {5, "F_4"}, {0, "x"}}, {{6, 0}, {5, "F_4"}, {0, "x"}}, 
   {{6, 1}, {5, "F_4"}, {0, "x"}}, {{6, 2}, {5, "F_4"}, {0, "x"}}, 
   {{6, 3}, {5, "F_4"}, {0, "x"}}, {{6, 4}, {5, "F_4"}, {0, "x"}}, 
   {{6, 5}, {5, "F_4"}, {0, "x"}}, {{6, 6}, {6, "E_6"}, {0, "x"}}, 
   {{7, 0}, {7, "E_7"}, {0, "x"}}, {{7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{7, 2}, {7, "E_7"}, {0, "x"}}, {{7, 3}, {7, "E_7"}, {0, "x"}}, 
   {{7, 4}, {7, "E_7"}, {0, "x"}}, {{7, 5}, {7, "E_7"}, {0, "x"}}, 
   {{7, 6}, {7, "E_7"}, {0, "x"}}, {{7, 7}, {7, "E_7"}, {0, "x"}}, 
   {{8, 0}, {7, "E_7"}, {0, "x"}}, {{8, 1}, {7, "E_7"}, {0, "x"}}, 
   {{8, 2}, {7, "E_7"}, {0, "x"}}, {{8, 3}, {7, "E_7"}, {0, "x"}}, 
   {{8, 4}, {7, "E_7"}, {0, "x"}}, {{8, 5}, {7, "E_7"}, {0, "x"}}, 
   {{8, 6}, {7, "E_7"}, {0, "x"}}, {{8, 7}, {7, "E_7"}, {0, "x"}}, 
   {{8, 8}, {7, "E_7"}, {0, "x"}}, {{12, 12}, {8, "E_8"}, {0, "x"}}}}, 
 {{{0, 1}, {1, 0}, {0, -1}, {-1, -1}}, {{{-5, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, 1}, {0, "x"}, {3, "G_2"}}, {{-4, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-3, 1}, {0, "x"}, {1, "SU(2)"}}, {{-3, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, 3}, {0, "x"}, {1, "SU(2)"}}, {{-2, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, 2}, {0, "x"}, {0, "x"}}, {{-2, 3}, {0, "x"}, {0, "x"}}, 
   {{-2, 4}, {1, "SU(2)"}, {0, "x"}}, {{-1, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, 2}, {0, "x"}, {0, "x"}}, {{-1, 3}, {0, "x"}, {0, "x"}}, 
   {{-1, 4}, {1, "SU(2)"}, {0, "x"}}, {{-1, 5}, {3, "G_2"}, {0, "x"}}, 
   {{0, 0}, {0, "x"}, {0, "x"}}, {{0, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 2}, {0, "x"}, {0, "x"}}, {{0, 3}, {0, "x"}, {0, "x"}}, 
   {{0, 4}, {1, "SU(2)"}, {0, "x"}}, {{0, 5}, {3, "G_2"}, {0, "x"}}, 
   {{0, 6}, {4, "SO(8)"}, {0, "x"}}, {{1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1}, {0, "x"}, {0, "x"}}, {{1, 2}, {0, "x"}, {0, "x"}}, 
   {{1, 3}, {0, "x"}, {0, "x"}}, {{1, 4}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 5}, {3, "G_2"}, {0, "x"}}, {{1, 6}, {4, "SO(8)"}, {0, "x"}}, 
   {{1, 7}, {5, "F_4"}, {0, "x"}}, {{2, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 1}, {0, "x"}, {0, "x"}}, {{2, 2}, {0, "x"}, {0, "x"}}, 
   {{2, 3}, {0, "x"}, {0, "x"}}, {{2, 4}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 5}, {3, "G_2"}, {0, "x"}}, {{2, 6}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 7}, {5, "F_4"}, {0, "x"}}, {{2, 8}, {5, "F_4"}, {0, "x"}}, 
   {{3, 0}, {1, "SU(2)"}, {0, "x"}}, {{3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 2}, {1, "SU(2)"}, {0, "x"}}, {{3, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 4}, {1, "SU(2)"}, {0, "x"}}, {{3, 5}, {3, "G_2"}, {0, "x"}}, 
   {{3, 6}, {4, "SO(8)"}, {0, "x"}}, {{3, 7}, {5, "F_4"}, {0, "x"}}, 
   {{3, 8}, {5, "F_4"}, {0, "x"}}, {{3, 9}, {6, "E_6"}, {0, "x"}}, 
   {{4, 0}, {3, "G_2"}, {0, "x"}}, {{4, 1}, {3, "G_2"}, {0, "x"}}, 
   {{4, 2}, {3, "G_2"}, {0, "x"}}, {{4, 3}, {3, "G_2"}, {0, "x"}}, 
   {{4, 4}, {3, "G_2"}, {0, "x"}}, {{4, 5}, {3, "G_2"}, {0, "x"}}, 
   {{4, 6}, {4, "SO(8)"}, {0, "x"}}, {{4, 7}, {5, "F_4"}, {0, "x"}}, 
   {{4, 8}, {5, "F_4"}, {0, "x"}}, {{4, 9}, {6, "E_6"}, {0, "x"}}, 
   {{4, 10}, {7, "E_7"}, {0, "x"}}, {{5, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 1}, {5, "F_4"}, {0, "x"}}, {{5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{5, 3}, {5, "F_4"}, {0, "x"}}, {{5, 4}, {5, "F_4"}, {0, "x"}}, 
   {{5, 5}, {5, "F_4"}, {0, "x"}}, {{5, 6}, {5, "F_4"}, {0, "x"}}, 
   {{5, 7}, {5, "F_4"}, {0, "x"}}, {{5, 8}, {5, "F_4"}, {0, "x"}}, 
   {{5, 9}, {6, "E_6"}, {0, "x"}}, {{5, 10}, {7, "E_7"}, {0, "x"}}, 
   {{5, 11}, {7, "E_7"}, {0, "x"}}, {{6, 0}, {5, "F_4"}, {0, "x"}}, 
   {{6, 1}, {5, "F_4"}, {0, "x"}}, {{6, 2}, {5, "F_4"}, {0, "x"}}, 
   {{6, 3}, {5, "F_4"}, {0, "x"}}, {{6, 4}, {5, "F_4"}, {0, "x"}}, 
   {{6, 5}, {5, "F_4"}, {0, "x"}}, {{6, 6}, {5, "F_4"}, {0, "x"}}, 
   {{6, 7}, {5, "F_4"}, {0, "x"}}, {{6, 8}, {5, "F_4"}, {0, "x"}}, 
   {{6, 9}, {6, "E_6"}, {0, "x"}}, {{6, 10}, {7, "E_7"}, {0, "x"}}, 
   {{6, 11}, {7, "E_7"}, {0, "x"}}, {{6, 12}, {7, "E_7"}, {0, "x"}}, 
   {{7, 1}, {7, "E_7"}, {0, "x"}}, {{7, 2}, {7, "E_7"}, {0, "x"}}, 
   {{7, 3}, {7, "E_7"}, {0, "x"}}, {{7, 4}, {7, "E_7"}, {0, "x"}}, 
   {{7, 5}, {7, "E_7"}, {0, "x"}}, {{7, 6}, {7, "E_7"}, {0, "x"}}, 
   {{7, 7}, {7, "E_7"}, {0, "x"}}, {{7, 8}, {7, "E_7"}, {0, "x"}}, 
   {{7, 9}, {7, "E_7"}, {0, "x"}}, {{7, 10}, {7, "E_7"}, {0, "x"}}, 
   {{7, 11}, {7, "E_7"}, {0, "x"}}, {{7, 12}, {7, "E_7"}, {0, "x"}}, 
   {{8, 2}, {7, "E_7"}, {0, "x"}}, {{8, 3}, {7, "E_7"}, {0, "x"}}, 
   {{8, 4}, {7, "E_7"}, {0, "x"}}, {{8, 5}, {7, "E_7"}, {0, "x"}}, 
   {{8, 6}, {7, "E_7"}, {0, "x"}}, {{8, 7}, {7, "E_7"}, {0, "x"}}, 
   {{8, 8}, {7, "E_7"}, {0, "x"}}, {{8, 9}, {7, "E_7"}, {0, "x"}}, 
   {{8, 10}, {7, "E_7"}, {0, "x"}}, {{8, 11}, {7, "E_7"}, {0, "x"}}, 
   {{8, 12}, {7, "E_7"}, {0, "x"}}, {{12, 18}, {8, "E_8"}, {0, "x"}}}}, 
 {{{0, 1}, {1, 0}, {0, -1}, {-1, -2}}, {{{0, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1}, {0, "x"}, {0, "x"}}, {{1, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 2}, {0, "x"}, {0, "x"}}, {{1, 3}, {0, "x"}, {0, "x"}}, 
   {{2, 3}, {0, "x"}, {0, "x"}}, {{2, 4}, {0, "x"}, {0, "x"}}, 
   {{2, 5}, {1, "SU(2)"}, {0, "x"}}, {{3, 5}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 6}, {2, "SU(3)"}, {0, "x"}}, {{3, 7}, {3, "G_2"}, {0, "x"}}, 
   {{4, 7}, {3, "G_2"}, {0, "x"}}, {{4, 8}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 9}, {5, "F_4"}, {0, "x"}}, {{5, 9}, {5, "F_4"}, {0, "x"}}, 
   {{5, 10}, {5, "F_4"}, {0, "x"}}, {{5, 11}, {5, "F_4"}, {0, "x"}}, 
   {{6, 11}, {5, "F_4"}, {0, "x"}}, {{6, 12}, {6, "E_6"}, {0, "x"}}, 
   {{7, 13}, {7, "E_7"}, {0, "x"}}, {{7, 14}, {7, "E_7"}, {0, "x"}}, 
   {{8, 15}, {7, "E_7"}, {0, "x"}}, {{8, 16}, {7, "E_7"}, {0, "x"}}, 
   {{12, 24}, {8, "E_8"}, {0, "x"}}}}, 
 {{{0, 1}, {1, 0}, {0, -1}, {-1, -1}, {-1, 0}}, 
  {{{-8, -5, 1}, {0, "x"}, {7, "E_7"}}, {{-8, -4, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-8, -4, 2}, {0, "x"}, {7, "E_7"}}, {{-8, -3, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-8, -3, 2}, {0, "x"}, {7, "E_7"}}, {{-8, -3, 3}, {1, "SU(2)"}, 
    {7, "E_7"}}, {{-8, -2, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-8, -2, 2}, {0, "x"}, {7, "E_7"}}, {{-8, -2, 3}, {1, "SU(2)"}, 
    {7, "E_7"}}, {{-8, -2, 4}, {3, "G_2"}, {7, "E_7"}}, 
   {{-7, -5, 1}, {0, "x"}, {7, "E_7"}}, {{-7, -4, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-7, -4, 2}, {0, "x"}, {7, "E_7"}}, {{-7, -3, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-7, -3, 2}, {0, "x"}, {7, "E_7"}}, {{-7, -3, 3}, {1, "SU(2)"}, 
    {7, "E_7"}}, {{-7, -2, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-7, -2, 2}, {0, "x"}, {7, "E_7"}}, {{-7, -2, 3}, {1, "SU(2)"}, 
    {7, "E_7"}}, {{-7, -2, 4}, {3, "G_2"}, {7, "E_7"}}, 
   {{-7, -1, 1}, {0, "x"}, {7, "E_7"}}, {{-7, -1, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-7, -1, 3}, {1, "SU(2)"}, {7, "E_7"}}, {{-7, -1, 4}, {3, "G_2"}, 
    {7, "E_7"}}, {{-7, -1, 5}, {5, "F_4"}, {7, "E_7"}}, 
   {{-6, -5, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -4, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -4, 2}, {0, "x"}, {5, "F_4"}}, {{-6, -3, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -3, 2}, {0, "x"}, {5, "F_4"}}, {{-6, -3, 3}, {1, "SU(2)"}, 
    {5, "F_4"}}, {{-6, -2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -2, 2}, {0, "x"}, {5, "F_4"}}, {{-6, -2, 3}, {1, "SU(2)"}, 
    {5, "F_4"}}, {{-6, -2, 4}, {3, "G_2"}, {5, "F_4"}}, 
   {{-6, -1, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -1, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -1, 3}, {1, "SU(2)"}, {5, "F_4"}}, {{-6, -1, 4}, {3, "G_2"}, 
    {5, "F_4"}}, {{-6, -1, 5}, {5, "F_4"}, {5, "F_4"}}, 
   {{-6, 0, 1}, {0, "x"}, {5, "F_4"}}, {{-6, 0, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-6, 0, 3}, {1, "SU(2)"}, {5, "F_4"}}, {{-6, 0, 4}, {3, "G_2"}, 
    {5, "F_4"}}, {{-6, 0, 5}, {5, "F_4"}, {5, "F_4"}}, 
   {{-6, 0, 6}, {5, "F_4"}, {5, "F_4"}}, {{-5, -5, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -4, 1}, {0, "x"}, {5, "F_4"}}, {{-5, -4, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -3, 1}, {0, "x"}, {5, "F_4"}}, {{-5, -3, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -3, 3}, {1, "SU(2)"}, {5, "F_4"}}, {{-5, -2, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-5, -2, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -2, 3}, {1, "SU(2)"}, {5, "F_4"}}, {{-5, -2, 4}, {3, "G_2"}, 
    {5, "F_4"}}, {{-5, -1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -1, 2}, {0, "x"}, {5, "F_4"}}, {{-5, -1, 3}, {1, "SU(2)"}, 
    {5, "F_4"}}, {{-5, -1, 4}, {3, "G_2"}, {5, "F_4"}}, 
   {{-5, -1, 5}, {5, "F_4"}, {5, "F_4"}}, {{-5, 0, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, 0, 2}, {0, "x"}, {5, "F_4"}}, {{-5, 0, 3}, {1, "SU(2)"}, 
    {5, "F_4"}}, {{-5, 0, 4}, {3, "G_2"}, {5, "F_4"}}, 
   {{-5, 0, 5}, {5, "F_4"}, {5, "F_4"}}, {{-5, 1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, 1, 2}, {0, "x"}, {5, "F_4"}}, {{-5, 1, 3}, {1, "SU(2)"}, 
    {5, "F_4"}}, {{-5, 1, 4}, {3, "G_2"}, {5, "F_4"}}, 
   {{-4, -5, 1}, {0, "x"}, {3, "G_2"}}, {{-4, -4, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -4, 2}, {0, "x"}, {3, "G_2"}}, {{-4, -3, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -3, 2}, {0, "x"}, {3, "G_2"}}, {{-4, -3, 3}, {1, "SU(2)"}, 
    {3, "G_2"}}, {{-4, -2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -2, 2}, {0, "x"}, {3, "G_2"}}, {{-4, -2, 3}, {1, "SU(2)"}, 
    {3, "G_2"}}, {{-4, -2, 4}, {3, "G_2"}, {3, "G_2"}}, 
   {{-4, -1, 1}, {0, "x"}, {3, "G_2"}}, {{-4, -1, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -1, 3}, {1, "SU(2)"}, {3, "G_2"}}, {{-4, -1, 4}, {3, "G_2"}, 
    {3, "G_2"}}, {{-4, 0, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-4, 0, 2}, {0, "x"}, {3, "G_2"}}, {{-4, 0, 3}, {1, "SU(2)"}, 
    {3, "G_2"}}, {{-4, 0, 4}, {3, "G_2"}, {3, "G_2"}}, 
   {{-4, 1, 1}, {0, "x"}, {3, "G_2"}}, {{-4, 1, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, 1, 3}, {1, "SU(2)"}, {3, "G_2"}}, {{-4, 2, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-4, 2, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, 2, 3}, {1, "SU(2)"}, {3, "G_2"}}, {{-3, -5, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-3, -4, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -4, 2}, {0, "x"}, {1, "SU(2)"}}, {{-3, -3, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-3, -3, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -3, 3}, {1, "SU(2)"}, {1, "SU(2)"}}, {{-3, -2, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-3, -2, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -2, 3}, {1, "SU(2)"}, {1, "SU(2)"}}, {{-3, -1, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-3, -1, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -1, 3}, {1, "SU(2)"}, {1, "SU(2)"}}, {{-3, 0, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-3, 0, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, 0, 3}, {1, "SU(2)"}, {1, "SU(2)"}}, {{-3, 1, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-3, 1, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, 2, 1}, {0, "x"}, {1, "SU(2)"}}, {{-3, 2, 2}, {0, "x"}, 
    {1, "SU(2)"}}, {{-3, 3, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, 3, 2}, {0, "x"}, {1, "SU(2)"}}, {{-2, -5, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-2, -4, 1}, {0, "x"}, {1, "SU(2)"}}, {{-2, -4, 2}, {0, "x"}, 
    {1, "SU(2)"}}, {{-2, -3, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -3, 2}, {0, "x"}, {0, "x"}}, {{-2, -2, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -2, 2}, {0, "x"}, {0, "x"}}, {{-2, -1, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -1, 2}, {0, "x"}, {0, "x"}}, {{-2, 0, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, 0, 2}, {0, "x"}, {0, "x"}}, {{-2, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, 2, 1}, {0, "x"}, {0, "x"}}, {{-2, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, 4, 1}, {1, "SU(2)"}, {0, "x"}}, {{-1, -5, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-1, -4, 1}, {0, "x"}, {1, "SU(2)"}}, {{-1, -3, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -2, 1}, {0, "x"}, {0, "x"}}, {{-1, -1, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, 0, 1}, {0, "x"}, {0, "x"}}, {{0, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 0}, {0, "x"}, {0, "x"}}, {{0, 2, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 3, 0}, {0, "x"}, {0, "x"}}, {{0, 4, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{0, 5, 0}, {3, "G_2"}, {0, "x"}}, {{0, 6, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{1, -5, 0}, {0, "x"}, {3, "G_2"}}, {{1, -4, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, -4, 1}, {0, "x"}, {1, "SU(2)"}}, {{1, -3, 0}, {0, "x"}, {0, "x"}}, 
   {{1, -3, 1}, {0, "x"}, {0, "x"}}, {{1, -2, 0}, {0, "x"}, {0, "x"}}, 
   {{1, -2, 1}, {0, "x"}, {0, "x"}}, {{1, -1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, -1, 1}, {0, "x"}, {0, "x"}}, {{1, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 0, 1}, {0, "x"}, {0, "x"}}, {{1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 1}, {0, "x"}, {0, "x"}}, {{1, 2, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 1}, {0, "x"}, {0, "x"}}, {{1, 3, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 3, 1}, {0, "x"}, {0, "x"}}, {{1, 4, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 4, 1}, {1, "SU(2)"}, {0, "x"}}, {{1, 5, 0}, {3, "G_2"}, {0, "x"}}, 
   {{1, 5, 1}, {3, "G_2"}, {0, "x"}}, {{1, 6, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{1, 6, 1}, {4, "SO(8)"}, {0, "x"}}, {{1, 7, 1}, {5, "F_4"}, {0, "x"}}, 
   {{2, -4, 0}, {0, "x"}, {1, "SU(2)"}}, {{2, -3, 0}, {0, "x"}, {0, "x"}}, 
   {{2, -3, 1}, {0, "x"}, {0, "x"}}, {{2, -2, 0}, {0, "x"}, {0, "x"}}, 
   {{2, -2, 1}, {0, "x"}, {0, "x"}}, {{2, -2, 2}, {0, "x"}, {0, "x"}}, 
   {{2, -1, 0}, {0, "x"}, {0, "x"}}, {{2, -1, 1}, {0, "x"}, {0, "x"}}, 
   {{2, -1, 2}, {0, "x"}, {0, "x"}}, {{2, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 0, 1}, {0, "x"}, {0, "x"}}, {{2, 0, 2}, {0, "x"}, {0, "x"}}, 
   {{2, 1, 0}, {0, "x"}, {0, "x"}}, {{2, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{2, 1, 2}, {0, "x"}, {0, "x"}}, {{2, 2, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 2, 1}, {0, "x"}, {0, "x"}}, {{2, 2, 2}, {0, "x"}, {0, "x"}}, 
   {{2, 3, 0}, {0, "x"}, {0, "x"}}, {{2, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{2, 3, 2}, {0, "x"}, {0, "x"}}, {{2, 4, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 4, 1}, {1, "SU(2)"}, {0, "x"}}, {{2, 4, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 5, 0}, {3, "G_2"}, {0, "x"}}, {{2, 5, 1}, {3, "G_2"}, {0, "x"}}, 
   {{2, 5, 2}, {3, "G_2"}, {0, "x"}}, {{2, 6, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 6, 1}, {4, "SO(8)"}, {0, "x"}}, {{2, 6, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 7, 1}, {5, "F_4"}, {0, "x"}}, {{2, 7, 2}, {5, "F_4"}, {0, "x"}}, 
   {{2, 8, 2}, {5, "F_4"}, {0, "x"}}, {{3, -3, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, -2, 0}, {1, "SU(2)"}, {0, "x"}}, {{3, -2, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{3, -1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, -1, 1}, {1, "SU(2)"}, {0, "x"}}, {{3, -1, 2}, {1, "SU(2)"}, 
    {0, "x"}}, {{3, 0, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 0, 1}, {1, "SU(2)"}, {0, "x"}}, {{3, 0, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 0, 3}, {2, "SU(3)"}, {0, "x"}}, {{3, 1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 1, 1}, {1, "SU(2)"}, {0, "x"}}, {{3, 1, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 1, 3}, {2, "SU(3)"}, {0, "x"}}, {{3, 2, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 2, 1}, {1, "SU(2)"}, {0, "x"}}, {{3, 2, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 2, 3}, {2, "SU(3)"}, {0, "x"}}, {{3, 3, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 3, 1}, {1, "SU(2)"}, {0, "x"}}, {{3, 3, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 3, 3}, {2, "SU(3)"}, {0, "x"}}, {{3, 4, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 4, 1}, {1, "SU(2)"}, {0, "x"}}, {{3, 4, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 4, 3}, {2, "SU(3)"}, {0, "x"}}, {{3, 5, 0}, {3, "G_2"}, {0, "x"}}, 
   {{3, 5, 1}, {3, "G_2"}, {0, "x"}}, {{3, 5, 2}, {3, "G_2"}, {0, "x"}}, 
   {{3, 5, 3}, {3, "G_2"}, {0, "x"}}, {{3, 6, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 6, 1}, {4, "SO(8)"}, {0, "x"}}, {{3, 6, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 6, 3}, {4, "SO(8)"}, {0, "x"}}, {{3, 7, 1}, {5, "F_4"}, {0, "x"}}, 
   {{3, 7, 2}, {5, "F_4"}, {0, "x"}}, {{3, 7, 3}, {5, "F_4"}, {0, "x"}}, 
   {{3, 8, 2}, {5, "F_4"}, {0, "x"}}, {{3, 8, 3}, {5, "F_4"}, {0, "x"}}, 
   {{3, 9, 3}, {6, "E_6"}, {0, "x"}}, {{4, -2, 0}, {3, "G_2"}, {0, "x"}}, 
   {{4, -1, 0}, {3, "G_2"}, {0, "x"}}, {{4, -1, 1}, {3, "G_2"}, {0, "x"}}, 
   {{4, 0, 0}, {3, "G_2"}, {0, "x"}}, {{4, 0, 1}, {3, "G_2"}, {0, "x"}}, 
   {{4, 0, 2}, {3, "G_2"}, {0, "x"}}, {{4, 1, 0}, {3, "G_2"}, {0, "x"}}, 
   {{4, 1, 1}, {3, "G_2"}, {0, "x"}}, {{4, 1, 2}, {3, "G_2"}, {0, "x"}}, 
   {{4, 1, 3}, {3, "G_2"}, {0, "x"}}, {{4, 2, 0}, {3, "G_2"}, {0, "x"}}, 
   {{4, 2, 1}, {3, "G_2"}, {0, "x"}}, {{4, 2, 2}, {3, "G_2"}, {0, "x"}}, 
   {{4, 2, 3}, {3, "G_2"}, {0, "x"}}, {{4, 2, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 3, 0}, {3, "G_2"}, {0, "x"}}, {{4, 3, 1}, {3, "G_2"}, {0, "x"}}, 
   {{4, 3, 2}, {3, "G_2"}, {0, "x"}}, {{4, 3, 3}, {3, "G_2"}, {0, "x"}}, 
   {{4, 3, 4}, {4, "SO(8)"}, {0, "x"}}, {{4, 4, 0}, {3, "G_2"}, {0, "x"}}, 
   {{4, 4, 1}, {3, "G_2"}, {0, "x"}}, {{4, 4, 2}, {3, "G_2"}, {0, "x"}}, 
   {{4, 4, 3}, {3, "G_2"}, {0, "x"}}, {{4, 4, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 5, 0}, {3, "G_2"}, {0, "x"}}, {{4, 5, 1}, {3, "G_2"}, {0, "x"}}, 
   {{4, 5, 2}, {3, "G_2"}, {0, "x"}}, {{4, 5, 3}, {3, "G_2"}, {0, "x"}}, 
   {{4, 5, 4}, {4, "SO(8)"}, {0, "x"}}, {{4, 6, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 6, 1}, {4, "SO(8)"}, {0, "x"}}, {{4, 6, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 6, 3}, {4, "SO(8)"}, {0, "x"}}, {{4, 6, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 7, 1}, {5, "F_4"}, {0, "x"}}, {{4, 7, 2}, {5, "F_4"}, {0, "x"}}, 
   {{4, 7, 3}, {5, "F_4"}, {0, "x"}}, {{4, 7, 4}, {5, "F_4"}, {0, "x"}}, 
   {{4, 8, 2}, {5, "F_4"}, {0, "x"}}, {{4, 8, 3}, {5, "F_4"}, {0, "x"}}, 
   {{4, 8, 4}, {5, "F_4"}, {0, "x"}}, {{4, 9, 3}, {6, "E_6"}, {0, "x"}}, 
   {{4, 9, 4}, {6, "E_6"}, {0, "x"}}, {{4, 10, 4}, {7, "E_7"}, {0, "x"}}, 
   {{5, -1, 0}, {5, "F_4"}, {0, "x"}}, {{5, 0, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 0, 1}, {5, "F_4"}, {0, "x"}}, {{5, 1, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 1, 1}, {5, "F_4"}, {0, "x"}}, {{5, 1, 2}, {5, "F_4"}, {0, "x"}}, 
   {{5, 2, 0}, {5, "F_4"}, {0, "x"}}, {{5, 2, 1}, {5, "F_4"}, {0, "x"}}, 
   {{5, 2, 2}, {5, "F_4"}, {0, "x"}}, {{5, 2, 3}, {5, "F_4"}, {0, "x"}}, 
   {{5, 3, 0}, {5, "F_4"}, {0, "x"}}, {{5, 3, 1}, {5, "F_4"}, {0, "x"}}, 
   {{5, 3, 2}, {5, "F_4"}, {0, "x"}}, {{5, 3, 3}, {5, "F_4"}, {0, "x"}}, 
   {{5, 3, 4}, {5, "F_4"}, {0, "x"}}, {{5, 4, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 4, 1}, {5, "F_4"}, {0, "x"}}, {{5, 4, 2}, {5, "F_4"}, {0, "x"}}, 
   {{5, 4, 3}, {5, "F_4"}, {0, "x"}}, {{5, 4, 4}, {5, "F_4"}, {0, "x"}}, 
   {{5, 4, 5}, {5, "F_4"}, {0, "x"}}, {{5, 5, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 5, 1}, {5, "F_4"}, {0, "x"}}, {{5, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{5, 5, 3}, {5, "F_4"}, {0, "x"}}, {{5, 5, 4}, {5, "F_4"}, {0, "x"}}, 
   {{5, 5, 5}, {5, "F_4"}, {0, "x"}}, {{5, 6, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 6, 1}, {5, "F_4"}, {0, "x"}}, {{5, 6, 2}, {5, "F_4"}, {0, "x"}}, 
   {{5, 6, 3}, {5, "F_4"}, {0, "x"}}, {{5, 6, 4}, {5, "F_4"}, {0, "x"}}, 
   {{5, 6, 5}, {5, "F_4"}, {0, "x"}}, {{5, 7, 1}, {5, "F_4"}, {0, "x"}}, 
   {{5, 7, 2}, {5, "F_4"}, {0, "x"}}, {{5, 7, 3}, {5, "F_4"}, {0, "x"}}, 
   {{5, 7, 4}, {5, "F_4"}, {0, "x"}}, {{5, 7, 5}, {5, "F_4"}, {0, "x"}}, 
   {{5, 8, 2}, {5, "F_4"}, {0, "x"}}, {{5, 8, 3}, {5, "F_4"}, {0, "x"}}, 
   {{5, 8, 4}, {5, "F_4"}, {0, "x"}}, {{5, 8, 5}, {5, "F_4"}, {0, "x"}}, 
   {{5, 9, 3}, {6, "E_6"}, {0, "x"}}, {{5, 9, 4}, {6, "E_6"}, {0, "x"}}, 
   {{5, 9, 5}, {6, "E_6"}, {0, "x"}}, {{5, 10, 4}, {7, "E_7"}, {0, "x"}}, 
   {{5, 10, 5}, {7, "E_7"}, {0, "x"}}, {{5, 11, 5}, {7, "E_7"}, {0, "x"}}, 
   {{6, 0, 0}, {5, "F_4"}, {0, "x"}}, {{6, 1, 0}, {5, "F_4"}, {0, "x"}}, 
   {{6, 1, 1}, {5, "F_4"}, {0, "x"}}, {{6, 2, 0}, {5, "F_4"}, {0, "x"}}, 
   {{6, 2, 1}, {5, "F_4"}, {0, "x"}}, {{6, 2, 2}, {5, "F_4"}, {0, "x"}}, 
   {{6, 3, 0}, {5, "F_4"}, {0, "x"}}, {{6, 3, 1}, {5, "F_4"}, {0, "x"}}, 
   {{6, 3, 2}, {5, "F_4"}, {0, "x"}}, {{6, 3, 3}, {5, "F_4"}, {0, "x"}}, 
   {{6, 4, 0}, {5, "F_4"}, {0, "x"}}, {{6, 4, 1}, {5, "F_4"}, {0, "x"}}, 
   {{6, 4, 2}, {5, "F_4"}, {0, "x"}}, {{6, 4, 3}, {5, "F_4"}, {0, "x"}}, 
   {{6, 4, 4}, {5, "F_4"}, {0, "x"}}, {{6, 5, 0}, {5, "F_4"}, {0, "x"}}, 
   {{6, 5, 1}, {5, "F_4"}, {0, "x"}}, {{6, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{6, 5, 3}, {5, "F_4"}, {0, "x"}}, {{6, 5, 4}, {5, "F_4"}, {0, "x"}}, 
   {{6, 5, 5}, {5, "F_4"}, {0, "x"}}, {{6, 6, 0}, {5, "F_4"}, {0, "x"}}, 
   {{6, 6, 1}, {5, "F_4"}, {0, "x"}}, {{6, 6, 2}, {5, "F_4"}, {0, "x"}}, 
   {{6, 6, 3}, {5, "F_4"}, {0, "x"}}, {{6, 6, 4}, {5, "F_4"}, {0, "x"}}, 
   {{6, 6, 5}, {5, "F_4"}, {0, "x"}}, {{6, 6, 6}, {6, "E_6"}, {0, "x"}}, 
   {{6, 7, 1}, {5, "F_4"}, {0, "x"}}, {{6, 7, 2}, {5, "F_4"}, {0, "x"}}, 
   {{6, 7, 3}, {5, "F_4"}, {0, "x"}}, {{6, 7, 4}, {5, "F_4"}, {0, "x"}}, 
   {{6, 7, 5}, {5, "F_4"}, {0, "x"}}, {{6, 7, 6}, {6, "E_6"}, {0, "x"}}, 
   {{6, 8, 2}, {5, "F_4"}, {0, "x"}}, {{6, 8, 3}, {5, "F_4"}, {0, "x"}}, 
   {{6, 8, 4}, {5, "F_4"}, {0, "x"}}, {{6, 8, 5}, {5, "F_4"}, {0, "x"}}, 
   {{6, 8, 6}, {6, "E_6"}, {0, "x"}}, {{6, 9, 3}, {6, "E_6"}, {0, "x"}}, 
   {{6, 9, 4}, {6, "E_6"}, {0, "x"}}, {{6, 9, 5}, {6, "E_6"}, {0, "x"}}, 
   {{6, 9, 6}, {6, "E_6"}, {0, "x"}}, {{6, 10, 4}, {7, "E_7"}, {0, "x"}}, 
   {{6, 10, 5}, {7, "E_7"}, {0, "x"}}, {{6, 10, 6}, {7, "E_7"}, {0, "x"}}, 
   {{6, 11, 5}, {7, "E_7"}, {0, "x"}}, {{6, 11, 6}, {7, "E_7"}, {0, "x"}}, 
   {{6, 12, 6}, {7, "E_7"}, {0, "x"}}, {{7, 1, 0}, {7, "E_7"}, {0, "x"}}, 
   {{7, 2, 0}, {7, "E_7"}, {0, "x"}}, {{7, 2, 1}, {7, "E_7"}, {0, "x"}}, 
   {{7, 3, 0}, {7, "E_7"}, {0, "x"}}, {{7, 3, 1}, {7, "E_7"}, {0, "x"}}, 
   {{7, 3, 2}, {7, "E_7"}, {0, "x"}}, {{7, 4, 0}, {7, "E_7"}, {0, "x"}}, 
   {{7, 4, 1}, {7, "E_7"}, {0, "x"}}, {{7, 4, 2}, {7, "E_7"}, {0, "x"}}, 
   {{7, 4, 3}, {7, "E_7"}, {0, "x"}}, {{7, 5, 0}, {7, "E_7"}, {0, "x"}}, 
   {{7, 5, 1}, {7, "E_7"}, {0, "x"}}, {{7, 5, 2}, {7, "E_7"}, {0, "x"}}, 
   {{7, 5, 3}, {7, "E_7"}, {0, "x"}}, {{7, 5, 4}, {7, "E_7"}, {0, "x"}}, 
   {{7, 6, 0}, {7, "E_7"}, {0, "x"}}, {{7, 6, 1}, {7, "E_7"}, {0, "x"}}, 
   {{7, 6, 2}, {7, "E_7"}, {0, "x"}}, {{7, 6, 3}, {7, "E_7"}, {0, "x"}}, 
   {{7, 6, 4}, {7, "E_7"}, {0, "x"}}, {{7, 6, 5}, {7, "E_7"}, {0, "x"}}, 
   {{7, 7, 1}, {7, "E_7"}, {0, "x"}}, {{7, 7, 2}, {7, "E_7"}, {0, "x"}}, 
   {{7, 7, 3}, {7, "E_7"}, {0, "x"}}, {{7, 7, 4}, {7, "E_7"}, {0, "x"}}, 
   {{7, 7, 5}, {7, "E_7"}, {0, "x"}}, {{7, 7, 6}, {7, "E_7"}, {0, "x"}}, 
   {{7, 8, 2}, {7, "E_7"}, {0, "x"}}, {{7, 8, 3}, {7, "E_7"}, {0, "x"}}, 
   {{7, 8, 4}, {7, "E_7"}, {0, "x"}}, {{7, 8, 5}, {7, "E_7"}, {0, "x"}}, 
   {{7, 8, 6}, {7, "E_7"}, {0, "x"}}, {{7, 8, 7}, {7, "E_7"}, {0, "x"}}, 
   {{7, 9, 3}, {7, "E_7"}, {0, "x"}}, {{7, 9, 4}, {7, "E_7"}, {0, "x"}}, 
   {{7, 9, 5}, {7, "E_7"}, {0, "x"}}, {{7, 9, 6}, {7, "E_7"}, {0, "x"}}, 
   {{7, 9, 7}, {7, "E_7"}, {0, "x"}}, {{7, 10, 4}, {7, "E_7"}, {0, "x"}}, 
   {{7, 10, 5}, {7, "E_7"}, {0, "x"}}, {{7, 10, 6}, {7, "E_7"}, {0, "x"}}, 
   {{7, 10, 7}, {7, "E_7"}, {0, "x"}}, {{7, 11, 5}, {7, "E_7"}, {0, "x"}}, 
   {{7, 11, 6}, {7, "E_7"}, {0, "x"}}, {{7, 11, 7}, {7, "E_7"}, {0, "x"}}, 
   {{7, 12, 6}, {7, "E_7"}, {0, "x"}}, {{7, 12, 7}, {7, "E_7"}, {0, "x"}}, 
   {{8, 2, 0}, {7, "E_7"}, {0, "x"}}, {{8, 3, 0}, {7, "E_7"}, {0, "x"}}, 
   {{8, 3, 1}, {7, "E_7"}, {0, "x"}}, {{8, 4, 0}, {7, "E_7"}, {0, "x"}}, 
   {{8, 4, 1}, {7, "E_7"}, {0, "x"}}, {{8, 4, 2}, {7, "E_7"}, {0, "x"}}, 
   {{8, 5, 0}, {7, "E_7"}, {0, "x"}}, {{8, 5, 1}, {7, "E_7"}, {0, "x"}}, 
   {{8, 5, 2}, {7, "E_7"}, {0, "x"}}, {{8, 5, 3}, {7, "E_7"}, {0, "x"}}, 
   {{8, 6, 0}, {7, "E_7"}, {0, "x"}}, {{8, 6, 1}, {7, "E_7"}, {0, "x"}}, 
   {{8, 6, 2}, {7, "E_7"}, {0, "x"}}, {{8, 6, 3}, {7, "E_7"}, {0, "x"}}, 
   {{8, 6, 4}, {7, "E_7"}, {0, "x"}}, {{8, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{8, 7, 2}, {7, "E_7"}, {0, "x"}}, {{8, 7, 3}, {7, "E_7"}, {0, "x"}}, 
   {{8, 7, 4}, {7, "E_7"}, {0, "x"}}, {{8, 7, 5}, {7, "E_7"}, {0, "x"}}, 
   {{8, 8, 2}, {7, "E_7"}, {0, "x"}}, {{8, 8, 3}, {7, "E_7"}, {0, "x"}}, 
   {{8, 8, 4}, {7, "E_7"}, {0, "x"}}, {{8, 8, 5}, {7, "E_7"}, {0, "x"}}, 
   {{8, 8, 6}, {7, "E_7"}, {0, "x"}}, {{8, 9, 3}, {7, "E_7"}, {0, "x"}}, 
   {{8, 9, 4}, {7, "E_7"}, {0, "x"}}, {{8, 9, 5}, {7, "E_7"}, {0, "x"}}, 
   {{8, 9, 6}, {7, "E_7"}, {0, "x"}}, {{8, 9, 7}, {7, "E_7"}, {0, "x"}}, 
   {{8, 10, 4}, {7, "E_7"}, {0, "x"}}, {{8, 10, 5}, {7, "E_7"}, {0, "x"}}, 
   {{8, 10, 6}, {7, "E_7"}, {0, "x"}}, {{8, 10, 7}, {7, "E_7"}, {0, "x"}}, 
   {{8, 10, 8}, {7, "E_7"}, {0, "x"}}, {{8, 11, 5}, {7, "E_7"}, {0, "x"}}, 
   {{8, 11, 6}, {7, "E_7"}, {0, "x"}}, {{8, 11, 7}, {7, "E_7"}, {0, "x"}}, 
   {{8, 11, 8}, {7, "E_7"}, {0, "x"}}, {{8, 12, 6}, {7, "E_7"}, {0, "x"}}, 
   {{8, 12, 7}, {7, "E_7"}, {0, "x"}}, {{8, 12, 8}, {7, "E_7"}, {0, "x"}}, 
   {{12, 18, 12}, {8, "E_8"}, {0, "x"}}}}, 
 {{{0, 1}, {1, 0}, {0, -1}, {-1, -2}, {-1, -1}}, 
  {{{-2, -5, 1}, {0, "x"}, {1, "SU(2)"}}, {{-2, -4, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -4, 2}, {0, "x"}, {0, "x"}}, {{-2, -3, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -3, 1}, {0, "x"}, {0, "x"}}, {{-1, -3, 2}, {0, "x"}, {0, "x"}}, 
   {{-1, -3, 3}, {0, "x"}, {0, "x"}}, {{-1, -2, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -2, 2}, {0, "x"}, {0, "x"}}, {{-1, -2, 3}, {0, "x"}, {0, "x"}}, 
   {{-1, -2, 4}, {1, "SU(2)"}, {0, "x"}}, {{-1, -1, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -1, 2}, {0, "x"}, {0, "x"}}, {{0, -1, 1}, {0, "x"}, {0, "x"}}, 
   {{0, -1, 2}, {0, "x"}, {0, "x"}}, {{0, -1, 3}, {0, "x"}, {0, "x"}}, 
   {{0, -1, 4}, {1, "SU(2)"}, {0, "x"}}, {{0, -1, 5}, {3, "G_2"}, {0, "x"}}, 
   {{0, 0, 0}, {0, "x"}, {0, "x"}}, {{0, 0, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 2}, {0, "x"}, {0, "x"}}, {{0, 0, 3}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 4}, {1, "SU(2)"}, {0, "x"}}, {{0, 0, 5}, {3, "G_2"}, {0, "x"}}, 
   {{0, 0, 6}, {4, "SO(8)"}, {0, "x"}}, {{0, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 1}, {0, "x"}, {0, "x"}}, {{0, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 3}, {0, "x"}, {0, "x"}}, {{1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 1}, {0, "x"}, {0, "x"}}, {{1, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 3}, {0, "x"}, {0, "x"}}, {{1, 1, 4}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 1, 5}, {3, "G_2"}, {0, "x"}}, {{1, 1, 6}, {4, "SO(8)"}, {0, "x"}}, 
   {{1, 2, 0}, {0, "x"}, {0, "x"}}, {{1, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 2}, {0, "x"}, {0, "x"}}, {{1, 2, 3}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 4}, {1, "SU(2)"}, {0, "x"}}, {{1, 2, 5}, {3, "G_2"}, {0, "x"}}, 
   {{1, 2, 6}, {4, "SO(8)"}, {0, "x"}}, {{1, 2, 7}, {5, "F_4"}, {0, "x"}}, 
   {{1, 3, 0}, {0, "x"}, {0, "x"}}, {{1, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 3, 2}, {0, "x"}, {0, "x"}}, {{1, 3, 3}, {0, "x"}, {0, "x"}}, 
   {{1, 3, 4}, {1, "SU(2)"}, {0, "x"}}, {{2, 3, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 3, 1}, {0, "x"}, {0, "x"}}, {{2, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{2, 3, 3}, {0, "x"}, {0, "x"}}, {{2, 3, 4}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 3, 5}, {3, "G_2"}, {0, "x"}}, {{2, 3, 6}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 3, 7}, {5, "F_4"}, {0, "x"}}, {{2, 4, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 4, 1}, {0, "x"}, {0, "x"}}, {{2, 4, 2}, {0, "x"}, {0, "x"}}, 
   {{2, 4, 3}, {0, "x"}, {0, "x"}}, {{2, 4, 4}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 4, 5}, {3, "G_2"}, {0, "x"}}, {{2, 4, 6}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 4, 7}, {5, "F_4"}, {0, "x"}}, {{2, 4, 8}, {5, "F_4"}, {0, "x"}}, 
   {{2, 5, 0}, {1, "SU(2)"}, {0, "x"}}, {{2, 5, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 5, 2}, {1, "SU(2)"}, {0, "x"}}, {{2, 5, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 5, 4}, {1, "SU(2)"}, {0, "x"}}, {{2, 5, 5}, {3, "G_2"}, {0, "x"}}, 
   {{3, 5, 0}, {1, "SU(2)"}, {0, "x"}}, {{3, 5, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 5, 2}, {1, "SU(2)"}, {0, "x"}}, {{3, 5, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 5, 4}, {1, "SU(2)"}, {0, "x"}}, {{3, 5, 5}, {3, "G_2"}, {0, "x"}}, 
   {{3, 5, 6}, {4, "SO(8)"}, {0, "x"}}, {{3, 5, 7}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 8}, {5, "F_4"}, {0, "x"}}, {{3, 6, 0}, {2, "SU(3)"}, {0, "x"}}, 
   {{3, 6, 1}, {2, "SU(3)"}, {0, "x"}}, {{3, 6, 2}, {2, "SU(3)"}, {0, "x"}}, 
   {{3, 6, 3}, {2, "SU(3)"}, {0, "x"}}, {{3, 6, 4}, {2, "SU(3)"}, {0, "x"}}, 
   {{3, 6, 5}, {3, "G_2"}, {0, "x"}}, {{3, 6, 6}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 6, 7}, {5, "F_4"}, {0, "x"}}, {{3, 6, 8}, {5, "F_4"}, {0, "x"}}, 
   {{3, 6, 9}, {6, "E_6"}, {0, "x"}}, {{3, 7, 1}, {3, "G_2"}, {0, "x"}}, 
   {{3, 7, 2}, {3, "G_2"}, {0, "x"}}, {{3, 7, 3}, {3, "G_2"}, {0, "x"}}, 
   {{3, 7, 4}, {3, "G_2"}, {0, "x"}}, {{3, 7, 5}, {3, "G_2"}, {0, "x"}}, 
   {{3, 7, 6}, {4, "SO(8)"}, {0, "x"}}, {{4, 7, 1}, {3, "G_2"}, {0, "x"}}, 
   {{4, 7, 2}, {3, "G_2"}, {0, "x"}}, {{4, 7, 3}, {3, "G_2"}, {0, "x"}}, 
   {{4, 7, 4}, {3, "G_2"}, {0, "x"}}, {{4, 7, 5}, {3, "G_2"}, {0, "x"}}, 
   {{4, 7, 6}, {4, "SO(8)"}, {0, "x"}}, {{4, 7, 7}, {5, "F_4"}, {0, "x"}}, 
   {{4, 7, 8}, {5, "F_4"}, {0, "x"}}, {{4, 7, 9}, {6, "E_6"}, {0, "x"}}, 
   {{4, 8, 2}, {4, "SO(8)"}, {0, "x"}}, {{4, 8, 3}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 8, 4}, {4, "SO(8)"}, {0, "x"}}, {{4, 8, 5}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 8, 6}, {4, "SO(8)"}, {0, "x"}}, {{4, 8, 7}, {5, "F_4"}, {0, "x"}}, 
   {{4, 8, 8}, {5, "F_4"}, {0, "x"}}, {{4, 8, 9}, {6, "E_6"}, {0, "x"}}, 
   {{4, 8, 10}, {7, "E_7"}, {0, "x"}}, {{4, 9, 3}, {5, "F_4"}, {0, "x"}}, 
   {{4, 9, 4}, {5, "F_4"}, {0, "x"}}, {{4, 9, 5}, {5, "F_4"}, {0, "x"}}, 
   {{4, 9, 6}, {5, "F_4"}, {0, "x"}}, {{4, 9, 7}, {5, "F_4"}, {0, "x"}}, 
   {{5, 9, 3}, {5, "F_4"}, {0, "x"}}, {{5, 9, 4}, {5, "F_4"}, {0, "x"}}, 
   {{5, 9, 5}, {5, "F_4"}, {0, "x"}}, {{5, 9, 6}, {5, "F_4"}, {0, "x"}}, 
   {{5, 9, 7}, {5, "F_4"}, {0, "x"}}, {{5, 9, 8}, {5, "F_4"}, {0, "x"}}, 
   {{5, 9, 9}, {6, "E_6"}, {0, "x"}}, {{5, 9, 10}, {7, "E_7"}, {0, "x"}}, 
   {{5, 10, 4}, {5, "F_4"}, {0, "x"}}, {{5, 10, 5}, {5, "F_4"}, {0, "x"}}, 
   {{5, 10, 6}, {5, "F_4"}, {0, "x"}}, {{5, 10, 7}, {5, "F_4"}, {0, "x"}}, 
   {{5, 10, 8}, {5, "F_4"}, {0, "x"}}, {{5, 10, 9}, {6, "E_6"}, {0, "x"}}, 
   {{5, 10, 10}, {7, "E_7"}, {0, "x"}}, {{5, 10, 11}, {7, "E_7"}, {0, "x"}}, 
   {{5, 11, 5}, {5, "F_4"}, {0, "x"}}, {{5, 11, 6}, {5, "F_4"}, {0, "x"}}, 
   {{5, 11, 7}, {5, "F_4"}, {0, "x"}}, {{5, 11, 8}, {5, "F_4"}, {0, "x"}}, 
   {{6, 11, 5}, {5, "F_4"}, {0, "x"}}, {{6, 11, 6}, {5, "F_4"}, {0, "x"}}, 
   {{6, 11, 7}, {5, "F_4"}, {0, "x"}}, {{6, 11, 8}, {5, "F_4"}, {0, "x"}}, 
   {{6, 11, 9}, {6, "E_6"}, {0, "x"}}, {{6, 11, 10}, {7, "E_7"}, {0, "x"}}, 
   {{6, 11, 11}, {7, "E_7"}, {0, "x"}}, {{6, 12, 6}, {6, "E_6"}, {0, "x"}}, 
   {{6, 12, 7}, {6, "E_6"}, {0, "x"}}, {{6, 12, 8}, {6, "E_6"}, {0, "x"}}, 
   {{6, 12, 9}, {6, "E_6"}, {0, "x"}}, {{6, 12, 10}, {7, "E_7"}, {0, "x"}}, 
   {{6, 12, 11}, {7, "E_7"}, {0, "x"}}, {{6, 12, 12}, {7, "E_7"}, {0, "x"}}, 
   {{7, 13, 7}, {7, "E_7"}, {0, "x"}}, {{7, 13, 8}, {7, "E_7"}, {0, "x"}}, 
   {{7, 13, 9}, {7, "E_7"}, {0, "x"}}, {{7, 13, 10}, {7, "E_7"}, {0, "x"}}, 
   {{7, 13, 11}, {7, "E_7"}, {0, "x"}}, {{7, 13, 12}, {7, "E_7"}, {0, "x"}}, 
   {{7, 14, 8}, {7, "E_7"}, {0, "x"}}, {{7, 14, 9}, {7, "E_7"}, {0, "x"}}, 
   {{7, 14, 10}, {7, "E_7"}, {0, "x"}}, {{7, 14, 11}, {7, "E_7"}, {0, "x"}}, 
   {{7, 14, 12}, {7, "E_7"}, {0, "x"}}, {{8, 15, 9}, {7, "E_7"}, {0, "x"}}, 
   {{8, 15, 10}, {7, "E_7"}, {0, "x"}}, {{8, 15, 11}, {7, "E_7"}, {0, "x"}}, 
   {{8, 15, 12}, {7, "E_7"}, {0, "x"}}, {{8, 16, 10}, {7, "E_7"}, {0, "x"}}, 
   {{8, 16, 11}, {7, "E_7"}, {0, "x"}}, {{8, 16, 12}, {7, "E_7"}, {0, "x"}}, 
   {{12, 24, 18}, {8, "E_8"}, {0, "x"}}}}, 
 {{{0, 1}, {1, 0}, {1, -1}, {0, -1}, {-1, 0}, {-1, 1}}, 
  {{{-6, -8, -5, 1}, {0, "x"}, {7, "E_7"}}, {{-6, -8, -4, 1}, {0, "x"}, 
    {7, "E_7"}}, {{-6, -8, -4, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -8, -3, 1}, {0, "x"}, {7, "E_7"}}, {{-6, -8, -1, 1}, {0, "x"}, 
    {7, "E_7"}}, {{-6, -8, 0, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -7, -5, 1}, {0, "x"}, {7, "E_7"}}, {{-6, -7, -4, 1}, {0, "x"}, 
    {7, "E_7"}}, {{-6, -7, -3, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -7, -2, 1}, {0, "x"}, {7, "E_7"}}, {{-6, -7, 0, 1}, {0, "x"}, 
    {7, "E_7"}}, {{-6, -5, -5, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -5, -3, 1}, {0, "x"}, {6, "E_6"}}, {{-6, -5, -2, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -5, -1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -5, 0, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -5, 2, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -4, -4, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -4, -4, 2}, {0, "x"}, {7, "E_7"}}, {{-6, -4, -2, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -4, -1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -4, 0, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -4, 0, 2}, {0, "x"}, 
    {4, "SO(8)"}}, {{-6, -4, 3, 1}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{-6, -4, 4, 2}, {3, "G_2"}, {4, "SO(8)"}}, {{-6, -3, -3, 1}, {0, "x"}, 
    {6, "E_6"}}, {{-6, -3, -3, 2}, {0, "x"}, {6, "E_6"}}, 
   {{-6, -3, -3, 3}, {0, "x"}, {6, "E_6"}}, {{-6, -3, -1, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -3, 0, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -3, 2, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -3, 4, 1}, {3, "G_2"}, 
    {5, "F_4"}}, {{-6, -3, 5, 2}, {5, "F_4"}, {3, "G_2"}}, 
   {{-6, -3, 6, 3}, {5, "F_4"}, {2, "SU(3)"}}, {{-6, -2, -2, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -2, -2, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -2, -2, 3}, {0, "x"}, {5, "F_4"}}, {{-6, -2, -2, 4}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -2, 0, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -2, 2, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -2, 3, 1}, {1, "SU(2)"}, 
    {5, "F_4"}}, {{-6, -2, 5, 1}, {5, "F_4"}, {5, "F_4"}}, 
   {{-6, -2, 6, 2}, {5, "F_4"}, {3, "G_2"}}, {{-6, -2, 7, 3}, {7, "E_7"}, 
    {1, "SU(2)"}}, {{-6, -2, 8, 4}, {7, "E_7"}, {0, "x"}}, 
   {{-6, -1, -1, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -1, -1, 2}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -1, -1, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -1, -1, 4}, {0, "x"}, {5, "F_4"}}, {{-6, -1, -1, 5}, {1, "SU(2)"}, 
    {5, "F_4"}}, {{-6, -1, 2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -1, 3, 1}, {1, "SU(2)"}, {5, "F_4"}}, {{-6, -1, 4, 1}, {3, "G_2"}, 
    {5, "F_4"}}, {{-6, -1, 6, 1}, {5, "F_4"}, {5, "F_4"}}, 
   {{-6, -1, 7, 2}, {7, "E_7"}, {3, "G_2"}}, {{-6, -1, 8, 3}, {7, "E_7"}, 
    {1, "SU(2)"}}, {{-6, 0, 0, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, 0, 0, 2}, {0, "x"}, {4, "SO(8)"}}, {{-6, 0, 0, 3}, {0, "x"}, 
    {4, "SO(8)"}}, {{-6, 0, 0, 4}, {1, "SU(2)"}, {4, "SO(8)"}}, 
   {{-6, 0, 0, 5}, {3, "G_2"}, {4, "SO(8)"}}, {{-6, 0, 0, 6}, {4, "SO(8)"}, 
    {4, "SO(8)"}}, {{-6, 0, 2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, 0, 3, 1}, {1, "SU(2)"}, {5, "F_4"}}, {{-6, 0, 4, 1}, {3, "G_2"}, 
    {5, "F_4"}}, {{-6, 0, 4, 2}, {3, "G_2"}, {3, "G_2"}}, 
   {{-6, 0, 5, 1}, {5, "F_4"}, {5, "F_4"}}, {{-6, 0, 7, 1}, {7, "E_7"}, 
    {5, "F_4"}}, {{-6, 0, 8, 2}, {7, "E_7"}, {3, "G_2"}}, 
   {{-5, -8, -4, 1}, {0, "x"}, {7, "E_7"}}, {{-5, -8, -2, 1}, {0, "x"}, 
    {7, "E_7"}}, {{-5, -8, -1, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-5, -8, -1, 2}, {0, "x"}, {7, "E_7"}}, {{-5, -8, 0, 2}, {0, "x"}, 
    {7, "E_7"}}, {{-5, -8, 0, 3}, {0, "x"}, {7, "E_7"}}, 
   {{-5, -7, -4, 1}, {0, "x"}, {7, "E_7"}}, {{-5, -7, -3, 1}, {0, "x"}, 
    {7, "E_7"}}, {{-5, -7, -1, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-5, -7, 0, 1}, {0, "x"}, {7, "E_7"}}, {{-5, -7, 0, 2}, {0, "x"}, 
    {7, "E_7"}}, {{-5, -6, -4, 1}, {0, "x"}, {6, "E_6"}}, 
   {{-5, -6, -3, 1}, {0, "x"}, {5, "F_4"}}, {{-5, -6, -2, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-5, -6, 0, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -4, -4, 1}, {0, "x"}, {6, "E_6"}}, {{-5, -4, -2, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-5, -4, -1, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -4, 0, 1}, {0, "x"}, {4, "SO(8)"}}, {{-5, -4, 2, 1}, {0, "x"}, 
    {4, "SO(8)"}}, {{-5, -4, 3, 1}, {1, "SU(2)"}, {4, "SO(8)"}}, 
   {{-5, -3, -4, 1}, {0, "x"}, {6, "E_6"}}, {{-5, -3, -3, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-5, -3, -3, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -3, -1, 1}, {0, "x"}, {4, "SO(8)"}}, {{-5, -3, 0, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-5, -3, 3, 1}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{-5, -3, 4, 1}, {3, "G_2"}, {3, "G_2"}}, {{-5, -3, 4, 2}, {3, "G_2"}, 
    {2, "SU(3)"}}, {{-5, -3, 5, 2}, {5, "F_4"}, {2, "SU(3)"}}, 
   {{-5, -2, -3, 1}, {0, "x"}, {5, "F_4"}}, {{-5, -2, -3, 2}, {0, "x"}, 
    {5, "F_4"}}, {{-5, -2, -2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -2, -2, 2}, {0, "x"}, {5, "F_4"}}, {{-5, -2, -2, 3}, {0, "x"}, 
    {5, "F_4"}}, {{-5, -2, 0, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-5, -2, 2, 1}, {0, "x"}, {3, "G_2"}}, {{-5, -2, 4, 1}, {3, "G_2"}, 
    {3, "G_2"}}, {{-5, -2, 5, 1}, {5, "F_4"}, {3, "G_2"}}, 
   {{-5, -2, 5, 2}, {5, "F_4"}, {1, "SU(2)"}}, {{-5, -2, 6, 2}, {5, "F_4"}, 
    {1, "SU(2)"}}, {{-5, -2, 6, 3}, {5, "F_4"}, {0, "x"}}, 
   {{-5, -2, 7, 3}, {7, "E_7"}, {0, "x"}}, {{-5, -1, -2, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-5, -1, -2, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -1, -2, 3}, {0, "x"}, {5, "F_4"}}, {{-5, -1, -1, 1}, {0, "x"}, 
    {4, "SO(8)"}}, {{-5, -1, -1, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -1, -1, 3}, {0, "x"}, {4, "SO(8)"}}, {{-5, -1, -1, 4}, {0, "x"}, 
    {4, "SO(8)"}}, {{-5, -1, 2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-5, -1, 3, 1}, {1, "SU(2)"}, {3, "G_2"}}, {{-5, -1, 5, 1}, {5, "F_4"}, 
    {3, "G_2"}}, {{-5, -1, 6, 1}, {5, "F_4"}, {3, "G_2"}}, 
   {{-5, -1, 6, 2}, {5, "F_4"}, {1, "SU(2)"}}, {{-5, -1, 7, 2}, {7, "E_7"}, 
    {1, "SU(2)"}}, {{-5, -1, 7, 3}, {7, "E_7"}, {0, "x"}}, 
   {{-5, -1, 8, 3}, {7, "E_7"}, {0, "x"}}, {{-5, -1, 8, 4}, {7, "E_7"}, 
    {0, "x"}}, {{-5, 0, -1, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, 0, -1, 2}, {0, "x"}, {4, "SO(8)"}}, {{-5, 0, -1, 3}, {0, "x"}, 
    {4, "SO(8)"}}, {{-5, 0, -1, 4}, {1, "SU(2)"}, {4, "SO(8)"}}, 
   {{-5, 0, 0, 1}, {0, "x"}, {3, "G_2"}}, {{-5, 0, 0, 2}, {0, "x"}, 
    {3, "G_2"}}, {{-5, 0, 0, 3}, {0, "x"}, {3, "G_2"}}, 
   {{-5, 0, 0, 4}, {1, "SU(2)"}, {3, "G_2"}}, {{-5, 0, 0, 5}, {3, "G_2"}, 
    {3, "G_2"}}, {{-5, 0, 2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-5, 0, 3, 1}, {1, "SU(2)"}, {3, "G_2"}}, {{-5, 0, 4, 1}, {3, "G_2"}, 
    {3, "G_2"}}, {{-5, 0, 6, 1}, {5, "F_4"}, {3, "G_2"}}, 
   {{-5, 0, 7, 1}, {7, "E_7"}, {3, "G_2"}}, {{-5, 0, 7, 2}, {7, "E_7"}, 
    {1, "SU(2)"}}, {{-5, 0, 8, 2}, {7, "E_7"}, {1, "SU(2)"}}, 
   {{-5, 0, 8, 3}, {7, "E_7"}, {0, "x"}}, {{-5, 1, 0, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-5, 1, 0, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-5, 1, 0, 3}, {1, "SU(2)"}, {3, "G_2"}}, {{-5, 1, 0, 4}, {3, "G_2"}, 
    {3, "G_2"}}, {{-5, 1, 3, 1}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{-5, 1, 4, 1}, {3, "G_2"}, {3, "G_2"}}, {{-5, 1, 7, 1}, {7, "E_7"}, 
    {3, "G_2"}}, {{-5, 1, 8, 2}, {7, "E_7"}, {1, "SU(2)"}}, 
   {{-4, -8, -3, 1}, {0, "x"}, {7, "E_7"}}, {{-4, -8, -2, 1}, {0, "x"}, 
    {7, "E_7"}}, {{-4, -8, -2, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-4, -8, -1, 1}, {0, "x"}, {7, "E_7"}}, {{-4, -8, -1, 2}, {0, "x"}, 
    {7, "E_7"}}, {{-4, -8, -1, 3}, {0, "x"}, {7, "E_7"}}, 
   {{-4, -8, 0, 2}, {0, "x"}, {7, "E_7"}}, {{-4, -8, 0, 3}, {0, "x"}, 
    {7, "E_7"}}, {{-4, -8, 0, 4}, {0, "x"}, {7, "E_7"}}, 
   {{-4, -7, -2, 1}, {0, "x"}, {7, "E_7"}}, {{-4, -7, -1, 1}, {0, "x"}, 
    {7, "E_7"}}, {{-4, -7, -1, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-4, -7, 0, 1}, {0, "x"}, {7, "E_7"}}, {{-4, -7, 0, 2}, {0, "x"}, 
    {7, "E_7"}}, {{-4, -7, 0, 3}, {0, "x"}, {7, "E_7"}}, 
   {{-4, -6, -3, 1}, {0, "x"}, {5, "F_4"}}, {{-4, -6, -1, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-4, -6, 0, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -6, 0, 2}, {0, "x"}, {5, "F_4"}}, {{-4, -5, -3, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-4, -5, -2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -5, 0, 1}, {0, "x"}, {5, "F_4"}}, {{-4, -3, -3, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-4, -3, -1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -3, 0, 1}, {0, "x"}, {2, "SU(3)"}}, {{-4, -3, 2, 1}, {0, "x"}, 
    {2, "SU(3)"}}, {{-4, -3, 3, 1}, {1, "SU(2)"}, {2, "SU(3)"}}, 
   {{-4, -3, 4, 1}, {3, "G_2"}, {2, "SU(3)"}}, {{-4, -2, -3, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-4, -2, -2, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -2, -2, 2}, {0, "x"}, {4, "SO(8)"}}, {{-4, -2, 0, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-4, -2, 3, 1}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-4, -2, 4, 1}, {3, "G_2"}, {1, "SU(2)"}}, {{-4, -2, 4, 2}, {3, "G_2"}, 
    {0, "x"}}, {{-4, -2, 5, 1}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{-4, -2, 5, 2}, {5, "F_4"}, {0, "x"}}, {{-4, -2, 6, 2}, {5, "F_4"}, 
    {0, "x"}}, {{-4, -1, -3, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -1, -2, 1}, {0, "x"}, {4, "SO(8)"}}, {{-4, -1, -2, 2}, {0, "x"}, 
    {4, "SO(8)"}}, {{-4, -1, -1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -1, -1, 2}, {0, "x"}, {3, "G_2"}}, {{-4, -1, -1, 3}, {0, "x"}, 
    {3, "G_2"}}, {{-4, -1, 2, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -1, 4, 1}, {3, "G_2"}, {1, "SU(2)"}}, {{-4, -1, 5, 1}, {5, "F_4"}, 
    {1, "SU(2)"}}, {{-4, -1, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{-4, -1, 6, 1}, {5, "F_4"}, {1, "SU(2)"}}, {{-4, -1, 6, 2}, {5, "F_4"}, 
    {0, "x"}}, {{-4, -1, 6, 3}, {5, "F_4"}, {0, "x"}}, 
   {{-4, -1, 7, 2}, {7, "E_7"}, {0, "x"}}, {{-4, -1, 7, 3}, {7, "E_7"}, 
    {0, "x"}}, {{-4, -1, 8, 3}, {7, "E_7"}, {0, "x"}}, 
   {{-4, 0, -2, 1}, {0, "x"}, {4, "SO(8)"}}, {{-4, 0, -2, 2}, {0, "x"}, 
    {4, "SO(8)"}}, {{-4, 0, -1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-4, 0, -1, 2}, {0, "x"}, {3, "G_2"}}, {{-4, 0, -1, 3}, {0, "x"}, 
    {3, "G_2"}}, {{-4, 0, 0, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, 0, 0, 2}, {0, "x"}, {1, "SU(2)"}}, {{-4, 0, 0, 3}, {0, "x"}, 
    {1, "SU(2)"}}, {{-4, 0, 0, 4}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-4, 0, 2, 1}, {0, "x"}, {1, "SU(2)"}}, {{-4, 0, 3, 1}, {1, "SU(2)"}, 
    {1, "SU(2)"}}, {{-4, 0, 5, 1}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{-4, 0, 6, 1}, {5, "F_4"}, {1, "SU(2)"}}, {{-4, 0, 6, 2}, {5, "F_4"}, 
    {0, "x"}}, {{-4, 0, 7, 1}, {7, "E_7"}, {1, "SU(2)"}}, 
   {{-4, 0, 7, 2}, {7, "E_7"}, {0, "x"}}, {{-4, 0, 7, 3}, {7, "E_7"}, 
    {0, "x"}}, {{-4, 0, 8, 2}, {7, "E_7"}, {0, "x"}}, 
   {{-4, 0, 8, 3}, {7, "E_7"}, {0, "x"}}, {{-4, 1, -1, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-4, 1, -1, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, 1, -1, 3}, {1, "SU(2)"}, {3, "G_2"}}, {{-4, 1, 0, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-4, 1, 0, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, 1, 0, 3}, {1, "SU(2)"}, {1, "SU(2)"}}, {{-4, 1, 3, 1}, {1, "SU(2)"}, 
    {1, "SU(2)"}}, {{-4, 1, 6, 1}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{-4, 1, 7, 1}, {7, "E_7"}, {1, "SU(2)"}}, {{-4, 1, 7, 2}, {7, "E_7"}, 
    {0, "x"}}, {{-4, 1, 8, 2}, {7, "E_7"}, {0, "x"}}, 
   {{-4, 1, 8, 3}, {7, "E_7"}, {0, "x"}}, {{-4, 2, 0, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-4, 2, 0, 2}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-4, 2, 2, 1}, {0, "x"}, {1, "SU(2)"}}, {{-4, 2, 4, 1}, {3, "G_2"}, 
    {1, "SU(2)"}}, {{-4, 2, 7, 1}, {7, "E_7"}, {1, "SU(2)"}}, 
   {{-4, 2, 8, 2}, {7, "E_7"}, {0, "x"}}, {{-3, -8, -2, 1}, {0, "x"}, 
    {7, "E_7"}}, {{-3, -8, -1, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-3, -8, -1, 2}, {0, "x"}, {7, "E_7"}}, {{-3, -8, 0, 2}, {0, "x"}, 
    {7, "E_7"}}, {{-3, -8, 0, 3}, {0, "x"}, {7, "E_7"}}, 
   {{-3, -7, -2, 1}, {0, "x"}, {7, "E_7"}}, {{-3, -7, -1, 1}, {0, "x"}, 
    {7, "E_7"}}, {{-3, -7, -1, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-3, -7, 0, 1}, {0, "x"}, {7, "E_7"}}, {{-3, -7, 0, 2}, {0, "x"}, 
    {7, "E_7"}}, {{-3, -7, 0, 3}, {0, "x"}, {7, "E_7"}}, 
   {{-3, -6, -2, 1}, {0, "x"}, {5, "F_4"}}, {{-3, -6, -1, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-3, -6, -1, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-3, -6, 0, 1}, {0, "x"}, {5, "F_4"}}, {{-3, -6, 0, 2}, {0, "x"}, 
    {5, "F_4"}}, {{-3, -6, 0, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-3, -5, -1, 1}, {0, "x"}, {5, "F_4"}}, {{-3, -5, 0, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-3, -5, 0, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-3, -4, -2, 1}, {0, "x"}, {3, "G_2"}}, {{-3, -4, 0, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-3, -2, -2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -2, 0, 1}, {0, "x"}, {0, "x"}}, {{-3, -2, 2, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, -2, 3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{-3, -2, 4, 1}, {3, "G_2"}, {0, "x"}}, {{-3, -2, 5, 1}, {5, "F_4"}, 
    {0, "x"}}, {{-3, -1, -2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -1, -1, 1}, {0, "x"}, {1, "SU(2)"}}, {{-3, -1, -1, 2}, {0, "x"}, 
    {1, "SU(2)"}}, {{-3, -1, 3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{-3, -1, 4, 1}, {3, "G_2"}, {0, "x"}}, {{-3, -1, 4, 2}, {3, "G_2"}, 
    {0, "x"}}, {{-3, -1, 5, 1}, {5, "F_4"}, {0, "x"}}, 
   {{-3, -1, 5, 2}, {5, "F_4"}, {0, "x"}}, {{-3, -1, 6, 1}, {5, "F_4"}, 
    {0, "x"}}, {{-3, -1, 6, 2}, {5, "F_4"}, {0, "x"}}, 
   {{-3, -1, 7, 2}, {7, "E_7"}, {0, "x"}}, {{-3, 0, -2, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-3, 0, -1, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, 0, -1, 2}, {0, "x"}, {1, "SU(2)"}}, {{-3, 0, 0, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, 0, 0, 2}, {0, "x"}, {0, "x"}}, 
   {{-3, 0, 0, 3}, {0, "x"}, {0, "x"}}, {{-3, 0, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-3, 0, 4, 1}, {3, "G_2"}, {0, "x"}}, {{-3, 0, 5, 1}, {5, "F_4"}, 
    {0, "x"}}, {{-3, 0, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{-3, 0, 6, 1}, {5, "F_4"}, {0, "x"}}, {{-3, 0, 6, 2}, {5, "F_4"}, 
    {0, "x"}}, {{-3, 0, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{-3, 0, 7, 2}, {7, "E_7"}, {0, "x"}}, {{-3, 0, 8, 2}, {7, "E_7"}, 
    {0, "x"}}, {{-3, 1, -2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, 1, -1, 1}, {0, "x"}, {1, "SU(2)"}}, {{-3, 1, -1, 2}, {0, "x"}, 
    {1, "SU(2)"}}, {{-3, 1, 0, 1}, {0, "x"}, {0, "x"}}, 
   {{-3, 1, 0, 2}, {0, "x"}, {0, "x"}}, {{-3, 1, 5, 1}, {5, "F_4"}, 
    {0, "x"}}, {{-3, 1, 6, 1}, {5, "F_4"}, {0, "x"}}, 
   {{-3, 1, 6, 2}, {5, "F_4"}, {0, "x"}}, {{-3, 1, 7, 1}, {7, "E_7"}, 
    {0, "x"}}, {{-3, 1, 7, 2}, {7, "E_7"}, {0, "x"}}, 
   {{-3, 1, 8, 2}, {7, "E_7"}, {0, "x"}}, {{-3, 2, -1, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-3, 2, -1, 2}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-3, 2, 0, 1}, {0, "x"}, {0, "x"}}, {{-3, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-3, 2, 6, 1}, {5, "F_4"}, {0, "x"}}, {{-3, 2, 7, 1}, {7, "E_7"}, 
    {0, "x"}}, {{-3, 2, 7, 2}, {7, "E_7"}, {0, "x"}}, 
   {{-3, 2, 8, 2}, {7, "E_7"}, {0, "x"}}, {{-3, 3, 2, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{-3, 3, 3, 1}, {2, "SU(3)"}, {0, "x"}}, 
   {{-3, 3, 7, 1}, {7, "E_7"}, {0, "x"}}, {{-3, 3, 8, 2}, {7, "E_7"}, 
    {0, "x"}}, {{-2, -8, -1, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-2, -8, 0, 2}, {0, "x"}, {7, "E_7"}}, {{-2, -7, -1, 1}, {0, "x"}, 
    {7, "E_7"}}, {{-2, -7, 0, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-2, -7, 0, 2}, {0, "x"}, {7, "E_7"}}, {{-2, -6, -1, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-2, -6, 0, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-2, -6, 0, 2}, {0, "x"}, {5, "F_4"}}, {{-2, -5, -1, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-2, -5, 0, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-2, -5, 0, 2}, {0, "x"}, {5, "F_4"}}, {{-2, -4, -1, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-2, -4, 0, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-2, -4, 0, 2}, {0, "x"}, {3, "G_2"}}, {{-2, -4, 3, 1}, {1, "SU(2)"}, 
    {3, "G_2"}}, {{-2, -3, 0, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -1, -1, 1}, {0, "x"}, {0, "x"}}, {{-2, -1, 2, 1}, {0, "x"}, 
    {0, "x"}}, {{-2, -1, 3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{-2, -1, 4, 1}, {3, "G_2"}, {0, "x"}}, {{-2, -1, 5, 1}, {5, "F_4"}, 
    {0, "x"}}, {{-2, -1, 6, 1}, {5, "F_4"}, {0, "x"}}, 
   {{-2, 0, -1, 1}, {0, "x"}, {0, "x"}}, {{-2, 0, 0, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, 0, 0, 2}, {0, "x"}, {0, "x"}}, {{-2, 0, 3, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{-2, 0, 4, 1}, {3, "G_2"}, {0, "x"}}, 
   {{-2, 0, 5, 1}, {5, "F_4"}, {0, "x"}}, {{-2, 0, 6, 1}, {5, "F_4"}, 
    {0, "x"}}, {{-2, 0, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{-2, 1, -1, 1}, {0, "x"}, {0, "x"}}, {{-2, 1, 0, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, 1, 4, 1}, {3, "G_2"}, {0, "x"}}, {{-2, 1, 5, 1}, {5, "F_4"}, 
    {0, "x"}}, {{-2, 1, 6, 1}, {5, "F_4"}, {0, "x"}}, 
   {{-2, 1, 7, 1}, {7, "E_7"}, {0, "x"}}, {{-2, 2, -1, 1}, {0, "x"}, 
    {0, "x"}}, {{-2, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, 2, 5, 1}, {5, "F_4"}, {0, "x"}}, {{-2, 2, 6, 1}, {5, "F_4"}, 
    {0, "x"}}, {{-2, 2, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{-2, 3, -1, 1}, {1, "SU(2)"}, {0, "x"}}, {{-2, 3, 2, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{-2, 3, 3, 1}, {2, "SU(3)"}, {0, "x"}}, 
   {{-2, 3, 6, 1}, {5, "F_4"}, {0, "x"}}, {{-2, 3, 7, 1}, {7, "E_7"}, 
    {0, "x"}}, {{-2, 4, 2, 1}, {3, "G_2"}, {0, "x"}}, 
   {{-2, 4, 3, 1}, {3, "G_2"}, {0, "x"}}, {{-2, 4, 4, 1}, {4, "SO(8)"}, 
    {0, "x"}}, {{-2, 4, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{-1, -7, 0, 1}, {0, "x"}, {7, "E_7"}}, {{-1, -6, 0, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-1, -5, 0, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-1, -4, 0, 1}, {0, "x"}, {3, "G_2"}}, {{-1, -4, 3, 1}, {1, "SU(2)"}, 
    {3, "G_2"}}, {{-1, -3, 0, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-1, -3, 3, 1}, {1, "SU(2)"}, {1, "SU(2)"}}, {{-1, -2, 0, 1}, {0, "x"}, 
    {0, "x"}}, {{-1, 0, 0, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 0, 0}, {0, "x"}, {0, "x"}}, {{0, 0, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 2, 0}, {0, "x"}, {0, "x"}}, {{0, 0, 3, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{0, 0, 4, 0}, {3, "G_2"}, {0, "x"}}, 
   {{0, 0, 5, 0}, {5, "F_4"}, {0, "x"}}, {{0, 0, 6, 0}, {5, "F_4"}, 
    {0, "x"}}, {{0, 1, -5, 0}, {0, "x"}, {5, "F_4"}}, 
   {{0, 1, -4, 0}, {0, "x"}, {3, "G_2"}}, {{0, 1, -3, 0}, {0, "x"}, 
    {1, "SU(2)"}}, {{0, 1, -2, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, -1, 0}, {0, "x"}, {0, "x"}}, {{0, 1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 2, 0}, {0, "x"}, {0, "x"}}, {{0, 1, 3, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{0, 1, 4, 0}, {3, "G_2"}, {0, "x"}}, 
   {{0, 1, 5, 0}, {5, "F_4"}, {0, "x"}}, {{0, 1, 6, 0}, {5, "F_4"}, 
    {0, "x"}}, {{0, 2, -4, 0}, {0, "x"}, {3, "G_2"}}, 
   {{0, 2, -3, 0}, {0, "x"}, {1, "SU(2)"}}, {{0, 2, -2, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 2, 2, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 2, 3, 0}, {1, "SU(2)"}, {0, "x"}}, {{0, 2, 4, 0}, {3, "G_2"}, 
    {0, "x"}}, {{0, 2, 5, 0}, {5, "F_4"}, {0, "x"}}, 
   {{0, 2, 6, 0}, {5, "F_4"}, {0, "x"}}, {{0, 3, -3, 0}, {1, "SU(2)"}, 
    {1, "SU(2)"}}, {{0, 3, 3, 0}, {2, "SU(3)"}, {0, "x"}}, 
   {{0, 3, 4, 0}, {3, "G_2"}, {0, "x"}}, {{0, 3, 5, 0}, {5, "F_4"}, 
    {0, "x"}}, {{0, 3, 6, 0}, {5, "F_4"}, {0, "x"}}, 
   {{0, 4, 4, 0}, {4, "SO(8)"}, {0, "x"}}, {{0, 4, 5, 0}, {5, "F_4"}, 
    {0, "x"}}, {{0, 4, 6, 0}, {5, "F_4"}, {0, "x"}}, 
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    {0, "x"}}, {{0, 6, 6, 0}, {6, "E_6"}, {0, "x"}}, 
   {{1, -5, -6, 0}, {0, "x"}, {5, "F_4"}}, {{1, -5, -5, 0}, {0, "x"}, 
    {5, "F_4"}}, {{1, -5, -4, 0}, {0, "x"}, {5, "F_4"}}, 
   {{1, -5, -3, 0}, {0, "x"}, {5, "F_4"}}, {{1, -5, -2, 0}, {0, "x"}, 
    {5, "F_4"}}, {{1, -5, -1, 0}, {0, "x"}, {5, "F_4"}}, 
   {{1, -4, -6, 0}, {0, "x"}, {5, "F_4"}}, {{1, -4, -5, 0}, {0, "x"}, 
    {5, "F_4"}}, {{1, -4, -4, 0}, {0, "x"}, {4, "SO(8)"}}, 
   {{1, -4, -3, 0}, {0, "x"}, {3, "G_2"}}, {{1, -4, -2, 0}, {0, "x"}, 
    {3, "G_2"}}, {{1, -4, -1, 0}, {0, "x"}, {3, "G_2"}}, 
   {{1, -4, 1, 0}, {0, "x"}, {3, "G_2"}}, {{1, -3, -6, 0}, {0, "x"}, 
    {5, "F_4"}}, {{1, -3, -5, 0}, {0, "x"}, {5, "F_4"}}, 
   {{1, -3, -4, 0}, {0, "x"}, {3, "G_2"}}, {{1, -3, -3, 0}, {0, "x"}, 
    {2, "SU(3)"}}, {{1, -3, -2, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, -3, -1, 0}, {0, "x"}, {1, "SU(2)"}}, {{1, -3, 1, 0}, {0, "x"}, 
    {1, "SU(2)"}}, {{1, -3, 2, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, -2, -6, 0}, {0, "x"}, {5, "F_4"}}, {{1, -2, -5, 0}, {0, "x"}, 
    {5, "F_4"}}, {{1, -2, -4, 0}, {0, "x"}, {3, "G_2"}}, 
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    {0, "x"}}, {{1, -2, -1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, -2, 1, 0}, {0, "x"}, {0, "x"}}, {{1, -2, 2, 0}, {0, "x"}, {0, "x"}}, 
   {{1, -2, 3, 0}, {1, "SU(2)"}, {0, "x"}}, {{1, -1, -6, 0}, {0, "x"}, 
    {5, "F_4"}}, {{1, -1, -5, 0}, {0, "x"}, {5, "F_4"}}, 
   {{1, -1, -4, 0}, {0, "x"}, {3, "G_2"}}, {{1, -1, -3, 0}, {0, "x"}, 
    {1, "SU(2)"}}, {{1, -1, -2, 0}, {0, "x"}, {0, "x"}}, 
   {{1, -1, -1, 0}, {0, "x"}, {0, "x"}}, {{1, -1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, -1, 2, 0}, {0, "x"}, {0, "x"}}, {{1, -1, 3, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{1, -1, 4, 0}, {3, "G_2"}, {0, "x"}}, 
   {{1, 0, -6, 0}, {0, "x"}, {5, "F_4"}}, {{1, 0, -5, 0}, {0, "x"}, 
    {5, "F_4"}}, {{1, 0, -4, 0}, {0, "x"}, {3, "G_2"}}, 
   {{1, 0, -3, 0}, {0, "x"}, {1, "SU(2)"}}, {{1, 0, -2, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 0, -1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 0, 1, 0}, {0, "x"}, {0, "x"}}, {{1, 0, 2, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 0, 3, 0}, {1, "SU(2)"}, {0, "x"}}, {{1, 0, 4, 0}, {3, "G_2"}, 
    {0, "x"}}, {{1, 0, 5, 0}, {5, "F_4"}, {0, "x"}}, 
   {{1, 1, -5, 0}, {0, "x"}, {5, "F_4"}}, {{1, 1, -4, 0}, {0, "x"}, 
    {3, "G_2"}}, {{1, 1, -3, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, 1, -2, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 2, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 3, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{1, 1, 4, 0}, {3, "G_2"}, {0, "x"}}, 
   {{1, 1, 5, 0}, {5, "F_4"}, {0, "x"}}, {{1, 1, 6, 0}, {5, "F_4"}, 
    {0, "x"}}, {{1, 2, -4, 0}, {0, "x"}, {3, "G_2"}}, 
   {{1, 2, -3, 0}, {0, "x"}, {1, "SU(2)"}}, {{1, 2, -2, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 2, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 2, 0}, {0, "x"}, {0, "x"}}, {{1, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 3, 0}, {1, "SU(2)"}, {0, "x"}}, {{1, 2, 4, 0}, {3, "G_2"}, 
    {0, "x"}}, {{1, 2, 5, 0}, {5, "F_4"}, {0, "x"}}, 
   {{1, 2, 5, 1}, {5, "F_4"}, {0, "x"}}, {{1, 2, 6, 0}, {5, "F_4"}, 
    {0, "x"}}, {{1, 2, 6, 1}, {5, "F_4"}, {0, "x"}}, 
   {{1, 2, 7, 1}, {7, "E_7"}, {0, "x"}}, {{1, 3, -3, 0}, {1, "SU(2)"}, 
    {1, "SU(2)"}}, {{1, 3, -2, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 3, 1, 0}, {1, "SU(2)"}, {0, "x"}}, {{1, 3, 2, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{1, 3, 3, 0}, {2, "SU(3)"}, {0, "x"}}, 
   {{1, 3, 3, 1}, {2, "SU(3)"}, {0, "x"}}, {{1, 3, 4, 0}, {3, "G_2"}, 
    {0, "x"}}, {{1, 3, 5, 0}, {5, "F_4"}, {0, "x"}}, 
   {{1, 3, 6, 0}, {5, "F_4"}, {0, "x"}}, {{1, 3, 6, 1}, {5, "F_4"}, 
    {0, "x"}}, {{1, 3, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{1, 4, -2, 0}, {3, "G_2"}, {0, "x"}}, {{1, 4, 1, 0}, {3, "G_2"}, 
    {0, "x"}}, {{1, 4, 2, 0}, {3, "G_2"}, {0, "x"}}, 
   {{1, 4, 3, 0}, {3, "G_2"}, {0, "x"}}, {{1, 4, 4, 0}, {4, "SO(8)"}, 
    {0, "x"}}, {{1, 4, 4, 1}, {4, "SO(8)"}, {0, "x"}}, 
   {{1, 4, 5, 0}, {5, "F_4"}, {0, "x"}}, {{1, 4, 6, 0}, {5, "F_4"}, 
    {0, "x"}}, {{1, 4, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{1, 5, 1, 0}, {5, "F_4"}, {0, "x"}}, {{1, 5, 2, 0}, {5, "F_4"}, 
    {0, "x"}}, {{1, 5, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{1, 5, 4, 0}, {5, "F_4"}, {0, "x"}}, {{1, 5, 5, 0}, {5, "F_4"}, 
    {0, "x"}}, {{1, 5, 5, 1}, {5, "F_4"}, {0, "x"}}, 
   {{1, 5, 6, 0}, {5, "F_4"}, {0, "x"}}, {{1, 6, 1, 0}, {5, "F_4"}, 
    {0, "x"}}, {{1, 6, 2, 0}, {5, "F_4"}, {0, "x"}}, 
   {{1, 6, 3, 0}, {5, "F_4"}, {0, "x"}}, {{1, 6, 4, 0}, {5, "F_4"}, 
    {0, "x"}}, {{1, 6, 5, 0}, {5, "F_4"}, {0, "x"}}, 
   {{1, 6, 6, 0}, {6, "E_6"}, {0, "x"}}, {{1, 6, 6, 1}, {6, "E_6"}, 
    {0, "x"}}, {{1, 7, 1, 0}, {7, "E_7"}, {0, "x"}}, 
   {{1, 7, 2, 0}, {7, "E_7"}, {0, "x"}}, {{1, 7, 3, 0}, {7, "E_7"}, 
    {0, "x"}}, {{1, 7, 4, 0}, {7, "E_7"}, {0, "x"}}, 
   {{1, 7, 5, 0}, {7, "E_7"}, {0, "x"}}, {{1, 7, 6, 0}, {7, "E_7"}, 
    {0, "x"}}, {{1, 7, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{2, -4, -6, 0}, {0, "x"}, {5, "F_4"}}, {{2, -4, -5, 0}, {0, "x"}, 
    {5, "F_4"}}, {{2, -4, -4, 0}, {0, "x"}, {4, "SO(8)"}}, 
   {{2, -4, -3, 0}, {0, "x"}, {3, "G_2"}}, {{2, -4, -2, 0}, {0, "x"}, 
    {3, "G_2"}}, {{2, -3, -6, 0}, {0, "x"}, {5, "F_4"}}, 
   {{2, -3, -5, 0}, {0, "x"}, {5, "F_4"}}, {{2, -3, -4, 0}, {0, "x"}, 
    {3, "G_2"}}, {{2, -3, -3, 0}, {0, "x"}, {2, "SU(3)"}}, 
   {{2, -3, -2, 0}, {0, "x"}, {1, "SU(2)"}}, {{2, -2, -6, 0}, {0, "x"}, 
    {5, "F_4"}}, {{2, -2, -5, 0}, {0, "x"}, {5, "F_4"}}, 
   {{2, -2, -4, 0}, {0, "x"}, {3, "G_2"}}, {{2, -2, -3, 0}, {0, "x"}, 
    {1, "SU(2)"}}, {{2, -2, -2, 0}, {0, "x"}, {0, "x"}}, 
   {{2, -2, 2, 0}, {1, "SU(2)"}, {0, "x"}}, {{2, -1, -6, 0}, {0, "x"}, 
    {5, "F_4"}}, {{2, -1, -5, 0}, {0, "x"}, {5, "F_4"}}, 
   {{2, -1, -4, 0}, {0, "x"}, {3, "G_2"}}, {{2, -1, -3, 0}, {0, "x"}, 
    {1, "SU(2)"}}, {{2, -1, -2, 0}, {0, "x"}, {0, "x"}}, 
   {{2, -1, 2, 0}, {1, "SU(2)"}, {0, "x"}}, {{2, -1, 3, 0}, {3, "G_2"}, 
    {0, "x"}}, {{2, -1, 3, 1}, {3, "G_2"}, {0, "x"}}, 
   {{2, 0, -6, 0}, {0, "x"}, {5, "F_4"}}, {{2, 0, -5, 0}, {0, "x"}, 
    {5, "F_4"}}, {{2, 0, -4, 0}, {0, "x"}, {3, "G_2"}}, 
   {{2, 0, -3, 0}, {0, "x"}, {1, "SU(2)"}}, {{2, 0, -2, 0}, {0, "x"}, 
    {0, "x"}}, {{2, 0, 2, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 0, 3, 0}, {3, "G_2"}, {0, "x"}}, {{2, 0, 3, 1}, {3, "G_2"}, 
    {0, "x"}}, {{2, 0, 4, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 0, 4, 1}, {4, "SO(8)"}, {0, "x"}}, {{2, 1, -5, 0}, {0, "x"}, 
    {5, "F_4"}}, {{2, 1, -4, 0}, {0, "x"}, {3, "G_2"}}, 
   {{2, 1, -3, 0}, {0, "x"}, {1, "SU(2)"}}, {{2, 1, 2, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 1, 3, 0}, {3, "G_2"}, {0, "x"}}, 
   {{2, 1, 4, 0}, {4, "SO(8)"}, {0, "x"}}, {{2, 1, 5, 0}, {5, "F_4"}, 
    {0, "x"}}, {{2, 2, -4, 0}, {0, "x"}, {3, "G_2"}}, 
   {{2, 2, -3, 0}, {0, "x"}, {1, "SU(2)"}}, {{2, 2, 2, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 2, 3, 0}, {3, "G_2"}, {0, "x"}}, 
   {{2, 2, 4, 0}, {4, "SO(8)"}, {0, "x"}}, {{2, 2, 5, 0}, {5, "F_4"}, 
    {0, "x"}}, {{2, 2, 6, 0}, {5, "F_4"}, {0, "x"}}, 
   {{2, 3, -3, 0}, {1, "SU(2)"}, {1, "SU(2)"}}, {{2, 3, 2, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 3, 3, 0}, {3, "G_2"}, {0, "x"}}, 
   {{2, 3, 3, 1}, {3, "G_2"}, {0, "x"}}, {{2, 3, 4, 0}, {4, "SO(8)"}, 
    {0, "x"}}, {{2, 3, 5, 0}, {5, "F_4"}, {0, "x"}}, 
   {{2, 3, 6, 0}, {5, "F_4"}, {0, "x"}}, {{2, 3, 6, 1}, {5, "F_4"}, 
    {0, "x"}}, {{2, 3, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{2, 4, 2, 0}, {3, "G_2"}, {0, "x"}}, {{2, 4, 3, 0}, {3, "G_2"}, 
    {0, "x"}}, {{2, 4, 3, 1}, {3, "G_2"}, {0, "x"}}, 
   {{2, 4, 4, 0}, {4, "SO(8)"}, {0, "x"}}, {{2, 4, 4, 1}, {4, "SO(8)"}, 
    {0, "x"}}, {{2, 4, 4, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 4, 5, 0}, {5, "F_4"}, {0, "x"}}, {{2, 4, 6, 0}, {5, "F_4"}, 
    {0, "x"}}, {{2, 4, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{2, 5, 2, 0}, {5, "F_4"}, {0, "x"}}, {{2, 5, 3, 0}, {5, "F_4"}, 
    {0, "x"}}, {{2, 5, 4, 0}, {5, "F_4"}, {0, "x"}}, 
   {{2, 5, 4, 1}, {5, "F_4"}, {0, "x"}}, {{2, 5, 5, 0}, {5, "F_4"}, 
    {0, "x"}}, {{2, 5, 5, 1}, {5, "F_4"}, {0, "x"}}, 
   {{2, 5, 5, 2}, {5, "F_4"}, {0, "x"}}, {{2, 5, 6, 0}, {5, "F_4"}, 
    {0, "x"}}, {{2, 6, 2, 0}, {5, "F_4"}, {0, "x"}}, 
   {{2, 6, 3, 0}, {5, "F_4"}, {0, "x"}}, {{2, 6, 4, 0}, {5, "F_4"}, 
    {0, "x"}}, {{2, 6, 5, 0}, {5, "F_4"}, {0, "x"}}, 
   {{2, 6, 5, 1}, {5, "F_4"}, {0, "x"}}, {{2, 6, 6, 0}, {6, "E_6"}, 
    {0, "x"}}, {{2, 6, 6, 1}, {6, "E_6"}, {0, "x"}}, 
   {{2, 6, 6, 2}, {6, "E_6"}, {0, "x"}}, {{2, 7, 2, 0}, {7, "E_7"}, 
    {0, "x"}}, {{2, 7, 3, 0}, {7, "E_7"}, {0, "x"}}, 
   {{2, 7, 3, 1}, {7, "E_7"}, {0, "x"}}, {{2, 7, 4, 0}, {7, "E_7"}, 
    {0, "x"}}, {{2, 7, 5, 0}, {7, "E_7"}, {0, "x"}}, 
   {{2, 7, 6, 0}, {7, "E_7"}, {0, "x"}}, {{2, 7, 6, 1}, {7, "E_7"}, 
    {0, "x"}}, {{2, 7, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{2, 7, 7, 2}, {7, "E_7"}, {0, "x"}}, {{2, 8, 2, 0}, {7, "E_7"}, 
    {0, "x"}}, {{2, 8, 3, 0}, {7, "E_7"}, {0, "x"}}, 
   {{2, 8, 3, 1}, {7, "E_7"}, {0, "x"}}, {{2, 8, 4, 0}, {7, "E_7"}, 
    {0, "x"}}, {{2, 8, 4, 1}, {7, "E_7"}, {0, "x"}}, 
   {{2, 8, 5, 0}, {7, "E_7"}, {0, "x"}}, {{2, 8, 6, 0}, {7, "E_7"}, 
    {0, "x"}}, {{2, 8, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{2, 8, 8, 2}, {7, "E_7"}, {0, "x"}}, {{3, -3, -6, 0}, {1, "SU(2)"}, 
    {5, "F_4"}}, {{3, -3, -5, 0}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{3, -3, -4, 0}, {1, "SU(2)"}, {3, "G_2"}}, {{3, -3, -3, 0}, {1, "SU(2)"}, 
    {2, "SU(3)"}}, {{3, -2, -6, 0}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{3, -2, -5, 0}, {1, "SU(2)"}, {5, "F_4"}}, {{3, -2, -4, 0}, {1, "SU(2)"}, 
    {3, "G_2"}}, {{3, -2, -3, 0}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{3, -1, -6, 0}, {1, "SU(2)"}, {5, "F_4"}}, {{3, -1, -5, 0}, {1, "SU(2)"}, 
    {5, "F_4"}}, {{3, -1, -4, 0}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{3, -1, -3, 0}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{3, 0, -6, 0}, {1, "SU(2)"}, {5, "F_4"}}, {{3, 0, -5, 0}, {1, "SU(2)"}, 
    {5, "F_4"}}, {{3, 0, -4, 0}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{3, 0, -3, 0}, {1, "SU(2)"}, {1, "SU(2)"}}, {{3, 0, 3, 0}, {4, "SO(8)"}, 
    {0, "x"}}, {{3, 1, -5, 0}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{3, 1, -4, 0}, {1, "SU(2)"}, {3, "G_2"}}, {{3, 1, 3, 0}, {4, "SO(8)"}, 
    {0, "x"}}, {{3, 1, 4, 0}, {5, "F_4"}, {0, "x"}}, 
   {{3, 1, 4, 1}, {5, "F_4"}, {0, "x"}}, {{3, 2, -4, 0}, {1, "SU(2)"}, 
    {3, "G_2"}}, {{3, 2, 3, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 2, 4, 0}, {5, "F_4"}, {0, "x"}}, {{3, 2, 5, 0}, {5, "F_4"}, 
    {0, "x"}}, {{3, 3, 3, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 3, 4, 0}, {5, "F_4"}, {0, "x"}}, {{3, 3, 5, 0}, {5, "F_4"}, 
    {0, "x"}}, {{3, 3, 6, 0}, {6, "E_6"}, {0, "x"}}, 
   {{3, 4, 3, 0}, {4, "SO(8)"}, {0, "x"}}, {{3, 4, 4, 0}, {5, "F_4"}, 
    {0, "x"}}, {{3, 4, 4, 1}, {5, "F_4"}, {0, "x"}}, 
   {{3, 4, 5, 0}, {5, "F_4"}, {0, "x"}}, {{3, 4, 6, 0}, {6, "E_6"}, 
    {0, "x"}}, {{3, 4, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{3, 5, 3, 0}, {5, "F_4"}, {0, "x"}}, {{3, 5, 4, 0}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 4, 1}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 5, 0}, {5, "F_4"}, {0, "x"}}, {{3, 5, 5, 1}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 6, 0}, {6, "E_6"}, {0, "x"}}, {{3, 6, 3, 0}, {5, "F_4"}, 
    {0, "x"}}, {{3, 6, 4, 0}, {5, "F_4"}, {0, "x"}}, 
   {{3, 6, 4, 1}, {5, "F_4"}, {0, "x"}}, {{3, 6, 5, 0}, {5, "F_4"}, 
    {0, "x"}}, {{3, 6, 5, 1}, {5, "F_4"}, {0, "x"}}, 
   {{3, 6, 5, 2}, {5, "F_4"}, {0, "x"}}, {{3, 6, 6, 0}, {6, "E_6"}, 
    {0, "x"}}, {{3, 6, 6, 1}, {6, "E_6"}, {0, "x"}}, 
   {{3, 6, 6, 2}, {6, "E_6"}, {0, "x"}}, {{3, 6, 6, 3}, {6, "E_6"}, 
    {0, "x"}}, {{3, 7, 3, 0}, {7, "E_7"}, {0, "x"}}, 
   {{3, 7, 4, 0}, {7, "E_7"}, {0, "x"}}, {{3, 7, 5, 0}, {7, "E_7"}, 
    {0, "x"}}, {{3, 7, 5, 1}, {7, "E_7"}, {0, "x"}}, 
   {{3, 7, 6, 0}, {7, "E_7"}, {0, "x"}}, {{3, 7, 6, 1}, {7, "E_7"}, 
    {0, "x"}}, {{3, 7, 6, 2}, {7, "E_7"}, {0, "x"}}, 
   {{3, 7, 7, 1}, {7, "E_7"}, {0, "x"}}, {{3, 7, 7, 2}, {7, "E_7"}, 
    {0, "x"}}, {{3, 7, 7, 3}, {7, "E_7"}, {0, "x"}}, 
   {{3, 8, 3, 0}, {7, "E_7"}, {0, "x"}}, {{3, 8, 4, 0}, {7, "E_7"}, 
    {0, "x"}}, {{3, 8, 5, 0}, {7, "E_7"}, {0, "x"}}, 
   {{3, 8, 6, 0}, {7, "E_7"}, {0, "x"}}, {{3, 8, 6, 1}, {7, "E_7"}, 
    {0, "x"}}, {{3, 8, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{3, 8, 7, 2}, {7, "E_7"}, {0, "x"}}, {{3, 8, 8, 2}, {7, "E_7"}, 
    {0, "x"}}, {{3, 8, 8, 3}, {7, "E_7"}, {0, "x"}}, 
   {{4, -2, -6, 0}, {3, "G_2"}, {5, "F_4"}}, {{4, -2, -5, 0}, {3, "G_2"}, 
    {5, "F_4"}}, {{4, -2, -4, 0}, {3, "G_2"}, {3, "G_2"}}, 
   {{4, -1, -6, 0}, {3, "G_2"}, {5, "F_4"}}, {{4, -1, -5, 0}, {3, "G_2"}, 
    {5, "F_4"}}, {{4, -1, -4, 0}, {3, "G_2"}, {3, "G_2"}}, 
   {{4, 0, -6, 0}, {3, "G_2"}, {5, "F_4"}}, {{4, 0, -5, 0}, {3, "G_2"}, 
    {5, "F_4"}}, {{4, 0, -4, 0}, {3, "G_2"}, {3, "G_2"}}, 
   {{4, 1, -5, 0}, {3, "G_2"}, {5, "F_4"}}, {{4, 2, 4, 0}, {5, "F_4"}, 
    {0, "x"}}, {{4, 3, 4, 0}, {5, "F_4"}, {0, "x"}}, 
   {{4, 3, 5, 0}, {6, "E_6"}, {0, "x"}}, {{4, 4, 4, 0}, {5, "F_4"}, 
    {0, "x"}}, {{4, 4, 5, 0}, {6, "E_6"}, {0, "x"}}, 
   {{4, 4, 6, 0}, {7, "E_7"}, {0, "x"}}, {{4, 5, 4, 0}, {5, "F_4"}, 
    {0, "x"}}, {{4, 5, 5, 0}, {6, "E_6"}, {0, "x"}}, 
   {{4, 5, 5, 1}, {6, "E_6"}, {0, "x"}}, {{4, 5, 6, 0}, {7, "E_7"}, 
    {0, "x"}}, {{4, 6, 4, 0}, {5, "F_4"}, {0, "x"}}, 
   {{4, 6, 5, 0}, {6, "E_6"}, {0, "x"}}, {{4, 6, 5, 1}, {6, "E_6"}, 
    {0, "x"}}, {{4, 6, 6, 0}, {7, "E_7"}, {0, "x"}}, 
   {{4, 6, 6, 1}, {7, "E_7"}, {0, "x"}}, {{4, 6, 6, 2}, {7, "E_7"}, 
    {0, "x"}}, {{4, 7, 4, 0}, {7, "E_7"}, {0, "x"}}, 
   {{4, 7, 5, 0}, {7, "E_7"}, {0, "x"}}, {{4, 7, 5, 1}, {7, "E_7"}, 
    {0, "x"}}, {{4, 7, 6, 0}, {7, "E_7"}, {0, "x"}}, 
   {{4, 7, 6, 1}, {7, "E_7"}, {0, "x"}}, {{4, 7, 6, 2}, {7, "E_7"}, 
    {0, "x"}}, {{4, 7, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{4, 7, 7, 2}, {7, "E_7"}, {0, "x"}}, {{4, 7, 7, 3}, {7, "E_7"}, 
    {0, "x"}}, {{4, 8, 4, 0}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 5, 0}, {7, "E_7"}, {0, "x"}}, {{4, 8, 5, 1}, {7, "E_7"}, 
    {0, "x"}}, {{4, 8, 6, 0}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 6, 1}, {7, "E_7"}, {0, "x"}}, {{4, 8, 6, 2}, {7, "E_7"}, 
    {0, "x"}}, {{4, 8, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 7, 2}, {7, "E_7"}, {0, "x"}}, {{4, 8, 7, 3}, {7, "E_7"}, 
    {0, "x"}}, {{4, 8, 8, 2}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 8, 3}, {7, "E_7"}, {0, "x"}}, {{4, 8, 8, 4}, {7, "E_7"}, 
    {0, "x"}}, {{5, -1, -6, 0}, {5, "F_4"}, {5, "F_4"}}, 
   {{5, -1, -5, 0}, {5, "F_4"}, {5, "F_4"}}, {{5, 0, -6, 0}, {5, "F_4"}, 
    {5, "F_4"}}, {{5, 0, -5, 0}, {5, "F_4"}, {5, "F_4"}}, 
   {{5, 4, 5, 0}, {7, "E_7"}, {0, "x"}}, {{5, 5, 5, 0}, {7, "E_7"}, 
    {0, "x"}}, {{5, 5, 6, 0}, {7, "E_7"}, {0, "x"}}, 
   {{5, 6, 5, 0}, {7, "E_7"}, {0, "x"}}, {{5, 6, 6, 0}, {7, "E_7"}, 
    {0, "x"}}, {{5, 6, 6, 1}, {7, "E_7"}, {0, "x"}}, 
   {{5, 7, 5, 0}, {7, "E_7"}, {0, "x"}}, {{5, 7, 6, 0}, {7, "E_7"}, 
    {0, "x"}}, {{5, 7, 6, 1}, {7, "E_7"}, {0, "x"}}, 
   {{5, 7, 7, 1}, {7, "E_7"}, {0, "x"}}, {{5, 7, 7, 2}, {7, "E_7"}, 
    {0, "x"}}, {{5, 8, 5, 0}, {7, "E_7"}, {0, "x"}}, 
   {{5, 8, 6, 0}, {7, "E_7"}, {0, "x"}}, {{5, 8, 6, 1}, {7, "E_7"}, 
    {0, "x"}}, {{5, 8, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{5, 8, 7, 2}, {7, "E_7"}, {0, "x"}}, {{6, 0, -6, 0}, {5, "F_4"}, 
    {5, "F_4"}}, {{6, 6, 6, 0}, {7, "E_7"}, {0, "x"}}, 
   {{6, 7, 6, 0}, {7, "E_7"}, {0, "x"}}, {{6, 8, 6, 0}, {7, "E_7"}, 
    {0, "x"}}, {{6, 12, 12, 6}, {8, "E_8"}, {0, "x"}}}}, 
 {{{0, 1}, {1, 0}, {1, -1}, {0, -1}, {-1, -1}, {-1, 0}}, 
  {{{-6, -6, -5, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -5, -5, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -5, -4, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -5, -4, 2}, {0, "x"}, {5, "F_4"}}, {{-6, -5, -3, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -5, -3, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -5, -3, 3}, {1, "SU(2)"}, {5, "F_4"}}, {{-6, -4, -3, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -4, -3, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -4, -3, 3}, {1, "SU(2)"}, {5, "F_4"}}, {{-6, -4, -2, 1}, {0, "x"}, 
    {4, "SO(8)"}}, {{-6, -4, -2, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-6, -4, -2, 3}, {1, "SU(2)"}, {4, "SO(8)"}}, 
   {{-6, -4, -2, 4}, {3, "G_2"}, {4, "SO(8)"}}, {{-6, -4, -1, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-6, -4, -1, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-6, -4, -1, 3}, {1, "SU(2)"}, {3, "G_2"}}, {{-6, -4, -1, 4}, {3, "G_2"}, 
    {3, "G_2"}}, {{-6, -4, -1, 5}, {5, "F_4"}, {3, "G_2"}}, 
   {{-6, -3, -1, 1}, {0, "x"}, {3, "G_2"}}, {{-6, -3, -1, 2}, {0, "x"}, 
    {3, "G_2"}}, {{-6, -3, -1, 3}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{-6, -3, -1, 4}, {3, "G_2"}, {3, "G_2"}}, {{-6, -3, -1, 5}, {5, "F_4"}, 
    {3, "G_2"}}, {{-6, -3, 0, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-6, -3, 0, 2}, {0, "x"}, {2, "SU(3)"}}, {{-6, -3, 0, 3}, {1, "SU(2)"}, 
    {2, "SU(3)"}}, {{-6, -3, 0, 4}, {3, "G_2"}, {2, "SU(3)"}}, 
   {{-6, -3, 0, 5}, {5, "F_4"}, {2, "SU(3)"}}, {{-6, -3, 0, 6}, {5, "F_4"}, 
    {2, "SU(3)"}}, {{-6, -2, 1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-6, -2, 1, 2}, {0, "x"}, {1, "SU(2)"}}, {{-6, -2, 1, 3}, {1, "SU(2)"}, 
    {1, "SU(2)"}}, {{-6, -2, 1, 4}, {3, "G_2"}, {1, "SU(2)"}}, 
   {{-6, -2, 1, 5}, {5, "F_4"}, {1, "SU(2)"}}, {{-6, -2, 1, 6}, {5, "F_4"}, 
    {1, "SU(2)"}}, {{-6, -2, 1, 7}, {7, "E_7"}, {1, "SU(2)"}}, 
   {{-6, -2, 2, 1}, {0, "x"}, {3, "G_2"}}, {{-6, -2, 2, 2}, {0, "x"}, 
    {1, "SU(2)"}}, {{-6, -2, 2, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-6, -2, 2, 4}, {3, "G_2"}, {0, "x"}}, {{-6, -2, 2, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-6, -2, 2, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-6, -2, 2, 7}, {7, "E_7"}, {0, "x"}}, {{-6, -2, 2, 8}, {7, "E_7"}, 
    {0, "x"}}, {{-6, -1, 3, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-6, -1, 3, 3}, {1, "SU(2)"}, {0, "x"}}, {{-6, -1, 3, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-6, -1, 3, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-6, -1, 3, 6}, {5, "F_4"}, {0, "x"}}, {{-6, -1, 3, 7}, {7, "E_7"}, 
    {0, "x"}}, {{-6, -1, 3, 8}, {7, "E_7"}, {0, "x"}}, 
   {{-6, -1, 4, 1}, {1, "SU(2)"}, {3, "G_2"}}, {{-6, -1, 4, 2}, {1, "SU(2)"}, 
    {1, "SU(2)"}}, {{-6, -1, 4, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-6, -1, 4, 4}, {3, "G_2"}, {0, "x"}}, {{-6, -1, 4, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-6, -1, 4, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-6, -1, 4, 7}, {7, "E_7"}, {0, "x"}}, {{-6, -1, 4, 8}, {7, "E_7"}, 
    {0, "x"}}, {{-6, 0, 5, 3}, {3, "G_2"}, {0, "x"}}, 
   {{-6, 0, 5, 4}, {3, "G_2"}, {0, "x"}}, {{-6, 0, 5, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-6, 0, 5, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-6, 0, 5, 7}, {7, "E_7"}, {0, "x"}}, {{-6, 0, 5, 8}, {7, "E_7"}, 
    {0, "x"}}, {{-6, 0, 6, 1}, {4, "SO(8)"}, {3, "G_2"}}, 
   {{-6, 0, 6, 2}, {4, "SO(8)"}, {1, "SU(2)"}}, {{-6, 0, 6, 3}, {4, "SO(8)"}, 
    {0, "x"}}, {{-6, 0, 6, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{-6, 0, 6, 5}, {5, "F_4"}, {0, "x"}}, {{-6, 0, 6, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-6, 0, 6, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-6, 0, 6, 8}, {7, "E_7"}, {0, "x"}}, {{-5, -5, -4, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-5, -4, -4, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -4, -3, 1}, {0, "x"}, {4, "SO(8)"}}, {{-5, -4, -3, 2}, {0, "x"}, 
    {4, "SO(8)"}}, {{-5, -4, -2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-5, -4, -2, 2}, {0, "x"}, {3, "G_2"}}, {{-5, -4, -2, 3}, {1, "SU(2)"}, 
    {3, "G_2"}}, {{-5, -3, -2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-5, -3, -2, 2}, {0, "x"}, {3, "G_2"}}, {{-5, -3, -2, 3}, {1, "SU(2)"}, 
    {3, "G_2"}}, {{-5, -3, -1, 1}, {0, "x"}, {2, "SU(3)"}}, 
   {{-5, -3, -1, 2}, {0, "x"}, {2, "SU(3)"}}, {{-5, -3, -1, 3}, {1, "SU(2)"}, 
    {2, "SU(3)"}}, {{-5, -3, -1, 4}, {3, "G_2"}, {2, "SU(3)"}}, 
   {{-5, -3, 0, 1}, {0, "x"}, {1, "SU(2)"}}, {{-5, -3, 0, 2}, {0, "x"}, 
    {1, "SU(2)"}}, {{-5, -3, 0, 3}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-5, -3, 0, 4}, {3, "G_2"}, {1, "SU(2)"}}, {{-5, -3, 0, 5}, {5, "F_4"}, 
    {1, "SU(2)"}}, {{-5, -2, 0, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-5, -2, 0, 2}, {0, "x"}, {1, "SU(2)"}}, {{-5, -2, 0, 3}, {1, "SU(2)"}, 
    {1, "SU(2)"}}, {{-5, -2, 0, 4}, {3, "G_2"}, {1, "SU(2)"}}, 
   {{-5, -2, 0, 5}, {5, "F_4"}, {1, "SU(2)"}}, {{-5, -2, 1, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-5, -2, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{-5, -2, 1, 3}, {1, "SU(2)"}, {0, "x"}}, {{-5, -2, 1, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-5, -2, 1, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-5, -2, 1, 6}, {5, "F_4"}, {0, "x"}}, {{-5, -1, 2, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-5, -1, 2, 2}, {0, "x"}, {0, "x"}}, 
   {{-5, -1, 2, 3}, {1, "SU(2)"}, {0, "x"}}, {{-5, -1, 2, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-5, -1, 2, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-5, -1, 2, 6}, {5, "F_4"}, {0, "x"}}, {{-5, -1, 2, 7}, {7, "E_7"}, 
    {0, "x"}}, {{-5, -1, 3, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-5, -1, 3, 2}, {0, "x"}, {0, "x"}}, {{-5, -1, 3, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{-5, -1, 3, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-5, -1, 3, 5}, {5, "F_4"}, {0, "x"}}, {{-5, -1, 3, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-5, -1, 3, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-5, -1, 3, 8}, {7, "E_7"}, {0, "x"}}, {{-5, 0, 4, 2}, {1, "SU(2)"}, 
    {0, "x"}}, {{-5, 0, 4, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-5, 0, 4, 4}, {3, "G_2"}, {0, "x"}}, {{-5, 0, 4, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-5, 0, 4, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-5, 0, 4, 7}, {7, "E_7"}, {0, "x"}}, {{-5, 0, 4, 8}, {7, "E_7"}, 
    {0, "x"}}, {{-5, 0, 5, 1}, {3, "G_2"}, {1, "SU(2)"}}, 
   {{-5, 0, 5, 2}, {3, "G_2"}, {0, "x"}}, {{-5, 0, 5, 3}, {3, "G_2"}, 
    {0, "x"}}, {{-5, 0, 5, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-5, 0, 5, 5}, {5, "F_4"}, {0, "x"}}, {{-5, 0, 5, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-5, 0, 5, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-5, 0, 5, 8}, {7, "E_7"}, {0, "x"}}, {{-5, 1, 6, 3}, {4, "SO(8)"}, 
    {0, "x"}}, {{-5, 1, 6, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{-5, 1, 6, 5}, {5, "F_4"}, {0, "x"}}, {{-5, 1, 6, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-5, 1, 6, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-5, 1, 6, 8}, {7, "E_7"}, {0, "x"}}, {{-5, 1, 7, 1}, {5, "F_4"}, 
    {1, "SU(2)"}}, {{-5, 1, 7, 2}, {5, "F_4"}, {0, "x"}}, 
   {{-5, 1, 7, 3}, {5, "F_4"}, {0, "x"}}, {{-5, 1, 7, 4}, {5, "F_4"}, 
    {0, "x"}}, {{-5, 1, 7, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-5, 1, 7, 6}, {5, "F_4"}, {0, "x"}}, {{-5, 1, 7, 7}, {7, "E_7"}, 
    {0, "x"}}, {{-5, 1, 7, 8}, {7, "E_7"}, {0, "x"}}, 
   {{-4, -4, -3, 1}, {0, "x"}, {3, "G_2"}}, {{-4, -3, -3, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-4, -3, -2, 1}, {0, "x"}, {2, "SU(3)"}}, 
   {{-4, -3, -2, 2}, {0, "x"}, {2, "SU(3)"}}, {{-4, -3, -1, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-4, -3, -1, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -3, -1, 3}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-4, -2, -1, 1}, {0, "x"}, {1, "SU(2)"}}, {{-4, -2, -1, 2}, {0, "x"}, 
    {1, "SU(2)"}}, {{-4, -2, -1, 3}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-4, -2, 0, 1}, {0, "x"}, {0, "x"}}, {{-4, -2, 0, 2}, {0, "x"}, 
    {0, "x"}}, {{-4, -2, 0, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-4, -2, 0, 4}, {3, "G_2"}, {0, "x"}}, {{-4, -2, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{-4, -2, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{-4, -2, 1, 3}, {1, "SU(2)"}, {0, "x"}}, {{-4, -2, 1, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-4, -2, 1, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-4, -1, 1, 1}, {0, "x"}, {0, "x"}}, {{-4, -1, 1, 2}, {0, "x"}, 
    {0, "x"}}, {{-4, -1, 1, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-4, -1, 1, 4}, {3, "G_2"}, {0, "x"}}, {{-4, -1, 1, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-4, -1, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-4, -1, 2, 2}, {0, "x"}, {0, "x"}}, {{-4, -1, 2, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{-4, -1, 2, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-4, -1, 2, 5}, {5, "F_4"}, {0, "x"}}, {{-4, -1, 2, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-4, 0, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{-4, 0, 3, 2}, {0, "x"}, {0, "x"}}, {{-4, 0, 3, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{-4, 0, 3, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-4, 0, 3, 5}, {5, "F_4"}, {0, "x"}}, {{-4, 0, 3, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-4, 0, 3, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-4, 0, 4, 1}, {1, "SU(2)"}, {0, "x"}}, {{-4, 0, 4, 2}, {1, "SU(2)"}, 
    {0, "x"}}, {{-4, 0, 4, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-4, 0, 4, 4}, {3, "G_2"}, {0, "x"}}, {{-4, 0, 4, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-4, 0, 4, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-4, 0, 4, 7}, {7, "E_7"}, {0, "x"}}, {{-4, 0, 4, 8}, {7, "E_7"}, 
    {0, "x"}}, {{-4, 1, 5, 2}, {3, "G_2"}, {0, "x"}}, 
   {{-4, 1, 5, 3}, {3, "G_2"}, {0, "x"}}, {{-4, 1, 5, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-4, 1, 5, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-4, 1, 5, 6}, {5, "F_4"}, {0, "x"}}, {{-4, 1, 5, 7}, {7, "E_7"}, 
    {0, "x"}}, {{-4, 1, 5, 8}, {7, "E_7"}, {0, "x"}}, 
   {{-4, 1, 6, 1}, {4, "SO(8)"}, {0, "x"}}, {{-4, 1, 6, 2}, {4, "SO(8)"}, 
    {0, "x"}}, {{-4, 1, 6, 3}, {4, "SO(8)"}, {0, "x"}}, 
   {{-4, 1, 6, 4}, {4, "SO(8)"}, {0, "x"}}, {{-4, 1, 6, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-4, 1, 6, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-4, 1, 6, 7}, {7, "E_7"}, {0, "x"}}, {{-4, 1, 6, 8}, {7, "E_7"}, 
    {0, "x"}}, {{-4, 2, 7, 3}, {5, "F_4"}, {0, "x"}}, 
   {{-4, 2, 7, 4}, {5, "F_4"}, {0, "x"}}, {{-4, 2, 7, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-4, 2, 7, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-4, 2, 7, 7}, {7, "E_7"}, {0, "x"}}, {{-4, 2, 7, 8}, {7, "E_7"}, 
    {0, "x"}}, {{-4, 2, 8, 2}, {5, "F_4"}, {0, "x"}}, 
   {{-4, 2, 8, 3}, {5, "F_4"}, {0, "x"}}, {{-4, 2, 8, 4}, {5, "F_4"}, 
    {0, "x"}}, {{-4, 2, 8, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-4, 2, 8, 6}, {5, "F_4"}, {0, "x"}}, {{-4, 2, 8, 7}, {7, "E_7"}, 
    {0, "x"}}, {{-4, 2, 8, 8}, {7, "E_7"}, {0, "x"}}, 
   {{-3, -3, -2, 1}, {0, "x"}, {1, "SU(2)"}}, {{-3, -2, -2, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-3, -2, -1, 1}, {0, "x"}, {0, "x"}}, 
   {{-3, -2, -1, 2}, {0, "x"}, {0, "x"}}, {{-3, -2, 0, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, -2, 0, 2}, {0, "x"}, {0, "x"}}, 
   {{-3, -2, 0, 3}, {1, "SU(2)"}, {0, "x"}}, {{-3, -1, 0, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, -1, 0, 2}, {0, "x"}, {0, "x"}}, 
   {{-3, -1, 0, 3}, {1, "SU(2)"}, {0, "x"}}, {{-3, -1, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, -1, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{-3, -1, 1, 3}, {1, "SU(2)"}, {0, "x"}}, {{-3, -1, 1, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-3, -1, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-3, -1, 2, 2}, {0, "x"}, {0, "x"}}, {{-3, -1, 2, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{-3, -1, 2, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-3, -1, 2, 5}, {5, "F_4"}, {0, "x"}}, {{-3, 0, 2, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, 0, 2, 2}, {0, "x"}, {0, "x"}}, 
   {{-3, 0, 2, 3}, {1, "SU(2)"}, {0, "x"}}, {{-3, 0, 2, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-3, 0, 2, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-3, 0, 3, 1}, {0, "x"}, {0, "x"}}, {{-3, 0, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{-3, 0, 3, 3}, {1, "SU(2)"}, {0, "x"}}, {{-3, 0, 3, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-3, 0, 3, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-3, 0, 3, 6}, {5, "F_4"}, {0, "x"}}, {{-3, 1, 4, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{-3, 1, 4, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-3, 1, 4, 3}, {1, "SU(2)"}, {0, "x"}}, {{-3, 1, 4, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-3, 1, 4, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-3, 1, 4, 6}, {5, "F_4"}, {0, "x"}}, {{-3, 1, 4, 7}, {7, "E_7"}, 
    {0, "x"}}, {{-3, 1, 5, 1}, {3, "G_2"}, {0, "x"}}, 
   {{-3, 1, 5, 2}, {3, "G_2"}, {0, "x"}}, {{-3, 1, 5, 3}, {3, "G_2"}, 
    {0, "x"}}, {{-3, 1, 5, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-3, 1, 5, 5}, {5, "F_4"}, {0, "x"}}, {{-3, 1, 5, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-3, 1, 5, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-3, 1, 5, 8}, {7, "E_7"}, {0, "x"}}, {{-3, 2, 6, 2}, {4, "SO(8)"}, 
    {0, "x"}}, {{-3, 2, 6, 3}, {4, "SO(8)"}, {0, "x"}}, 
   {{-3, 2, 6, 4}, {4, "SO(8)"}, {0, "x"}}, {{-3, 2, 6, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-3, 2, 6, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-3, 2, 6, 7}, {7, "E_7"}, {0, "x"}}, {{-3, 2, 6, 8}, {7, "E_7"}, 
    {0, "x"}}, {{-3, 2, 7, 1}, {5, "F_4"}, {0, "x"}}, 
   {{-3, 2, 7, 2}, {5, "F_4"}, {0, "x"}}, {{-3, 2, 7, 3}, {5, "F_4"}, 
    {0, "x"}}, {{-3, 2, 7, 4}, {5, "F_4"}, {0, "x"}}, 
   {{-3, 2, 7, 5}, {5, "F_4"}, {0, "x"}}, {{-3, 2, 7, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-3, 2, 7, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-3, 2, 7, 8}, {7, "E_7"}, {0, "x"}}, {{-3, 3, 8, 3}, {5, "F_4"}, 
    {0, "x"}}, {{-3, 3, 8, 4}, {5, "F_4"}, {0, "x"}}, 
   {{-3, 3, 8, 5}, {5, "F_4"}, {0, "x"}}, {{-3, 3, 8, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-3, 3, 8, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-3, 3, 8, 8}, {7, "E_7"}, {0, "x"}}, {{-3, 3, 9, 3}, {6, "E_6"}, 
    {0, "x"}}, {{-3, 3, 9, 4}, {6, "E_6"}, {0, "x"}}, 
   {{-3, 3, 9, 5}, {6, "E_6"}, {0, "x"}}, {{-3, 3, 9, 6}, {6, "E_6"}, 
    {0, "x"}}, {{-3, 3, 9, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-3, 3, 9, 8}, {7, "E_7"}, {0, "x"}}, {{-2, -2, -1, 1}, {0, "x"}, 
    {0, "x"}}, {{-2, -1, -1, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -1, 0, 1}, {0, "x"}, {0, "x"}}, {{-2, -1, 0, 2}, {0, "x"}, 
    {0, "x"}}, {{-2, -1, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -1, 1, 2}, {0, "x"}, {0, "x"}}, {{-2, -1, 1, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{-2, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, 0, 1, 2}, {0, "x"}, {0, "x"}}, {{-2, 0, 1, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{-2, 0, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, 0, 2, 2}, {0, "x"}, {0, "x"}}, {{-2, 0, 2, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{-2, 0, 2, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-2, 0, 3, 1}, {0, "x"}, {0, "x"}}, {{-2, 0, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, 0, 3, 3}, {1, "SU(2)"}, {0, "x"}}, {{-2, 0, 3, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-2, 0, 3, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-2, 1, 3, 1}, {0, "x"}, {0, "x"}}, {{-2, 1, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, 1, 3, 3}, {1, "SU(2)"}, {0, "x"}}, {{-2, 1, 3, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-2, 1, 3, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-2, 1, 4, 1}, {1, "SU(2)"}, {0, "x"}}, {{-2, 1, 4, 2}, {1, "SU(2)"}, 
    {0, "x"}}, {{-2, 1, 4, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-2, 1, 4, 4}, {3, "G_2"}, {0, "x"}}, {{-2, 1, 4, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-2, 1, 4, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-2, 2, 5, 1}, {3, "G_2"}, {0, "x"}}, {{-2, 2, 5, 2}, {3, "G_2"}, 
    {0, "x"}}, {{-2, 2, 5, 3}, {3, "G_2"}, {0, "x"}}, 
   {{-2, 2, 5, 4}, {3, "G_2"}, {0, "x"}}, {{-2, 2, 5, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-2, 2, 5, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-2, 2, 5, 7}, {7, "E_7"}, {0, "x"}}, {{-2, 2, 6, 1}, {4, "SO(8)"}, 
    {0, "x"}}, {{-2, 2, 6, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{-2, 2, 6, 3}, {4, "SO(8)"}, {0, "x"}}, {{-2, 2, 6, 4}, {4, "SO(8)"}, 
    {0, "x"}}, {{-2, 2, 6, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-2, 2, 6, 6}, {5, "F_4"}, {0, "x"}}, {{-2, 2, 6, 7}, {7, "E_7"}, 
    {0, "x"}}, {{-2, 2, 6, 8}, {7, "E_7"}, {0, "x"}}, 
   {{-2, 3, 7, 2}, {5, "F_4"}, {0, "x"}}, {{-2, 3, 7, 3}, {5, "F_4"}, 
    {0, "x"}}, {{-2, 3, 7, 4}, {5, "F_4"}, {0, "x"}}, 
   {{-2, 3, 7, 5}, {5, "F_4"}, {0, "x"}}, {{-2, 3, 7, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-2, 3, 7, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-2, 3, 7, 8}, {7, "E_7"}, {0, "x"}}, {{-2, 3, 8, 2}, {5, "F_4"}, 
    {0, "x"}}, {{-2, 3, 8, 3}, {5, "F_4"}, {0, "x"}}, 
   {{-2, 3, 8, 4}, {5, "F_4"}, {0, "x"}}, {{-2, 3, 8, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-2, 3, 8, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-2, 3, 8, 7}, {7, "E_7"}, {0, "x"}}, {{-2, 3, 8, 8}, {7, "E_7"}, 
    {0, "x"}}, {{-2, 4, 9, 3}, {6, "E_6"}, {0, "x"}}, 
   {{-2, 4, 9, 4}, {6, "E_6"}, {0, "x"}}, {{-2, 4, 9, 5}, {6, "E_6"}, 
    {0, "x"}}, {{-2, 4, 9, 6}, {6, "E_6"}, {0, "x"}}, 
   {{-2, 4, 9, 7}, {7, "E_7"}, {0, "x"}}, {{-2, 4, 9, 8}, {7, "E_7"}, 
    {0, "x"}}, {{-2, 4, 10, 4}, {7, "E_7"}, {0, "x"}}, 
   {{-2, 4, 10, 5}, {7, "E_7"}, {0, "x"}}, {{-2, 4, 10, 6}, {7, "E_7"}, 
    {0, "x"}}, {{-2, 4, 10, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-2, 4, 10, 8}, {7, "E_7"}, {0, "x"}}, {{-1, -1, 0, 1}, {0, "x"}, 
    {0, "x"}}, {{-1, 0, 0, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, 0, 1, 1}, {0, "x"}, {0, "x"}}, {{-1, 0, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{-1, 0, 2, 1}, {0, "x"}, {0, "x"}}, {{-1, 0, 2, 2}, {0, "x"}, {0, "x"}}, 
   {{-1, 0, 2, 3}, {1, "SU(2)"}, {0, "x"}}, {{-1, 1, 2, 1}, {0, "x"}, 
    {0, "x"}}, {{-1, 1, 2, 2}, {0, "x"}, {0, "x"}}, 
   {{-1, 1, 2, 3}, {1, "SU(2)"}, {0, "x"}}, {{-1, 1, 3, 1}, {0, "x"}, 
    {0, "x"}}, {{-1, 1, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{-1, 1, 3, 3}, {1, "SU(2)"}, {0, "x"}}, {{-1, 1, 3, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-1, 1, 4, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{-1, 1, 4, 2}, {1, "SU(2)"}, {0, "x"}}, {{-1, 1, 4, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{-1, 1, 4, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-1, 1, 4, 5}, {5, "F_4"}, {0, "x"}}, {{-1, 2, 4, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{-1, 2, 4, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-1, 2, 4, 3}, {1, "SU(2)"}, {0, "x"}}, {{-1, 2, 4, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-1, 2, 4, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-1, 2, 5, 1}, {3, "G_2"}, {0, "x"}}, {{-1, 2, 5, 2}, {3, "G_2"}, 
    {0, "x"}}, {{-1, 2, 5, 3}, {3, "G_2"}, {0, "x"}}, 
   {{-1, 2, 5, 4}, {3, "G_2"}, {0, "x"}}, {{-1, 2, 5, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-1, 2, 5, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-1, 3, 6, 1}, {4, "SO(8)"}, {0, "x"}}, {{-1, 3, 6, 2}, {4, "SO(8)"}, 
    {0, "x"}}, {{-1, 3, 6, 3}, {4, "SO(8)"}, {0, "x"}}, 
   {{-1, 3, 6, 4}, {4, "SO(8)"}, {0, "x"}}, {{-1, 3, 6, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-1, 3, 6, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-1, 3, 6, 7}, {7, "E_7"}, {0, "x"}}, {{-1, 3, 7, 1}, {5, "F_4"}, 
    {0, "x"}}, {{-1, 3, 7, 2}, {5, "F_4"}, {0, "x"}}, 
   {{-1, 3, 7, 3}, {5, "F_4"}, {0, "x"}}, {{-1, 3, 7, 4}, {5, "F_4"}, 
    {0, "x"}}, {{-1, 3, 7, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-1, 3, 7, 6}, {5, "F_4"}, {0, "x"}}, {{-1, 3, 7, 7}, {7, "E_7"}, 
    {0, "x"}}, {{-1, 3, 7, 8}, {7, "E_7"}, {0, "x"}}, 
   {{-1, 4, 8, 2}, {5, "F_4"}, {0, "x"}}, {{-1, 4, 8, 3}, {5, "F_4"}, 
    {0, "x"}}, {{-1, 4, 8, 4}, {5, "F_4"}, {0, "x"}}, 
   {{-1, 4, 8, 5}, {5, "F_4"}, {0, "x"}}, {{-1, 4, 8, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-1, 4, 8, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-1, 4, 8, 8}, {7, "E_7"}, {0, "x"}}, {{-1, 4, 9, 3}, {6, "E_6"}, 
    {0, "x"}}, {{-1, 4, 9, 4}, {6, "E_6"}, {0, "x"}}, 
   {{-1, 4, 9, 5}, {6, "E_6"}, {0, "x"}}, {{-1, 4, 9, 6}, {6, "E_6"}, 
    {0, "x"}}, {{-1, 4, 9, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-1, 4, 9, 8}, {7, "E_7"}, {0, "x"}}, {{-1, 5, 10, 4}, {7, "E_7"}, 
    {0, "x"}}, {{-1, 5, 10, 5}, {7, "E_7"}, {0, "x"}}, 
   {{-1, 5, 10, 6}, {7, "E_7"}, {0, "x"}}, {{-1, 5, 10, 7}, {7, "E_7"}, 
    {0, "x"}}, {{-1, 5, 10, 8}, {7, "E_7"}, {0, "x"}}, 
   {{-1, 5, 11, 5}, {7, "E_7"}, {0, "x"}}, {{-1, 5, 11, 6}, {7, "E_7"}, 
    {0, "x"}}, {{-1, 5, 11, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-1, 5, 11, 8}, {7, "E_7"}, {0, "x"}}, {{0, 0, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 0, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 1, 1}, {0, "x"}, {0, "x"}}, {{0, 1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 1, 1}, {0, "x"}, {0, "x"}}, {{0, 1, 2, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 2, 1}, {0, "x"}, {0, "x"}}, {{0, 1, 2, 2}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 3, 0}, {0, "x"}, {0, "x"}}, {{0, 1, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 3, 2}, {0, "x"}, {0, "x"}}, {{0, 1, 3, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{0, 2, 3, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 2, 3, 1}, {0, "x"}, {0, "x"}}, {{0, 2, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{0, 2, 3, 3}, {1, "SU(2)"}, {0, "x"}}, {{0, 2, 4, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{0, 2, 4, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{0, 2, 4, 2}, {1, "SU(2)"}, {0, "x"}}, {{0, 2, 4, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{0, 2, 4, 4}, {3, "G_2"}, {0, "x"}}, 
   {{0, 2, 5, 0}, {3, "G_2"}, {0, "x"}}, {{0, 2, 5, 1}, {3, "G_2"}, 
    {0, "x"}}, {{0, 2, 5, 2}, {3, "G_2"}, {0, "x"}}, 
   {{0, 2, 5, 3}, {3, "G_2"}, {0, "x"}}, {{0, 2, 5, 4}, {3, "G_2"}, 
    {0, "x"}}, {{0, 2, 5, 5}, {5, "F_4"}, {0, "x"}}, 
   {{0, 3, 5, 0}, {3, "G_2"}, {0, "x"}}, {{0, 3, 5, 1}, {3, "G_2"}, 
    {0, "x"}}, {{0, 3, 5, 2}, {3, "G_2"}, {0, "x"}}, 
   {{0, 3, 5, 3}, {3, "G_2"}, {0, "x"}}, {{0, 3, 5, 4}, {3, "G_2"}, 
    {0, "x"}}, {{0, 3, 5, 5}, {5, "F_4"}, {0, "x"}}, 
   {{0, 3, 6, 0}, {4, "SO(8)"}, {0, "x"}}, {{0, 3, 6, 1}, {4, "SO(8)"}, 
    {0, "x"}}, {{0, 3, 6, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{0, 3, 6, 3}, {4, "SO(8)"}, {0, "x"}}, {{0, 3, 6, 4}, {4, "SO(8)"}, 
    {0, "x"}}, {{0, 3, 6, 5}, {5, "F_4"}, {0, "x"}}, 
   {{0, 3, 6, 6}, {5, "F_4"}, {0, "x"}}, {{0, 4, 7, 1}, {5, "F_4"}, 
    {0, "x"}}, {{0, 4, 7, 2}, {5, "F_4"}, {0, "x"}}, 
   {{0, 4, 7, 3}, {5, "F_4"}, {0, "x"}}, {{0, 4, 7, 4}, {5, "F_4"}, 
    {0, "x"}}, {{0, 4, 7, 5}, {5, "F_4"}, {0, "x"}}, 
   {{0, 4, 7, 6}, {5, "F_4"}, {0, "x"}}, {{0, 4, 7, 7}, {7, "E_7"}, 
    {0, "x"}}, {{0, 4, 8, 2}, {5, "F_4"}, {0, "x"}}, 
   {{0, 4, 8, 3}, {5, "F_4"}, {0, "x"}}, {{0, 4, 8, 4}, {5, "F_4"}, 
    {0, "x"}}, {{0, 4, 8, 5}, {5, "F_4"}, {0, "x"}}, 
   {{0, 4, 8, 6}, {5, "F_4"}, {0, "x"}}, {{0, 4, 8, 7}, {7, "E_7"}, 
    {0, "x"}}, {{0, 4, 8, 8}, {7, "E_7"}, {0, "x"}}, 
   {{0, 5, 9, 3}, {6, "E_6"}, {0, "x"}}, {{0, 5, 9, 4}, {6, "E_6"}, 
    {0, "x"}}, {{0, 5, 9, 5}, {6, "E_6"}, {0, "x"}}, 
   {{0, 5, 9, 6}, {6, "E_6"}, {0, "x"}}, {{0, 5, 9, 7}, {7, "E_7"}, 
    {0, "x"}}, {{0, 5, 9, 8}, {7, "E_7"}, {0, "x"}}, 
   {{0, 5, 10, 4}, {7, "E_7"}, {0, "x"}}, {{0, 5, 10, 5}, {7, "E_7"}, 
    {0, "x"}}, {{0, 5, 10, 6}, {7, "E_7"}, {0, "x"}}, 
   {{0, 5, 10, 7}, {7, "E_7"}, {0, "x"}}, {{0, 5, 10, 8}, {7, "E_7"}, 
    {0, "x"}}, {{0, 6, 11, 5}, {7, "E_7"}, {0, "x"}}, 
   {{0, 6, 11, 6}, {7, "E_7"}, {0, "x"}}, {{0, 6, 11, 7}, {7, "E_7"}, 
    {0, "x"}}, {{0, 6, 11, 8}, {7, "E_7"}, {0, "x"}}, 
   {{0, 6, 12, 6}, {7, "E_7"}, {0, "x"}}, {{0, 6, 12, 7}, {7, "E_7"}, 
    {0, "x"}}, {{0, 6, 12, 8}, {7, "E_7"}, {0, "x"}}, 
   {{1, -2, -5, 0}, {0, "x"}, {3, "G_2"}}, {{1, -2, -4, 0}, {0, "x"}, 
    {1, "SU(2)"}}, {{1, -1, -4, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, -1, -3, 0}, {0, "x"}, {0, "x"}}, {{1, -1, -2, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 0, -2, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 0, -1, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 2, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 2, 0}, {0, "x"}, {0, "x"}}, {{1, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 3, 0}, {0, "x"}, {0, "x"}}, {{1, 2, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 3, 2}, {0, "x"}, {0, "x"}}, {{1, 2, 4, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{1, 2, 4, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 2, 4, 2}, {1, "SU(2)"}, {0, "x"}}, {{1, 2, 4, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{1, 3, 4, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 3, 4, 1}, {1, "SU(2)"}, {0, "x"}}, {{1, 3, 4, 2}, {1, "SU(2)"}, 
    {0, "x"}}, {{1, 3, 4, 3}, {2, "SU(3)"}, {0, "x"}}, 
   {{1, 3, 5, 0}, {3, "G_2"}, {0, "x"}}, {{1, 3, 5, 1}, {3, "G_2"}, 
    {0, "x"}}, {{1, 3, 5, 2}, {3, "G_2"}, {0, "x"}}, 
   {{1, 3, 5, 3}, {3, "G_2"}, {0, "x"}}, {{1, 3, 5, 4}, {3, "G_2"}, 
    {0, "x"}}, {{1, 3, 6, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{1, 3, 6, 1}, {4, "SO(8)"}, {0, "x"}}, {{1, 3, 6, 2}, {4, "SO(8)"}, 
    {0, "x"}}, {{1, 3, 6, 3}, {4, "SO(8)"}, {0, "x"}}, 
   {{1, 3, 6, 4}, {4, "SO(8)"}, {0, "x"}}, {{1, 3, 6, 5}, {5, "F_4"}, 
    {0, "x"}}, {{1, 4, 6, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{1, 4, 6, 1}, {4, "SO(8)"}, {0, "x"}}, {{1, 4, 6, 2}, {4, "SO(8)"}, 
    {0, "x"}}, {{1, 4, 6, 3}, {4, "SO(8)"}, {0, "x"}}, 
   {{1, 4, 6, 4}, {4, "SO(8)"}, {0, "x"}}, {{1, 4, 6, 5}, {5, "F_4"}, 
    {0, "x"}}, {{1, 4, 7, 1}, {5, "F_4"}, {0, "x"}}, 
   {{1, 4, 7, 2}, {5, "F_4"}, {0, "x"}}, {{1, 4, 7, 3}, {5, "F_4"}, 
    {0, "x"}}, {{1, 4, 7, 4}, {5, "F_4"}, {0, "x"}}, 
   {{1, 4, 7, 5}, {5, "F_4"}, {0, "x"}}, {{1, 4, 7, 6}, {5, "F_4"}, 
    {0, "x"}}, {{1, 5, 8, 2}, {5, "F_4"}, {0, "x"}}, 
   {{1, 5, 8, 3}, {5, "F_4"}, {0, "x"}}, {{1, 5, 8, 4}, {5, "F_4"}, 
    {0, "x"}}, {{1, 5, 8, 5}, {5, "F_4"}, {0, "x"}}, 
   {{1, 5, 8, 6}, {5, "F_4"}, {0, "x"}}, {{1, 5, 8, 7}, {7, "E_7"}, 
    {0, "x"}}, {{1, 5, 9, 3}, {6, "E_6"}, {0, "x"}}, 
   {{1, 5, 9, 4}, {6, "E_6"}, {0, "x"}}, {{1, 5, 9, 5}, {6, "E_6"}, 
    {0, "x"}}, {{1, 5, 9, 6}, {6, "E_6"}, {0, "x"}}, 
   {{1, 5, 9, 7}, {7, "E_7"}, {0, "x"}}, {{1, 5, 9, 8}, {7, "E_7"}, 
    {0, "x"}}, {{1, 6, 10, 4}, {7, "E_7"}, {0, "x"}}, 
   {{1, 6, 10, 5}, {7, "E_7"}, {0, "x"}}, {{1, 6, 10, 6}, {7, "E_7"}, 
    {0, "x"}}, {{1, 6, 10, 7}, {7, "E_7"}, {0, "x"}}, 
   {{1, 6, 10, 8}, {7, "E_7"}, {0, "x"}}, {{1, 6, 11, 5}, {7, "E_7"}, 
    {0, "x"}}, {{1, 6, 11, 6}, {7, "E_7"}, {0, "x"}}, 
   {{1, 6, 11, 7}, {7, "E_7"}, {0, "x"}}, {{1, 6, 11, 8}, {7, "E_7"}, 
    {0, "x"}}, {{1, 7, 12, 6}, {7, "E_7"}, {0, "x"}}, 
   {{1, 7, 12, 7}, {7, "E_7"}, {0, "x"}}, {{1, 7, 12, 8}, {7, "E_7"}, 
    {0, "x"}}, {{2, -2, -6, 0}, {0, "x"}, {4, "SO(8)"}}, 
   {{2, -1, -4, 0}, {0, "x"}, {1, "SU(2)"}}, {{2, -1, -3, 0}, {0, "x"}, 
    {0, "x"}}, {{2, 0, -3, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 0, -2, 0}, {0, "x"}, {0, "x"}}, {{2, 2, 2, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 2, 3, 0}, {1, "SU(2)"}, {0, "x"}}, {{2, 2, 3, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 3, 3, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 3, 3, 1}, {1, "SU(2)"}, {0, "x"}}, {{2, 3, 4, 0}, {2, "SU(3)"}, 
    {0, "x"}}, {{2, 3, 4, 1}, {2, "SU(3)"}, {0, "x"}}, 
   {{2, 3, 4, 2}, {2, "SU(3)"}, {0, "x"}}, {{2, 3, 5, 0}, {3, "G_2"}, 
    {0, "x"}}, {{2, 3, 5, 1}, {3, "G_2"}, {0, "x"}}, 
   {{2, 3, 5, 2}, {3, "G_2"}, {0, "x"}}, {{2, 3, 5, 3}, {3, "G_2"}, 
    {0, "x"}}, {{2, 4, 5, 0}, {3, "G_2"}, {0, "x"}}, 
   {{2, 4, 5, 1}, {3, "G_2"}, {0, "x"}}, {{2, 4, 5, 2}, {3, "G_2"}, 
    {0, "x"}}, {{2, 4, 5, 3}, {3, "G_2"}, {0, "x"}}, 
   {{2, 4, 6, 0}, {4, "SO(8)"}, {0, "x"}}, {{2, 4, 6, 1}, {4, "SO(8)"}, 
    {0, "x"}}, {{2, 4, 6, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 4, 6, 3}, {4, "SO(8)"}, {0, "x"}}, {{2, 4, 6, 4}, {4, "SO(8)"}, 
    {0, "x"}}, {{2, 4, 7, 1}, {5, "F_4"}, {0, "x"}}, 
   {{2, 4, 7, 2}, {5, "F_4"}, {0, "x"}}, {{2, 4, 7, 3}, {5, "F_4"}, 
    {0, "x"}}, {{2, 4, 7, 4}, {5, "F_4"}, {0, "x"}}, 
   {{2, 4, 7, 5}, {5, "F_4"}, {0, "x"}}, {{2, 5, 7, 1}, {5, "F_4"}, 
    {0, "x"}}, {{2, 5, 7, 2}, {5, "F_4"}, {0, "x"}}, 
   {{2, 5, 7, 3}, {5, "F_4"}, {0, "x"}}, {{2, 5, 7, 4}, {5, "F_4"}, 
    {0, "x"}}, {{2, 5, 7, 5}, {5, "F_4"}, {0, "x"}}, 
   {{2, 5, 8, 2}, {5, "F_4"}, {0, "x"}}, {{2, 5, 8, 3}, {5, "F_4"}, 
    {0, "x"}}, {{2, 5, 8, 4}, {5, "F_4"}, {0, "x"}}, 
   {{2, 5, 8, 5}, {5, "F_4"}, {0, "x"}}, {{2, 5, 8, 6}, {5, "F_4"}, 
    {0, "x"}}, {{2, 6, 9, 3}, {6, "E_6"}, {0, "x"}}, 
   {{2, 6, 9, 4}, {6, "E_6"}, {0, "x"}}, {{2, 6, 9, 5}, {6, "E_6"}, 
    {0, "x"}}, {{2, 6, 9, 6}, {6, "E_6"}, {0, "x"}}, 
   {{2, 6, 9, 7}, {7, "E_7"}, {0, "x"}}, {{2, 6, 10, 4}, {7, "E_7"}, 
    {0, "x"}}, {{2, 6, 10, 5}, {7, "E_7"}, {0, "x"}}, 
   {{2, 6, 10, 6}, {7, "E_7"}, {0, "x"}}, {{2, 6, 10, 7}, {7, "E_7"}, 
    {0, "x"}}, {{2, 6, 10, 8}, {7, "E_7"}, {0, "x"}}, 
   {{2, 7, 11, 5}, {7, "E_7"}, {0, "x"}}, {{2, 7, 11, 6}, {7, "E_7"}, 
    {0, "x"}}, {{2, 7, 11, 7}, {7, "E_7"}, {0, "x"}}, 
   {{2, 7, 11, 8}, {7, "E_7"}, {0, "x"}}, {{2, 7, 12, 6}, {7, "E_7"}, 
    {0, "x"}}, {{2, 7, 12, 7}, {7, "E_7"}, {0, "x"}}, 
   {{2, 7, 12, 8}, {7, "E_7"}, {0, "x"}}, {{3, -1, -5, 0}, {0, "x"}, 
    {3, "G_2"}}, {{3, 0, -3, 0}, {0, "x"}, {0, "x"}}, 
   {{3, 3, 3, 0}, {2, "SU(3)"}, {0, "x"}}, {{3, 3, 4, 0}, {3, "G_2"}, 
    {0, "x"}}, {{3, 3, 4, 1}, {3, "G_2"}, {0, "x"}}, 
   {{3, 4, 4, 0}, {3, "G_2"}, {0, "x"}}, {{3, 4, 4, 1}, {3, "G_2"}, 
    {0, "x"}}, {{3, 4, 5, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 4, 5, 1}, {4, "SO(8)"}, {0, "x"}}, {{3, 4, 5, 2}, {4, "SO(8)"}, 
    {0, "x"}}, {{3, 4, 6, 0}, {5, "F_4"}, {0, "x"}}, 
   {{3, 4, 6, 1}, {5, "F_4"}, {0, "x"}}, {{3, 4, 6, 2}, {5, "F_4"}, 
    {0, "x"}}, {{3, 4, 6, 3}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 6, 0}, {5, "F_4"}, {0, "x"}}, {{3, 5, 6, 1}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 6, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 6, 3}, {5, "F_4"}, {0, "x"}}, {{3, 5, 7, 1}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 7, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 7, 3}, {5, "F_4"}, {0, "x"}}, {{3, 5, 7, 4}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 8, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 8, 3}, {5, "F_4"}, {0, "x"}}, {{3, 5, 8, 4}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 8, 5}, {5, "F_4"}, {0, "x"}}, 
   {{3, 6, 8, 2}, {5, "F_4"}, {0, "x"}}, {{3, 6, 8, 3}, {5, "F_4"}, 
    {0, "x"}}, {{3, 6, 8, 4}, {5, "F_4"}, {0, "x"}}, 
   {{3, 6, 8, 5}, {5, "F_4"}, {0, "x"}}, {{3, 6, 9, 3}, {6, "E_6"}, 
    {0, "x"}}, {{3, 6, 9, 4}, {6, "E_6"}, {0, "x"}}, 
   {{3, 6, 9, 5}, {6, "E_6"}, {0, "x"}}, {{3, 6, 9, 6}, {6, "E_6"}, 
    {0, "x"}}, {{3, 7, 10, 4}, {7, "E_7"}, {0, "x"}}, 
   {{3, 7, 10, 5}, {7, "E_7"}, {0, "x"}}, {{3, 7, 10, 6}, {7, "E_7"}, 
    {0, "x"}}, {{3, 7, 10, 7}, {7, "E_7"}, {0, "x"}}, 
   {{3, 7, 11, 5}, {7, "E_7"}, {0, "x"}}, {{3, 7, 11, 6}, {7, "E_7"}, 
    {0, "x"}}, {{3, 7, 11, 7}, {7, "E_7"}, {0, "x"}}, 
   {{3, 7, 11, 8}, {7, "E_7"}, {0, "x"}}, {{3, 8, 12, 6}, {7, "E_7"}, 
    {0, "x"}}, {{3, 8, 12, 7}, {7, "E_7"}, {0, "x"}}, 
   {{3, 8, 12, 8}, {7, "E_7"}, {0, "x"}}, {{4, -1, -6, 0}, {1, "SU(2)"}, 
    {4, "SO(8)"}}, {{4, 0, -4, 0}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{4, 4, 4, 0}, {4, "SO(8)"}, {0, "x"}}, {{4, 4, 5, 0}, {5, "F_4"}, 
    {0, "x"}}, {{4, 4, 5, 1}, {5, "F_4"}, {0, "x"}}, 
   {{4, 5, 5, 0}, {5, "F_4"}, {0, "x"}}, {{4, 5, 5, 1}, {5, "F_4"}, 
    {0, "x"}}, {{4, 5, 6, 0}, {5, "F_4"}, {0, "x"}}, 
   {{4, 5, 6, 1}, {5, "F_4"}, {0, "x"}}, {{4, 5, 6, 2}, {5, "F_4"}, 
    {0, "x"}}, {{4, 5, 7, 1}, {5, "F_4"}, {0, "x"}}, 
   {{4, 5, 7, 2}, {5, "F_4"}, {0, "x"}}, {{4, 5, 7, 3}, {5, "F_4"}, 
    {0, "x"}}, {{4, 6, 7, 1}, {5, "F_4"}, {0, "x"}}, 
   {{4, 6, 7, 2}, {5, "F_4"}, {0, "x"}}, {{4, 6, 7, 3}, {5, "F_4"}, 
    {0, "x"}}, {{4, 6, 8, 2}, {6, "E_6"}, {0, "x"}}, 
   {{4, 6, 8, 3}, {6, "E_6"}, {0, "x"}}, {{4, 6, 8, 4}, {6, "E_6"}, 
    {0, "x"}}, {{4, 7, 9, 3}, {7, "E_7"}, {0, "x"}}, 
   {{4, 7, 9, 4}, {7, "E_7"}, {0, "x"}}, {{4, 7, 9, 5}, {7, "E_7"}, 
    {0, "x"}}, {{4, 7, 10, 4}, {7, "E_7"}, {0, "x"}}, 
   {{4, 7, 10, 5}, {7, "E_7"}, {0, "x"}}, {{4, 7, 10, 6}, {7, "E_7"}, 
    {0, "x"}}, {{4, 8, 11, 5}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 11, 6}, {7, "E_7"}, {0, "x"}}, {{4, 8, 11, 7}, {7, "E_7"}, 
    {0, "x"}}, {{4, 8, 12, 6}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 12, 7}, {7, "E_7"}, {0, "x"}}, {{4, 8, 12, 8}, {7, "E_7"}, 
    {0, "x"}}, {{5, 0, -5, 0}, {3, "G_2"}, {3, "G_2"}}, 
   {{5, 5, 5, 0}, {5, "F_4"}, {0, "x"}}, {{5, 5, 6, 0}, {5, "F_4"}, 
    {0, "x"}}, {{5, 5, 6, 1}, {5, "F_4"}, {0, "x"}}, 
   {{5, 6, 6, 0}, {5, "F_4"}, {0, "x"}}, {{5, 6, 6, 1}, {5, "F_4"}, 
    {0, "x"}}, {{5, 6, 7, 1}, {6, "E_6"}, {0, "x"}}, 
   {{5, 6, 7, 2}, {6, "E_6"}, {0, "x"}}, {{5, 7, 8, 2}, {7, "E_7"}, 
    {0, "x"}}, {{5, 7, 8, 3}, {7, "E_7"}, {0, "x"}}, 
   {{5, 7, 9, 3}, {7, "E_7"}, {0, "x"}}, {{5, 7, 9, 4}, {7, "E_7"}, 
    {0, "x"}}, {{5, 8, 10, 4}, {7, "E_7"}, {0, "x"}}, 
   {{5, 8, 10, 5}, {7, "E_7"}, {0, "x"}}, {{5, 8, 11, 5}, {7, "E_7"}, 
    {0, "x"}}, {{5, 8, 11, 6}, {7, "E_7"}, {0, "x"}}, 
   {{6, 0, -6, 0}, {4, "SO(8)"}, {4, "SO(8)"}}, {{6, 6, 6, 0}, {6, "E_6"}, 
    {0, "x"}}, {{6, 7, 7, 1}, {7, "E_7"}, {0, "x"}}, 
   {{6, 7, 8, 2}, {7, "E_7"}, {0, "x"}}, {{6, 8, 9, 3}, {7, "E_7"}, 
    {0, "x"}}, {{6, 8, 10, 4}, {7, "E_7"}, {0, "x"}}, 
   {{6, 12, 18, 12}, {8, "E_8"}, {0, "x"}}}}, 
 {{{0, 1}, {1, 0}, {0, -1}, {-1, -2}, {-1, -1}, {-1, 0}}, 
  {{{-6, -11, -5, 1}, {0, "x"}, {5, "F_4"}}, {{-5, -11, -5, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-5, -10, -5, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -10, -4, 2}, {0, "x"}, {5, "F_4"}}, {{-5, -9, -4, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-5, -9, -4, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -9, -3, 3}, {1, "SU(2)"}, {5, "F_4"}}, {{-4, -9, -4, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-4, -9, -4, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -9, -3, 3}, {1, "SU(2)"}, {5, "F_4"}}, {{-4, -8, -4, 1}, {0, "x"}, 
    {4, "SO(8)"}}, {{-4, -8, -3, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -8, -3, 3}, {1, "SU(2)"}, {4, "SO(8)"}}, 
   {{-4, -8, -2, 4}, {3, "G_2"}, {4, "SO(8)"}}, {{-4, -7, -3, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-4, -7, -3, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -7, -2, 3}, {1, "SU(2)"}, {3, "G_2"}}, {{-4, -7, -2, 4}, {3, "G_2"}, 
    {3, "G_2"}}, {{-4, -7, -1, 5}, {5, "F_4"}, {3, "G_2"}}, 
   {{-3, -7, -3, 1}, {0, "x"}, {3, "G_2"}}, {{-3, -7, -3, 2}, {0, "x"}, 
    {3, "G_2"}}, {{-3, -7, -2, 3}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{-3, -7, -2, 4}, {3, "G_2"}, {3, "G_2"}}, {{-3, -7, -1, 5}, {5, "F_4"}, 
    {3, "G_2"}}, {{-3, -6, -3, 1}, {0, "x"}, {2, "SU(3)"}}, 
   {{-3, -6, -2, 2}, {0, "x"}, {2, "SU(3)"}}, {{-3, -6, -2, 3}, {1, "SU(2)"}, 
    {2, "SU(3)"}}, {{-3, -6, -1, 4}, {3, "G_2"}, {2, "SU(3)"}}, 
   {{-3, -6, -1, 5}, {5, "F_4"}, {2, "SU(3)"}}, {{-3, -6, 0, 6}, {5, "F_4"}, 
    {2, "SU(3)"}}, {{-3, -5, -2, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -5, -2, 2}, {0, "x"}, {1, "SU(2)"}}, {{-3, -5, -1, 3}, {1, "SU(2)"}, 
    {1, "SU(2)"}}, {{-3, -5, -1, 4}, {3, "G_2"}, {1, "SU(2)"}}, 
   {{-3, -5, 0, 5}, {5, "F_4"}, {1, "SU(2)"}}, {{-3, -5, 0, 6}, {5, "F_4"}, 
    {1, "SU(2)"}}, {{-2, -5, -2, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -5, -2, 2}, {0, "x"}, {1, "SU(2)"}}, {{-2, -5, -1, 3}, {1, "SU(2)"}, 
    {1, "SU(2)"}}, {{-2, -5, -1, 4}, {3, "G_2"}, {1, "SU(2)"}}, 
   {{-2, -5, 0, 5}, {5, "F_4"}, {1, "SU(2)"}}, {{-2, -5, 1, 7}, {7, "E_7"}, 
    {1, "SU(2)"}}, {{-2, -4, -2, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -4, -1, 1}, {0, "x"}, {0, "x"}}, {{-2, -4, -1, 2}, {0, "x"}, 
    {0, "x"}}, {{-2, -4, -1, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-2, -4, 0, 4}, {3, "G_2"}, {0, "x"}}, {{-2, -4, 0, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-2, -4, 1, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-2, -4, 2, 8}, {7, "E_7"}, {0, "x"}}, {{-2, -3, -1, 1}, {0, "x"}, 
    {0, "x"}}, {{-2, -3, -1, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, -3, 0, 2}, {0, "x"}, {0, "x"}}, {{-2, -3, 0, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{-2, -3, 0, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-2, -3, 1, 5}, {5, "F_4"}, {0, "x"}}, {{-2, -3, 1, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-1, -3, -1, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -3, -1, 2}, {0, "x"}, {0, "x"}}, {{-1, -3, 0, 2}, {0, "x"}, 
    {0, "x"}}, {{-1, -3, 0, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-1, -3, 0, 4}, {3, "G_2"}, {0, "x"}}, {{-1, -3, 1, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-1, -3, 2, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-1, -2, -1, 1}, {0, "x"}, {0, "x"}}, {{-1, -2, 0, 1}, {0, "x"}, 
    {0, "x"}}, {{-1, -2, 0, 2}, {0, "x"}, {0, "x"}}, 
   {{-1, -2, 0, 3}, {1, "SU(2)"}, {0, "x"}}, {{-1, -2, 1, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{-1, -2, 1, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-1, -2, 1, 5}, {5, "F_4"}, {0, "x"}}, {{-1, -2, 2, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-1, -2, 3, 8}, {7, "E_7"}, {0, "x"}}, 
   {{-1, -1, 0, 1}, {0, "x"}, {0, "x"}}, {{-1, -1, 0, 2}, {0, "x"}, 
    {0, "x"}}, {{-1, -1, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{-1, -1, 1, 3}, {1, "SU(2)"}, {0, "x"}}, {{-1, -1, 1, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-1, -1, 2, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-1, -1, 2, 5}, {5, "F_4"}, {0, "x"}}, {{-1, -1, 2, 6}, {5, "F_4"}, 
    {0, "x"}}, {{0, -1, 0, 1}, {0, "x"}, {0, "x"}}, 
   {{0, -1, 0, 2}, {0, "x"}, {0, "x"}}, {{0, -1, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{0, -1, 1, 3}, {1, "SU(2)"}, {0, "x"}}, {{0, -1, 1, 4}, {3, "G_2"}, 
    {0, "x"}}, {{0, -1, 2, 4}, {3, "G_2"}, {0, "x"}}, 
   {{0, -1, 2, 5}, {5, "F_4"}, {0, "x"}}, {{0, -1, 3, 7}, {7, "E_7"}, 
    {0, "x"}}, {{0, 0, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 0, 1}, {0, "x"}, {0, "x"}}, {{0, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 1, 2}, {0, "x"}, {0, "x"}}, {{0, 0, 1, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{0, 0, 2, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{0, 0, 2, 4}, {3, "G_2"}, {0, "x"}}, {{0, 0, 2, 5}, {5, "F_4"}, 
    {0, "x"}}, {{0, 0, 3, 5}, {5, "F_4"}, {0, "x"}}, 
   {{0, 0, 3, 6}, {5, "F_4"}, {0, "x"}}, {{0, 0, 4, 8}, {7, "E_7"}, 
    {0, "x"}}, {{0, 1, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{0, 1, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 1, 2}, {0, "x"}, {0, "x"}}, {{0, 1, 2, 2}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 2, 3}, {1, "SU(2)"}, {0, "x"}}, {{0, 1, 2, 4}, {3, "G_2"}, 
    {0, "x"}}, {{0, 1, 3, 4}, {3, "G_2"}, {0, "x"}}, 
   {{0, 1, 3, 5}, {5, "F_4"}, {0, "x"}}, {{0, 1, 3, 6}, {5, "F_4"}, 
    {0, "x"}}, {{1, 1, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 1, 2}, {0, "x"}, {0, "x"}}, {{1, 1, 2, 2}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 2, 3}, {1, "SU(2)"}, {0, "x"}}, {{1, 1, 2, 4}, {3, "G_2"}, 
    {0, "x"}}, {{1, 1, 3, 4}, {3, "G_2"}, {0, "x"}}, 
   {{1, 1, 3, 5}, {5, "F_4"}, {0, "x"}}, {{1, 1, 4, 6}, {5, "F_4"}, 
    {0, "x"}}, {{1, 1, 4, 7}, {7, "E_7"}, {0, "x"}}, 
   {{1, 2, 1, 0}, {0, "x"}, {0, "x"}}, {{1, 2, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 2, 1}, {0, "x"}, {0, "x"}}, {{1, 2, 2, 2}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 2, 3}, {1, "SU(2)"}, {0, "x"}}, {{1, 2, 3, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{1, 2, 3, 4}, {3, "G_2"}, {0, "x"}}, 
   {{1, 2, 3, 5}, {5, "F_4"}, {0, "x"}}, {{1, 2, 4, 5}, {5, "F_4"}, 
    {0, "x"}}, {{1, 2, 4, 6}, {5, "F_4"}, {0, "x"}}, 
   {{1, 2, 5, 7}, {7, "E_7"}, {0, "x"}}, {{1, 2, 5, 8}, {7, "E_7"}, 
    {0, "x"}}, {{1, 3, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 3, 2, 0}, {0, "x"}, {0, "x"}}, {{1, 3, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 3, 2, 2}, {0, "x"}, {0, "x"}}, {{1, 3, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{1, 3, 3, 3}, {1, "SU(2)"}, {0, "x"}}, {{1, 3, 3, 4}, {3, "G_2"}, 
    {0, "x"}}, {{1, 3, 4, 4}, {3, "G_2"}, {0, "x"}}, 
   {{1, 3, 4, 5}, {5, "F_4"}, {0, "x"}}, {{1, 3, 4, 6}, {5, "F_4"}, 
    {0, "x"}}, {{2, 3, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 3, 2, 0}, {0, "x"}, {0, "x"}}, {{2, 3, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{2, 3, 2, 2}, {0, "x"}, {0, "x"}}, {{2, 3, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{2, 3, 3, 3}, {1, "SU(2)"}, {0, "x"}}, {{2, 3, 3, 4}, {3, "G_2"}, 
    {0, "x"}}, {{2, 3, 4, 4}, {3, "G_2"}, {0, "x"}}, 
   {{2, 3, 4, 5}, {5, "F_4"}, {0, "x"}}, {{2, 3, 5, 6}, {5, "F_4"}, 
    {0, "x"}}, {{2, 3, 5, 7}, {7, "E_7"}, {0, "x"}}, 
   {{2, 3, 6, 8}, {7, "E_7"}, {0, "x"}}, {{2, 4, 2, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 4, 2, 1}, {0, "x"}, {0, "x"}}, {{2, 4, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{2, 4, 3, 2}, {0, "x"}, {0, "x"}}, {{2, 4, 3, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 4, 4, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 4, 4, 4}, {3, "G_2"}, {0, "x"}}, {{2, 4, 4, 5}, {5, "F_4"}, 
    {0, "x"}}, {{2, 4, 5, 5}, {5, "F_4"}, {0, "x"}}, 
   {{2, 4, 5, 6}, {5, "F_4"}, {0, "x"}}, {{2, 4, 6, 7}, {7, "E_7"}, 
    {0, "x"}}, {{2, 4, 6, 8}, {7, "E_7"}, {0, "x"}}, 
   {{2, 5, 2, 0}, {1, "SU(2)"}, {0, "x"}}, {{2, 5, 3, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 5, 3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 5, 3, 2}, {1, "SU(2)"}, {0, "x"}}, {{2, 5, 4, 2}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 5, 4, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 5, 4, 4}, {3, "G_2"}, {0, "x"}}, {{2, 5, 5, 4}, {3, "G_2"}, 
    {0, "x"}}, {{2, 5, 5, 5}, {5, "F_4"}, {0, "x"}}, 
   {{2, 5, 5, 6}, {5, "F_4"}, {0, "x"}}, {{3, 5, 2, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{3, 5, 3, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 5, 3, 1}, {1, "SU(2)"}, {0, "x"}}, {{3, 5, 3, 2}, {1, "SU(2)"}, 
    {0, "x"}}, {{3, 5, 4, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 5, 4, 3}, {2, "SU(3)"}, {0, "x"}}, {{3, 5, 4, 4}, {3, "G_2"}, 
    {0, "x"}}, {{3, 5, 5, 4}, {3, "G_2"}, {0, "x"}}, 
   {{3, 5, 5, 5}, {5, "F_4"}, {0, "x"}}, {{3, 5, 6, 6}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 6, 7}, {7, "E_7"}, {0, "x"}}, 
   {{3, 5, 7, 8}, {7, "E_7"}, {0, "x"}}, {{3, 6, 3, 0}, {2, "SU(3)"}, 
    {0, "x"}}, {{3, 6, 3, 1}, {2, "SU(3)"}, {0, "x"}}, 
   {{3, 6, 4, 1}, {2, "SU(3)"}, {0, "x"}}, {{3, 6, 4, 2}, {2, "SU(3)"}, 
    {0, "x"}}, {{3, 6, 4, 3}, {2, "SU(3)"}, {0, "x"}}, 
   {{3, 6, 5, 3}, {3, "G_2"}, {0, "x"}}, {{3, 6, 5, 4}, {3, "G_2"}, 
    {0, "x"}}, {{3, 6, 5, 5}, {5, "F_4"}, {0, "x"}}, 
   {{3, 6, 6, 5}, {5, "F_4"}, {0, "x"}}, {{3, 6, 6, 6}, {5, "F_4"}, 
    {0, "x"}}, {{3, 6, 7, 7}, {7, "E_7"}, {0, "x"}}, 
   {{3, 6, 7, 8}, {7, "E_7"}, {0, "x"}}, {{3, 7, 4, 0}, {3, "G_2"}, 
    {0, "x"}}, {{3, 7, 4, 1}, {3, "G_2"}, {0, "x"}}, 
   {{3, 7, 4, 2}, {3, "G_2"}, {0, "x"}}, {{3, 7, 5, 2}, {3, "G_2"}, 
    {0, "x"}}, {{3, 7, 5, 3}, {3, "G_2"}, {0, "x"}}, 
   {{3, 7, 5, 4}, {3, "G_2"}, {0, "x"}}, {{3, 7, 6, 4}, {4, "SO(8)"}, 
    {0, "x"}}, {{3, 7, 6, 5}, {5, "F_4"}, {0, "x"}}, 
   {{3, 7, 6, 6}, {5, "F_4"}, {0, "x"}}, {{4, 7, 4, 0}, {3, "G_2"}, 
    {0, "x"}}, {{4, 7, 4, 1}, {3, "G_2"}, {0, "x"}}, 
   {{4, 7, 4, 2}, {3, "G_2"}, {0, "x"}}, {{4, 7, 5, 2}, {3, "G_2"}, 
    {0, "x"}}, {{4, 7, 5, 3}, {3, "G_2"}, {0, "x"}}, 
   {{4, 7, 5, 4}, {4, "SO(8)"}, {0, "x"}}, {{4, 7, 6, 4}, {4, "SO(8)"}, 
    {0, "x"}}, {{4, 7, 6, 5}, {5, "F_4"}, {0, "x"}}, 
   {{4, 7, 7, 6}, {5, "F_4"}, {0, "x"}}, {{4, 7, 7, 7}, {7, "E_7"}, 
    {0, "x"}}, {{4, 7, 8, 8}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 4, 0}, {4, "SO(8)"}, {0, "x"}}, {{4, 8, 5, 1}, {4, "SO(8)"}, 
    {0, "x"}}, {{4, 8, 5, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 8, 5, 3}, {4, "SO(8)"}, {0, "x"}}, {{4, 8, 6, 3}, {4, "SO(8)"}, 
    {0, "x"}}, {{4, 8, 6, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 8, 6, 5}, {5, "F_4"}, {0, "x"}}, {{4, 8, 7, 5}, {5, "F_4"}, 
    {0, "x"}}, {{4, 8, 7, 6}, {5, "F_4"}, {0, "x"}}, 
   {{4, 8, 8, 7}, {7, "E_7"}, {0, "x"}}, {{4, 8, 8, 8}, {7, "E_7"}, 
    {0, "x"}}, {{4, 9, 5, 0}, {5, "F_4"}, {0, "x"}}, 
   {{4, 9, 5, 1}, {5, "F_4"}, {0, "x"}}, {{4, 9, 6, 2}, {5, "F_4"}, 
    {0, "x"}}, {{4, 9, 6, 3}, {5, "F_4"}, {0, "x"}}, 
   {{4, 9, 6, 4}, {5, "F_4"}, {0, "x"}}, {{4, 9, 7, 4}, {5, "F_4"}, 
    {0, "x"}}, {{4, 9, 7, 5}, {5, "F_4"}, {0, "x"}}, 
   {{4, 9, 7, 6}, {5, "F_4"}, {0, "x"}}, {{5, 9, 5, 0}, {5, "F_4"}, 
    {0, "x"}}, {{5, 9, 5, 1}, {5, "F_4"}, {0, "x"}}, 
   {{5, 9, 6, 2}, {5, "F_4"}, {0, "x"}}, {{5, 9, 6, 3}, {5, "F_4"}, 
    {0, "x"}}, {{5, 9, 6, 4}, {5, "F_4"}, {0, "x"}}, 
   {{5, 9, 7, 4}, {5, "F_4"}, {0, "x"}}, {{5, 9, 7, 5}, {5, "F_4"}, 
    {0, "x"}}, {{5, 9, 8, 6}, {5, "F_4"}, {0, "x"}}, 
   {{5, 9, 8, 7}, {7, "E_7"}, {0, "x"}}, {{5, 9, 9, 8}, {7, "E_7"}, 
    {0, "x"}}, {{5, 10, 5, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 10, 6, 1}, {5, "F_4"}, {0, "x"}}, {{5, 10, 6, 2}, {5, "F_4"}, 
    {0, "x"}}, {{5, 10, 7, 3}, {5, "F_4"}, {0, "x"}}, 
   {{5, 10, 7, 4}, {5, "F_4"}, {0, "x"}}, {{5, 10, 7, 5}, {5, "F_4"}, 
    {0, "x"}}, {{5, 10, 8, 5}, {5, "F_4"}, {0, "x"}}, 
   {{5, 10, 8, 6}, {5, "F_4"}, {0, "x"}}, {{5, 10, 9, 7}, {7, "E_7"}, 
    {0, "x"}}, {{5, 10, 9, 8}, {7, "E_7"}, {0, "x"}}, 
   {{5, 11, 6, 0}, {5, "F_4"}, {0, "x"}}, {{5, 11, 6, 1}, {5, "F_4"}, 
    {0, "x"}}, {{5, 11, 7, 2}, {5, "F_4"}, {0, "x"}}, 
   {{5, 11, 7, 3}, {5, "F_4"}, {0, "x"}}, {{5, 11, 8, 4}, {5, "F_4"}, 
    {0, "x"}}, {{5, 11, 8, 5}, {5, "F_4"}, {0, "x"}}, 
   {{5, 11, 8, 6}, {5, "F_4"}, {0, "x"}}, {{6, 11, 6, 0}, {5, "F_4"}, 
    {0, "x"}}, {{6, 11, 6, 1}, {5, "F_4"}, {0, "x"}}, 
   {{6, 11, 7, 2}, {5, "F_4"}, {0, "x"}}, {{6, 11, 7, 3}, {5, "F_4"}, 
    {0, "x"}}, {{6, 11, 8, 4}, {5, "F_4"}, {0, "x"}}, 
   {{6, 11, 8, 5}, {5, "F_4"}, {0, "x"}}, {{6, 11, 9, 6}, {6, "E_6"}, 
    {0, "x"}}, {{6, 11, 9, 7}, {7, "E_7"}, {0, "x"}}, 
   {{6, 11, 10, 8}, {7, "E_7"}, {0, "x"}}, {{6, 12, 6, 0}, {6, "E_6"}, 
    {0, "x"}}, {{6, 12, 7, 1}, {6, "E_6"}, {0, "x"}}, 
   {{6, 12, 7, 2}, {6, "E_6"}, {0, "x"}}, {{6, 12, 8, 3}, {6, "E_6"}, 
    {0, "x"}}, {{6, 12, 8, 4}, {6, "E_6"}, {0, "x"}}, 
   {{6, 12, 9, 5}, {6, "E_6"}, {0, "x"}}, {{6, 12, 9, 6}, {6, "E_6"}, 
    {0, "x"}}, {{6, 12, 10, 7}, {7, "E_7"}, {0, "x"}}, 
   {{6, 12, 10, 8}, {7, "E_7"}, {0, "x"}}, {{7, 13, 7, 1}, {7, "E_7"}, 
    {0, "x"}}, {{7, 13, 8, 2}, {7, "E_7"}, {0, "x"}}, 
   {{7, 13, 8, 3}, {7, "E_7"}, {0, "x"}}, {{7, 13, 9, 4}, {7, "E_7"}, 
    {0, "x"}}, {{7, 13, 9, 5}, {7, "E_7"}, {0, "x"}}, 
   {{7, 13, 10, 6}, {7, "E_7"}, {0, "x"}}, {{7, 13, 10, 7}, {7, "E_7"}, 
    {0, "x"}}, {{7, 13, 11, 8}, {7, "E_7"}, {0, "x"}}, 
   {{7, 14, 8, 2}, {7, "E_7"}, {0, "x"}}, {{7, 14, 9, 3}, {7, "E_7"}, 
    {0, "x"}}, {{7, 14, 9, 4}, {7, "E_7"}, {0, "x"}}, 
   {{7, 14, 10, 5}, {7, "E_7"}, {0, "x"}}, {{7, 14, 10, 6}, {7, "E_7"}, 
    {0, "x"}}, {{7, 14, 11, 7}, {7, "E_7"}, {0, "x"}}, 
   {{7, 14, 11, 8}, {7, "E_7"}, {0, "x"}}, {{8, 15, 9, 3}, {7, "E_7"}, 
    {0, "x"}}, {{8, 15, 10, 4}, {7, "E_7"}, {0, "x"}}, 
   {{8, 15, 10, 5}, {7, "E_7"}, {0, "x"}}, {{8, 15, 11, 6}, {7, "E_7"}, 
    {0, "x"}}, {{8, 15, 11, 7}, {7, "E_7"}, {0, "x"}}, 
   {{8, 15, 12, 8}, {7, "E_7"}, {0, "x"}}, {{8, 16, 10, 4}, {7, "E_7"}, 
    {0, "x"}}, {{8, 16, 11, 5}, {7, "E_7"}, {0, "x"}}, 
   {{8, 16, 11, 6}, {7, "E_7"}, {0, "x"}}, {{8, 16, 12, 7}, {7, "E_7"}, 
    {0, "x"}}, {{8, 16, 12, 8}, {7, "E_7"}, {0, "x"}}, 
   {{12, 24, 18, 12}, {8, "E_8"}, {0, "x"}}}}, 
 {{{0, 1}, {1, 0}, {0, -1}, {-1, -2}, {-2, -3}, {-1, -1}}, 
  {{{0, 0, 0, 0}, {0, "x"}, {0, "x"}}, {{0, 0, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 1, 1}, {0, "x"}, {0, "x"}}, {{0, 1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 1, 1}, {0, "x"}, {0, "x"}}, {{0, 1, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 2, 1}, {0, "x"}, {0, "x"}}, {{1, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 3, 1}, {0, "x"}, {0, "x"}}, {{1, 2, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 4, 2}, {0, "x"}, {0, "x"}}, {{1, 3, 4, 2}, {0, "x"}, {0, "x"}}, 
   {{1, 3, 5, 2}, {0, "x"}, {0, "x"}}, {{1, 3, 5, 3}, {0, "x"}, {0, "x"}}, 
   {{2, 3, 4, 2}, {0, "x"}, {0, "x"}}, {{2, 3, 5, 2}, {0, "x"}, {0, "x"}}, 
   {{2, 3, 5, 3}, {0, "x"}, {0, "x"}}, {{2, 4, 5, 2}, {0, "x"}, {0, "x"}}, 
   {{2, 4, 5, 3}, {0, "x"}, {0, "x"}}, {{2, 4, 6, 3}, {0, "x"}, {0, "x"}}, 
   {{2, 4, 7, 3}, {0, "x"}, {0, "x"}}, {{2, 4, 7, 4}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 5, 7, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 5, 7, 4}, {1, "SU(2)"}, {0, "x"}}, {{2, 5, 8, 4}, {1, "SU(2)"}, 
    {0, "x"}}, {{3, 5, 7, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 5, 7, 4}, {1, "SU(2)"}, {0, "x"}}, {{3, 5, 8, 4}, {1, "SU(2)"}, 
    {0, "x"}}, {{3, 6, 8, 4}, {2, "SU(3)"}, {0, "x"}}, 
   {{3, 6, 9, 4}, {2, "SU(3)"}, {0, "x"}}, {{3, 6, 9, 5}, {3, "G_2"}, 
    {0, "x"}}, {{3, 6, 10, 5}, {3, "G_2"}, {0, "x"}}, 
   {{3, 7, 10, 5}, {3, "G_2"}, {0, "x"}}, {{3, 7, 11, 5}, {3, "G_2"}, 
    {0, "x"}}, {{4, 7, 10, 5}, {3, "G_2"}, {0, "x"}}, 
   {{4, 7, 11, 5}, {3, "G_2"}, {0, "x"}}, {{4, 7, 11, 6}, {4, "SO(8)"}, 
    {0, "x"}}, {{4, 8, 11, 5}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 8, 11, 6}, {4, "SO(8)"}, {0, "x"}}, {{4, 8, 12, 6}, {4, "SO(8)"}, 
    {0, "x"}}, {{4, 9, 13, 6}, {5, "F_4"}, {0, "x"}}, 
   {{4, 9, 13, 7}, {5, "F_4"}, {0, "x"}}, {{5, 9, 13, 6}, {5, "F_4"}, 
    {0, "x"}}, {{5, 9, 13, 7}, {5, "F_4"}, {0, "x"}}, 
   {{5, 9, 14, 7}, {5, "F_4"}, {0, "x"}}, {{5, 10, 14, 7}, {5, "F_4"}, 
    {0, "x"}}, {{5, 10, 15, 7}, {5, "F_4"}, {0, "x"}}, 
   {{5, 10, 15, 8}, {5, "F_4"}, {0, "x"}}, {{5, 11, 16, 8}, {5, "F_4"}, 
    {0, "x"}}, {{6, 11, 16, 8}, {5, "F_4"}, {0, "x"}}, 
   {{6, 11, 17, 8}, {5, "F_4"}, {0, "x"}}, {{6, 12, 17, 9}, {6, "E_6"}, 
    {0, "x"}}, {{6, 12, 18, 9}, {6, "E_6"}, {0, "x"}}, 
   {{7, 13, 19, 10}, {7, "E_7"}, {0, "x"}}, {{7, 14, 20, 10}, {7, "E_7"}, 
    {0, "x"}}, {{7, 14, 21, 11}, {7, "E_7"}, {0, "x"}}, 
   {{8, 15, 22, 11}, {7, "E_7"}, {0, "x"}}, {{8, 16, 23, 12}, {7, "E_7"}, 
    {0, "x"}}, {{8, 16, 24, 12}, {7, "E_7"}, {0, "x"}}, 
   {{12, 24, 36, 18}, {8, "E_8"}, {0, "x"}}}}, 
 {{{0, 1}, {1, 0}, {1, -1}, {0, -1}, {-1, -1}, {-1, 0}, {-1, 1}}, 
  {{{-6, -8, -10, -5, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -8, -10, -4, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -8, -9, -4, 1}, {0, "x"}, {7, "E_7"}}, {{-6, -8, -9, -4, 2}, 
    {0, "x"}, {7, "E_7"}}, {{-6, -8, -9, -3, 3}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -7, -8, -4, 1}, {0, "x"}, {7, "E_7"}}, {{-6, -7, -8, -3, 2}, 
    {0, "x"}, {7, "E_7"}}, {{-6, -7, -8, -3, 3}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -7, -8, -2, 4}, {0, "x"}, {7, "E_7"}}, {{-6, -7, -7, -3, 1}, 
    {0, "x"}, {7, "E_7"}}, {{-6, -7, -7, -3, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -7, -7, -2, 3}, {0, "x"}, {7, "E_7"}}, {{-6, -7, -7, -2, 4}, 
    {0, "x"}, {7, "E_7"}}, {{-6, -7, -7, -1, 5}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -6, -6, -3, 1}, {0, "x"}, {6, "E_6"}}, {{-6, -6, -6, -2, 2}, 
    {0, "x"}, {6, "E_6"}}, {{-6, -6, -6, -2, 3}, {0, "x"}, {6, "E_6"}}, 
   {{-6, -6, -6, -1, 4}, {0, "x"}, {6, "E_6"}}, {{-6, -6, -6, -1, 5}, 
    {0, "x"}, {6, "E_6"}}, {{-6, -6, -6, 0, 6}, {0, "x"}, {6, "E_6"}}, 
   {{-6, -6, -5, -2, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -6, -5, -2, 2}, 
    {0, "x"}, {5, "F_4"}}, {{-6, -6, -5, -1, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -6, -5, -1, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -6, -5, 0, 5}, {0, "x"}, {5, "F_4"}}, {{-6, -6, -5, 0, 6}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -5, -5, -2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -5, -5, -2, 2}, {0, "x"}, {5, "F_4"}}, {{-6, -5, -5, -1, 3}, 
    {0, "x"}, {5, "F_4"}}, {{-6, -5, -5, -1, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -5, -5, 0, 5}, {0, "x"}, {5, "F_4"}}, {{-6, -5, -5, 0, 6}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -5, -4, -2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -5, -4, -1, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -5, -4, -1, 2}, 
    {0, "x"}, {5, "F_4"}}, {{-6, -5, -4, -1, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -5, -4, 0, 4}, {0, "x"}, {5, "F_4"}}, {{-6, -5, -4, 0, 5}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -5, -4, 1, 6}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -5, -3, -1, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -5, -3, -1, 2}, 
    {0, "x"}, {5, "F_4"}}, {{-6, -5, -3, 0, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -5, -3, 0, 3}, {0, "x"}, {5, "F_4"}}, {{-6, -5, -3, 0, 4}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -5, -3, 1, 5}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -5, -3, 1, 6}, {0, "x"}, {5, "F_4"}}, {{-6, -4, -3, -1, 1}, 
    {0, "x"}, {5, "F_4"}}, {{-6, -4, -3, -1, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -4, -3, 0, 2}, {0, "x"}, {5, "F_4"}}, {{-6, -4, -3, 0, 3}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -4, -3, 0, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -4, -3, 1, 5}, {0, "x"}, {5, "F_4"}}, {{-6, -4, -3, 1, 6}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -4, -2, -1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -4, -2, 0, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -4, -2, 0, 2}, {0, "x"}, 
    {4, "SO(8)"}}, {{-6, -4, -2, 0, 3}, {0, "x"}, {4, "SO(8)"}}, 
   {{-6, -4, -2, 1, 3}, {0, "x"}, {4, "SO(8)"}}, 
   {{-6, -4, -2, 1, 4}, {0, "x"}, {4, "SO(8)"}}, 
   {{-6, -4, -2, 1, 5}, {0, "x"}, {4, "SO(8)"}}, 
   {{-6, -4, -2, 2, 6}, {0, "x"}, {4, "SO(8)"}}, 
   {{-6, -4, -1, 0, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -4, -1, 0, 2}, {0, "x"}, 
    {4, "SO(8)"}}, {{-6, -4, -1, 1, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-6, -4, -1, 1, 3}, {0, "x"}, {3, "G_2"}}, {{-6, -4, -1, 1, 4}, {0, "x"}, 
    {3, "G_2"}}, {{-6, -4, -1, 2, 4}, {0, "x"}, {3, "G_2"}}, 
   {{-6, -4, -1, 2, 5}, {0, "x"}, {3, "G_2"}}, {{-6, -4, -1, 2, 6}, 
    {1, "SU(2)"}, {3, "G_2"}}, {{-6, -3, -1, 0, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -3, -1, 0, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-6, -3, -1, 1, 2}, {0, "x"}, {3, "G_2"}}, {{-6, -3, -1, 1, 3}, {0, "x"}, 
    {3, "G_2"}}, {{-6, -3, -1, 1, 4}, {0, "x"}, {3, "G_2"}}, 
   {{-6, -3, -1, 2, 4}, {0, "x"}, {3, "G_2"}}, {{-6, -3, -1, 2, 5}, {0, "x"}, 
    {3, "G_2"}}, {{-6, -3, -1, 2, 6}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{-6, -3, 0, 0, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -3, 0, 1, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -3, 0, 1, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-6, -3, 0, 1, 3}, {0, "x"}, {3, "G_2"}}, {{-6, -3, 0, 2, 3}, {0, "x"}, 
    {2, "SU(3)"}}, {{-6, -3, 0, 2, 4}, {0, "x"}, {2, "SU(3)"}}, 
   {{-6, -3, 0, 2, 5}, {1, "SU(2)"}, {2, "SU(3)"}}, 
   {{-6, -3, 0, 3, 5}, {1, "SU(2)"}, {2, "SU(3)"}}, 
   {{-6, -3, 0, 3, 6}, {2, "SU(3)"}, {2, "SU(3)"}}, 
   {{-6, -2, 1, 1, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -2, 1, 1, 2}, {0, "x"}, 
    {3, "G_2"}}, {{-6, -2, 1, 2, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-6, -2, 1, 2, 3}, {0, "x"}, {1, "SU(2)"}}, 
   {{-6, -2, 1, 2, 4}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-6, -2, 1, 3, 4}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-6, -2, 1, 3, 5}, {2, "SU(3)"}, {1, "SU(2)"}}, 
   {{-6, -2, 2, 1, 1}, {0, "x"}, {5, "F_4"}}, {{-6, -2, 2, 2, 1}, {0, "x"}, 
    {5, "F_4"}}, {{-6, -2, 2, 2, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-6, -2, 2, 2, 3}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-6, -2, 2, 3, 3}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-6, -2, 2, 3, 4}, {2, "SU(3)"}, {0, "x"}}, 
   {{-6, -2, 2, 3, 5}, {3, "G_2"}, {0, "x"}}, {{-6, -2, 2, 4, 5}, {3, "G_2"}, 
    {0, "x"}}, {{-6, -1, 3, 2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -1, 3, 2, 2}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{-6, -1, 3, 3, 2}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{-6, -1, 3, 3, 3}, {2, "SU(3)"}, {1, "SU(2)"}}, 
   {{-6, -1, 3, 3, 4}, {3, "G_2"}, {0, "x"}}, {{-6, -1, 3, 4, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-6, -1, 3, 4, 5}, {4, "SO(8)"}, {0, "x"}}, 
   {{-6, -1, 4, 2, 1}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{-6, -1, 4, 3, 1}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{-6, -1, 4, 3, 2}, {2, "SU(3)"}, {3, "G_2"}}, 
   {{-6, -1, 4, 3, 3}, {3, "G_2"}, {1, "SU(2)"}}, 
   {{-6, -1, 4, 4, 3}, {3, "G_2"}, {1, "SU(2)"}}, 
   {{-6, -1, 4, 4, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{-6, -1, 4, 4, 5}, {5, "F_4"}, {0, "x"}}, {{-6, -1, 4, 5, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-6, 0, 5, 3, 1}, {3, "G_2"}, {5, "F_4"}}, 
   {{-6, 0, 5, 3, 2}, {3, "G_2"}, {3, "G_2"}}, {{-6, 0, 5, 4, 2}, {3, "G_2"}, 
    {3, "G_2"}}, {{-6, 0, 5, 4, 3}, {4, "SO(8)"}, {1, "SU(2)"}}, 
   {{-6, 0, 5, 4, 4}, {5, "F_4"}, {0, "x"}}, {{-6, 0, 5, 5, 4}, {5, "F_4"}, 
    {0, "x"}}, {{-6, 0, 5, 5, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-6, 0, 6, 3, 1}, {4, "SO(8)"}, {5, "F_4"}}, 
   {{-6, 0, 6, 4, 1}, {4, "SO(8)"}, {5, "F_4"}}, 
   {{-6, 0, 6, 4, 2}, {4, "SO(8)"}, {3, "G_2"}}, 
   {{-6, 0, 6, 4, 3}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{-6, 0, 6, 5, 3}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{-6, 0, 6, 5, 4}, {5, "F_4"}, {0, "x"}}, {{-6, 0, 6, 5, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-6, 0, 6, 6, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-5, -8, -11, -5, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-5, -8, -10, -5, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-5, -8, -10, -4, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-5, -7, -9, -4, 1}, {0, "x"}, {7, "E_7"}}, {{-5, -7, -9, -4, 2}, 
    {0, "x"}, {7, "E_7"}}, {{-5, -7, -9, -3, 3}, {0, "x"}, {7, "E_7"}}, 
   {{-5, -7, -8, -4, 1}, {0, "x"}, {7, "E_7"}}, {{-5, -7, -8, -3, 2}, 
    {0, "x"}, {7, "E_7"}}, {{-5, -7, -8, -3, 3}, {0, "x"}, {7, "E_7"}}, 
   {{-5, -7, -8, -2, 4}, {0, "x"}, {7, "E_7"}}, {{-5, -6, -7, -3, 1}, 
    {0, "x"}, {6, "E_6"}}, {{-5, -6, -7, -3, 2}, {0, "x"}, {6, "E_6"}}, 
   {{-5, -6, -7, -2, 3}, {0, "x"}, {6, "E_6"}}, {{-5, -6, -7, -2, 4}, 
    {0, "x"}, {6, "E_6"}}, {{-5, -6, -7, -1, 5}, {0, "x"}, {6, "E_6"}}, 
   {{-5, -6, -6, -3, 1}, {0, "x"}, {5, "F_4"}}, {{-5, -6, -6, -2, 2}, 
    {0, "x"}, {5, "F_4"}}, {{-5, -6, -6, -2, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -6, -6, -1, 4}, {0, "x"}, {5, "F_4"}}, {{-5, -6, -6, -1, 5}, 
    {0, "x"}, {5, "F_4"}}, {{-5, -5, -6, -3, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -5, -6, -2, 2}, {0, "x"}, {5, "F_4"}}, {{-5, -5, -6, -2, 3}, 
    {0, "x"}, {5, "F_4"}}, {{-5, -5, -6, -1, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -5, -6, -1, 5}, {0, "x"}, {5, "F_4"}}, {{-5, -5, -5, -2, 1}, 
    {0, "x"}, {5, "F_4"}}, {{-5, -5, -5, -2, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -5, -5, -1, 3}, {0, "x"}, {5, "F_4"}}, {{-5, -5, -5, -1, 4}, 
    {0, "x"}, {5, "F_4"}}, {{-5, -5, -5, 0, 5}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -5, -4, -2, 1}, {0, "x"}, {5, "F_4"}}, {{-5, -5, -4, -1, 1}, 
    {0, "x"}, {5, "F_4"}}, {{-5, -5, -4, -1, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -5, -4, -1, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -5, -4, 0, 4}, {0, "x"}, {5, "F_4"}}, {{-5, -5, -4, 0, 5}, {0, "x"}, 
    {5, "F_4"}}, {{-5, -4, -4, -2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -4, -4, -1, 1}, {0, "x"}, {5, "F_4"}}, {{-5, -4, -4, -1, 2}, 
    {0, "x"}, {5, "F_4"}}, {{-5, -4, -4, -1, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -4, -4, 0, 4}, {0, "x"}, {5, "F_4"}}, {{-5, -4, -4, 0, 5}, {0, "x"}, 
    {5, "F_4"}}, {{-5, -4, -3, -1, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -4, -3, -1, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -4, -3, 0, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -4, -3, 0, 3}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -4, -3, 0, 4}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -4, -3, 1, 5}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -4, -2, -1, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -4, -2, 0, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -4, -2, 0, 2}, {0, "x"}, {3, "G_2"}}, {{-5, -4, -2, 0, 3}, {0, "x"}, 
    {3, "G_2"}}, {{-5, -4, -2, 1, 3}, {0, "x"}, {3, "G_2"}}, 
   {{-5, -4, -2, 1, 4}, {0, "x"}, {3, "G_2"}}, {{-5, -4, -2, 1, 5}, {0, "x"}, 
    {3, "G_2"}}, {{-5, -3, -2, -1, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -3, -2, 0, 1}, {0, "x"}, {3, "G_2"}}, {{-5, -3, -2, 0, 2}, {0, "x"}, 
    {3, "G_2"}}, {{-5, -3, -2, 0, 3}, {0, "x"}, {3, "G_2"}}, 
   {{-5, -3, -2, 1, 3}, {0, "x"}, {3, "G_2"}}, {{-5, -3, -2, 1, 4}, {0, "x"}, 
    {3, "G_2"}}, {{-5, -3, -2, 1, 5}, {0, "x"}, {3, "G_2"}}, 
   {{-5, -3, -1, 0, 1}, {0, "x"}, {3, "G_2"}}, {{-5, -3, -1, 0, 2}, {0, "x"}, 
    {3, "G_2"}}, {{-5, -3, -1, 1, 2}, {0, "x"}, {2, "SU(3)"}}, 
   {{-5, -3, -1, 1, 3}, {0, "x"}, {2, "SU(3)"}}, 
   {{-5, -3, -1, 1, 4}, {0, "x"}, {2, "SU(3)"}}, 
   {{-5, -3, -1, 2, 4}, {0, "x"}, {2, "SU(3)"}}, 
   {{-5, -3, -1, 2, 5}, {0, "x"}, {2, "SU(3)"}}, 
   {{-5, -3, 0, 0, 1}, {0, "x"}, {3, "G_2"}}, {{-5, -3, 0, 1, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-5, -3, 0, 1, 2}, {0, "x"}, {2, "SU(3)"}}, 
   {{-5, -3, 0, 1, 3}, {0, "x"}, {1, "SU(2)"}}, {{-5, -3, 0, 2, 3}, {0, "x"}, 
    {1, "SU(2)"}}, {{-5, -3, 0, 2, 4}, {0, "x"}, {1, "SU(2)"}}, 
   {{-5, -3, 0, 2, 5}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-5, -3, 0, 3, 5}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-5, -2, 0, 0, 1}, {0, "x"}, {3, "G_2"}}, {{-5, -2, 0, 1, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-5, -2, 0, 1, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-5, -2, 0, 1, 3}, {0, "x"}, {1, "SU(2)"}}, {{-5, -2, 0, 2, 3}, {0, "x"}, 
    {1, "SU(2)"}}, {{-5, -2, 0, 2, 4}, {0, "x"}, {1, "SU(2)"}}, 
   {{-5, -2, 0, 2, 5}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-5, -2, 1, 1, 1}, {0, "x"}, {3, "G_2"}}, {{-5, -2, 1, 1, 2}, {0, "x"}, 
    {1, "SU(2)"}}, {{-5, -2, 1, 2, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-5, -2, 1, 2, 3}, {0, "x"}, {0, "x"}}, {{-5, -2, 1, 2, 4}, {1, "SU(2)"}, 
    {0, "x"}}, {{-5, -2, 1, 3, 4}, {1, "SU(2)"}, {0, "x"}}, 
   {{-5, -1, 2, 1, 1}, {0, "x"}, {3, "G_2"}}, {{-5, -1, 2, 2, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-5, -1, 2, 2, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-5, -1, 2, 2, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-5, -1, 2, 3, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-5, -1, 2, 3, 4}, {2, "SU(3)"}, {0, "x"}}, {{-5, -1, 3, 2, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-5, -1, 3, 2, 2}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-5, -1, 3, 3, 2}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-5, -1, 3, 3, 3}, {2, "SU(3)"}, {0, "x"}}, 
   {{-5, -1, 3, 3, 4}, {3, "G_2"}, {0, "x"}}, {{-5, -1, 3, 4, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-5, 0, 4, 2, 1}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{-5, 0, 4, 3, 1}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{-5, 0, 4, 3, 2}, {2, "SU(3)"}, {1, "SU(2)"}}, 
   {{-5, 0, 4, 3, 3}, {3, "G_2"}, {0, "x"}}, {{-5, 0, 4, 4, 3}, {3, "G_2"}, 
    {0, "x"}}, {{-5, 0, 4, 4, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{-5, 0, 5, 3, 1}, {3, "G_2"}, {3, "G_2"}}, {{-5, 0, 5, 3, 2}, {3, "G_2"}, 
    {1, "SU(2)"}}, {{-5, 0, 5, 4, 2}, {3, "G_2"}, {1, "SU(2)"}}, 
   {{-5, 0, 5, 4, 3}, {4, "SO(8)"}, {0, "x"}}, {{-5, 0, 5, 4, 4}, {5, "F_4"}, 
    {0, "x"}}, {{-5, 0, 5, 5, 4}, {5, "F_4"}, {0, "x"}}, 
   {{-5, 1, 6, 3, 1}, {4, "SO(8)"}, {3, "G_2"}}, 
   {{-5, 1, 6, 4, 1}, {4, "SO(8)"}, {3, "G_2"}}, 
   {{-5, 1, 6, 4, 2}, {4, "SO(8)"}, {1, "SU(2)"}}, 
   {{-5, 1, 6, 4, 3}, {5, "F_4"}, {0, "x"}}, {{-5, 1, 6, 5, 3}, {5, "F_4"}, 
    {0, "x"}}, {{-5, 1, 6, 5, 4}, {5, "F_4"}, {0, "x"}}, 
   {{-5, 1, 7, 4, 1}, {5, "F_4"}, {3, "G_2"}}, {{-5, 1, 7, 4, 2}, {5, "F_4"}, 
    {1, "SU(2)"}}, {{-5, 1, 7, 5, 2}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{-5, 1, 7, 5, 3}, {5, "F_4"}, {0, "x"}}, {{-5, 1, 7, 5, 4}, {5, "F_4"}, 
    {0, "x"}}, {{-5, 1, 7, 6, 4}, {5, "F_4"}, {0, "x"}}, 
   {{-4, -8, -11, -5, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-4, -7, -10, -5, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-4, -7, -10, -4, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-4, -7, -9, -4, 1}, {0, "x"}, {7, "E_7"}}, {{-4, -7, -9, -4, 2}, 
    {0, "x"}, {7, "E_7"}}, {{-4, -7, -9, -3, 3}, {0, "x"}, {7, "E_7"}}, 
   {{-4, -6, -8, -4, 1}, {0, "x"}, {6, "E_6"}}, {{-4, -6, -8, -3, 2}, 
    {0, "x"}, {6, "E_6"}}, {{-4, -6, -8, -3, 3}, {0, "x"}, {6, "E_6"}}, 
   {{-4, -6, -8, -2, 4}, {0, "x"}, {6, "E_6"}}, {{-4, -6, -7, -3, 1}, 
    {0, "x"}, {5, "F_4"}}, {{-4, -6, -7, -3, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -6, -7, -2, 3}, {0, "x"}, {5, "F_4"}}, {{-4, -6, -7, -2, 4}, 
    {0, "x"}, {5, "F_4"}}, {{-4, -5, -7, -3, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -5, -7, -3, 2}, {0, "x"}, {5, "F_4"}}, {{-4, -5, -7, -2, 3}, 
    {0, "x"}, {5, "F_4"}}, {{-4, -5, -7, -2, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -5, -6, -3, 1}, {0, "x"}, {5, "F_4"}}, {{-4, -5, -6, -2, 2}, 
    {0, "x"}, {5, "F_4"}}, {{-4, -5, -6, -2, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -5, -6, -1, 4}, {0, "x"}, {5, "F_4"}}, {{-4, -5, -5, -2, 1}, 
    {0, "x"}, {5, "F_4"}}, {{-4, -5, -5, -2, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -5, -5, -1, 3}, {0, "x"}, {5, "F_4"}}, {{-4, -5, -5, -1, 4}, 
    {0, "x"}, {5, "F_4"}}, {{-4, -4, -5, -2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -4, -5, -2, 2}, {0, "x"}, {5, "F_4"}}, {{-4, -4, -5, -1, 3}, 
    {0, "x"}, {5, "F_4"}}, {{-4, -4, -5, -1, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -4, -4, -2, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -4, -4, -1, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -4, -4, -1, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -4, -4, -1, 3}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -4, -4, 0, 4}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -4, -3, -1, 1}, {0, "x"}, {3, "G_2"}}, {{-4, -4, -3, -1, 2}, 
    {0, "x"}, {3, "G_2"}}, {{-4, -4, -3, 0, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -4, -3, 0, 3}, {0, "x"}, {3, "G_2"}}, {{-4, -4, -3, 0, 4}, {0, "x"}, 
    {3, "G_2"}}, {{-4, -3, -3, -1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -3, -3, -1, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -3, -3, 0, 2}, {0, "x"}, {3, "G_2"}}, {{-4, -3, -3, 0, 3}, {0, "x"}, 
    {3, "G_2"}}, {{-4, -3, -3, 0, 4}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -3, -2, -1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -3, -2, 0, 1}, {0, "x"}, {2, "SU(3)"}}, 
   {{-4, -3, -2, 0, 2}, {0, "x"}, {2, "SU(3)"}}, 
   {{-4, -3, -2, 0, 3}, {0, "x"}, {2, "SU(3)"}}, 
   {{-4, -3, -2, 1, 3}, {0, "x"}, {2, "SU(3)"}}, 
   {{-4, -3, -2, 1, 4}, {0, "x"}, {2, "SU(3)"}}, 
   {{-4, -3, -1, 0, 1}, {0, "x"}, {2, "SU(3)"}}, 
   {{-4, -3, -1, 0, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -3, -1, 1, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -3, -1, 1, 3}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -3, -1, 1, 4}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -3, -1, 2, 4}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -2, -1, 0, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -2, -1, 0, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -2, -1, 1, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -2, -1, 1, 3}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -2, -1, 1, 4}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -2, -1, 2, 4}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -2, 0, 0, 1}, {0, "x"}, {1, "SU(2)"}}, {{-4, -2, 0, 1, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-4, -2, 0, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{-4, -2, 0, 1, 3}, {0, "x"}, {0, "x"}}, {{-4, -2, 0, 2, 3}, {0, "x"}, 
    {0, "x"}}, {{-4, -2, 0, 2, 4}, {0, "x"}, {0, "x"}}, 
   {{-4, -2, 1, 1, 1}, {0, "x"}, {1, "SU(2)"}}, {{-4, -2, 1, 1, 2}, {0, "x"}, 
    {0, "x"}}, {{-4, -2, 1, 2, 2}, {0, "x"}, {0, "x"}}, 
   {{-4, -2, 1, 2, 3}, {0, "x"}, {0, "x"}}, {{-4, -1, 1, 1, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-4, -1, 1, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{-4, -1, 1, 2, 2}, {0, "x"}, {0, "x"}}, {{-4, -1, 1, 2, 3}, {0, "x"}, 
    {0, "x"}}, {{-4, -1, 2, 1, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -1, 2, 2, 1}, {0, "x"}, {1, "SU(2)"}}, {{-4, -1, 2, 2, 2}, {0, "x"}, 
    {0, "x"}}, {{-4, -1, 2, 2, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-4, -1, 2, 3, 3}, {1, "SU(2)"}, {0, "x"}}, {{-4, 0, 3, 2, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-4, 0, 3, 2, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-4, 0, 3, 3, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-4, 0, 3, 3, 3}, {2, "SU(3)"}, {0, "x"}}, 
   {{-4, 0, 4, 2, 1}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-4, 0, 4, 3, 1}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-4, 0, 4, 3, 2}, {2, "SU(3)"}, {0, "x"}}, {{-4, 0, 4, 3, 3}, {3, "G_2"}, 
    {0, "x"}}, {{-4, 0, 4, 4, 3}, {3, "G_2"}, {0, "x"}}, 
   {{-4, 1, 5, 3, 1}, {3, "G_2"}, {1, "SU(2)"}}, 
   {{-4, 1, 5, 3, 2}, {3, "G_2"}, {0, "x"}}, {{-4, 1, 5, 4, 2}, {3, "G_2"}, 
    {0, "x"}}, {{-4, 1, 5, 4, 3}, {4, "SO(8)"}, {0, "x"}}, 
   {{-4, 1, 6, 3, 1}, {4, "SO(8)"}, {1, "SU(2)"}}, 
   {{-4, 1, 6, 4, 1}, {4, "SO(8)"}, {1, "SU(2)"}}, 
   {{-4, 1, 6, 4, 2}, {4, "SO(8)"}, {0, "x"}}, {{-4, 1, 6, 4, 3}, {5, "F_4"}, 
    {0, "x"}}, {{-4, 1, 6, 5, 3}, {5, "F_4"}, {0, "x"}}, 
   {{-4, 2, 7, 4, 1}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{-4, 2, 7, 4, 2}, {5, "F_4"}, {0, "x"}}, {{-4, 2, 7, 5, 2}, {5, "F_4"}, 
    {0, "x"}}, {{-4, 2, 7, 5, 3}, {5, "F_4"}, {0, "x"}}, 
   {{-4, 2, 8, 5, 1}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{-4, 2, 8, 5, 2}, {5, "F_4"}, {0, "x"}}, {{-4, 2, 8, 5, 3}, {5, "F_4"}, 
    {0, "x"}}, {{-4, 2, 8, 6, 3}, {5, "F_4"}, {0, "x"}}, 
   {{-3, -7, -11, -5, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-3, -7, -10, -5, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-3, -7, -10, -4, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-3, -6, -9, -4, 1}, {0, "x"}, {6, "E_6"}}, {{-3, -6, -9, -4, 2}, 
    {0, "x"}, {6, "E_6"}}, {{-3, -6, -9, -3, 3}, {0, "x"}, {6, "E_6"}}, 
   {{-3, -6, -8, -4, 1}, {0, "x"}, {5, "F_4"}}, {{-3, -6, -8, -3, 2}, 
    {0, "x"}, {5, "F_4"}}, {{-3, -6, -8, -3, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-3, -5, -8, -4, 1}, {0, "x"}, {5, "F_4"}}, {{-3, -5, -8, -3, 2}, 
    {0, "x"}, {5, "F_4"}}, {{-3, -5, -8, -3, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-3, -5, -7, -3, 1}, {0, "x"}, {5, "F_4"}}, {{-3, -5, -7, -3, 2}, 
    {0, "x"}, {5, "F_4"}}, {{-3, -5, -7, -2, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-3, -5, -6, -3, 1}, {0, "x"}, {5, "F_4"}}, {{-3, -5, -6, -2, 2}, 
    {0, "x"}, {5, "F_4"}}, {{-3, -5, -6, -2, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-3, -4, -6, -3, 1}, {0, "x"}, {5, "F_4"}}, {{-3, -4, -6, -2, 2}, 
    {0, "x"}, {5, "F_4"}}, {{-3, -4, -6, -2, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-3, -4, -5, -2, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-3, -4, -5, -2, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-3, -4, -5, -1, 3}, {0, "x"}, {4, "SO(8)"}}, 
   {{-3, -4, -4, -2, 1}, {0, "x"}, {3, "G_2"}}, {{-3, -4, -4, -1, 1}, 
    {0, "x"}, {3, "G_2"}}, {{-3, -4, -4, -1, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -4, -4, -1, 3}, {0, "x"}, {3, "G_2"}}, {{-3, -3, -4, -2, 1}, 
    {0, "x"}, {3, "G_2"}}, {{-3, -3, -4, -1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -3, -4, -1, 2}, {0, "x"}, {3, "G_2"}}, {{-3, -3, -4, -1, 3}, 
    {0, "x"}, {3, "G_2"}}, {{-3, -3, -3, -1, 1}, {0, "x"}, {2, "SU(3)"}}, 
   {{-3, -3, -3, -1, 2}, {0, "x"}, {2, "SU(3)"}}, 
   {{-3, -3, -3, 0, 2}, {0, "x"}, {2, "SU(3)"}}, 
   {{-3, -3, -3, 0, 3}, {0, "x"}, {2, "SU(3)"}}, 
   {{-3, -3, -2, -1, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -3, -2, 0, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -3, -2, 0, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -3, -2, 0, 3}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -3, -2, 1, 3}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -2, -2, -1, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -2, -2, 0, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -2, -2, 0, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -2, -2, 0, 3}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -2, -2, 1, 3}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -2, -1, 0, 1}, {0, "x"}, {0, "x"}}, {{-3, -2, -1, 0, 2}, {0, "x"}, 
    {0, "x"}}, {{-3, -2, -1, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{-3, -2, -1, 1, 3}, {0, "x"}, {0, "x"}}, {{-3, -2, 0, 0, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, -2, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-3, -2, 0, 1, 2}, {0, "x"}, {0, "x"}}, {{-3, -2, 0, 1, 3}, {0, "x"}, 
    {0, "x"}}, {{-3, -2, 0, 2, 3}, {0, "x"}, {0, "x"}}, 
   {{-3, -1, 0, 0, 1}, {0, "x"}, {0, "x"}}, {{-3, -1, 0, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, -1, 0, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{-3, -1, 0, 1, 3}, {0, "x"}, {0, "x"}}, {{-3, -1, 1, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, -1, 1, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{-3, -1, 1, 2, 2}, {0, "x"}, {0, "x"}}, {{-3, -1, 2, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, -1, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-3, -1, 2, 2, 2}, {0, "x"}, {0, "x"}}, {{-3, 0, 2, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, 0, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-3, 0, 2, 2, 2}, {0, "x"}, {0, "x"}}, {{-3, 0, 3, 2, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, 0, 3, 2, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-3, 0, 3, 3, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-3, 1, 4, 2, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{-3, 1, 4, 3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{-3, 1, 4, 3, 2}, {2, "SU(3)"}, {0, "x"}}, {{-3, 1, 5, 3, 1}, {3, "G_2"}, 
    {0, "x"}}, {{-3, 1, 5, 3, 2}, {3, "G_2"}, {0, "x"}}, 
   {{-3, 1, 5, 4, 2}, {3, "G_2"}, {0, "x"}}, {{-3, 2, 6, 3, 1}, {4, "SO(8)"}, 
    {0, "x"}}, {{-3, 2, 6, 4, 1}, {4, "SO(8)"}, {0, "x"}}, 
   {{-3, 2, 6, 4, 2}, {4, "SO(8)"}, {0, "x"}}, {{-3, 2, 7, 4, 1}, {5, "F_4"}, 
    {0, "x"}}, {{-3, 2, 7, 4, 2}, {5, "F_4"}, {0, "x"}}, 
   {{-3, 2, 7, 5, 2}, {5, "F_4"}, {0, "x"}}, {{-3, 3, 8, 5, 1}, {5, "F_4"}, 
    {0, "x"}}, {{-3, 3, 8, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{-3, 3, 9, 5, 1}, {6, "E_6"}, {0, "x"}}, {{-3, 3, 9, 6, 2}, {6, "E_6"}, 
    {0, "x"}}, {{-2, -7, -11, -5, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-2, -6, -10, -5, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-2, -6, -10, -4, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-2, -6, -9, -4, 1}, {0, "x"}, {6, "E_6"}}, {{-2, -6, -9, -4, 2}, 
    {0, "x"}, {6, "E_6"}}, {{-2, -5, -8, -4, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-2, -5, -8, -3, 2}, {0, "x"}, {5, "F_4"}}, {{-2, -5, -7, -3, 1}, 
    {0, "x"}, {5, "F_4"}}, {{-2, -5, -7, -3, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-2, -4, -7, -3, 1}, {0, "x"}, {5, "F_4"}}, {{-2, -4, -7, -3, 2}, 
    {0, "x"}, {5, "F_4"}}, {{-2, -4, -6, -3, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-2, -4, -6, -2, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-2, -4, -5, -2, 1}, {0, "x"}, {3, "G_2"}}, {{-2, -4, -5, -2, 2}, 
    {0, "x"}, {3, "G_2"}}, {{-2, -3, -5, -2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-2, -3, -5, -2, 2}, {0, "x"}, {3, "G_2"}}, {{-2, -3, -4, -2, 1}, 
    {0, "x"}, {2, "SU(3)"}}, {{-2, -3, -4, -1, 1}, {0, "x"}, {2, "SU(3)"}}, 
   {{-2, -3, -4, -1, 2}, {0, "x"}, {2, "SU(3)"}}, 
   {{-2, -3, -3, -1, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -3, -3, -1, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -3, -3, 0, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -2, -3, -1, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -2, -3, -1, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -2, -3, 0, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -2, -2, -1, 1}, {0, "x"}, {0, "x"}}, {{-2, -2, -2, 0, 1}, {0, "x"}, 
    {0, "x"}}, {{-2, -2, -2, 0, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, -2, -1, 0, 1}, {0, "x"}, {0, "x"}}, {{-2, -2, -1, 0, 2}, {0, "x"}, 
    {0, "x"}}, {{-2, -2, -1, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, -1, -1, 0, 1}, {0, "x"}, {0, "x"}}, {{-2, -1, -1, 0, 2}, {0, "x"}, 
    {0, "x"}}, {{-2, -1, -1, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, -1, 0, 0, 1}, {0, "x"}, {0, "x"}}, {{-2, -1, 0, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{-2, -1, 0, 1, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, -1, 1, 1, 1}, {0, "x"}, {0, "x"}}, {{-2, 0, 1, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{-2, 0, 2, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, 0, 2, 2, 1}, {0, "x"}, {0, "x"}}, {{-2, 0, 3, 2, 1}, {0, "x"}, 
    {0, "x"}}, {{-2, 1, 3, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, 1, 4, 2, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{-2, 1, 4, 3, 1}, {1, "SU(2)"}, {0, "x"}}, {{-2, 2, 5, 3, 1}, {3, "G_2"}, 
    {0, "x"}}, {{-2, 2, 6, 3, 1}, {4, "SO(8)"}, {0, "x"}}, 
   {{-2, 2, 6, 4, 1}, {4, "SO(8)"}, {0, "x"}}, {{-2, 3, 7, 4, 1}, {5, "F_4"}, 
    {0, "x"}}, {{-2, 3, 8, 5, 1}, {5, "F_4"}, {0, "x"}}, 
   {{-2, 4, 9, 5, 1}, {6, "E_6"}, {0, "x"}}, {{-2, 4, 10, 6, 1}, {7, "E_7"}, 
    {0, "x"}}, {{-1, -6, -11, -5, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-1, -6, -10, -5, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-1, -5, -9, -4, 1}, {0, "x"}, {6, "E_6"}}, {{-1, -5, -8, -4, 1}, 
    {0, "x"}, {5, "F_4"}}, {{-1, -4, -7, -3, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-1, -4, -6, -3, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-1, -3, -6, -3, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-1, -3, -5, -2, 1}, {0, "x"}, {3, "G_2"}}, {{-1, -3, -4, -2, 1}, 
    {0, "x"}, {1, "SU(2)"}}, {{-1, -3, -4, -1, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-1, -2, -4, -2, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-1, -2, -4, -1, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-1, -2, -3, -1, 1}, {0, "x"}, {0, "x"}}, {{-1, -2, -2, -1, 1}, {0, "x"}, 
    {0, "x"}}, {{-1, -2, -2, 0, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -1, -2, -1, 1}, {0, "x"}, {0, "x"}}, {{-1, -1, -2, 0, 1}, {0, "x"}, 
    {0, "x"}}, {{-1, -1, -1, 0, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -1, 0, 0, 1}, {0, "x"}, {0, "x"}}, {{-1, -1, 0, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{-1, 0, 0, 0, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 0, 0, 0}, {0, "x"}, {0, "x"}}, {{0, 0, 1, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 0, 1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{0, 1, 2, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 1, 3, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 3, 2, 0}, {0, "x"}, {0, "x"}}, {{0, 2, 3, 2, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 2, 4, 2, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{0, 2, 5, 2, 0}, {3, "G_2"}, {0, "x"}}, {{0, 2, 5, 3, 0}, {3, "G_2"}, 
    {0, "x"}}, {{0, 3, 5, 3, 0}, {3, "G_2"}, {0, "x"}}, 
   {{0, 3, 6, 3, 0}, {4, "SO(8)"}, {0, "x"}}, {{0, 4, 7, 4, 0}, {5, "F_4"}, 
    {0, "x"}}, {{0, 4, 8, 4, 0}, {5, "F_4"}, {0, "x"}}, 
   {{0, 5, 9, 5, 0}, {6, "E_6"}, {0, "x"}}, {{0, 5, 10, 5, 0}, {7, "E_7"}, 
    {0, "x"}}, {{0, 6, 11, 6, 0}, {7, "E_7"}, {0, "x"}}, 
   {{0, 6, 12, 6, 0}, {7, "E_7"}, {0, "x"}}, {{1, -5, -11, -6, 0}, {0, "x"}, 
    {7, "E_7"}}, {{1, -5, -11, -5, 1}, {0, "x"}, {7, "E_7"}}, 
   {{1, -5, -10, -5, 0}, {0, "x"}, {7, "E_7"}}, {{1, -5, -10, -5, 1}, 
    {0, "x"}, {7, "E_7"}}, {{1, -4, -9, -5, 0}, {0, "x"}, {6, "E_6"}}, 
   {{1, -4, -9, -4, 1}, {0, "x"}, {6, "E_6"}}, {{1, -4, -8, -4, 0}, {0, "x"}, 
    {5, "F_4"}}, {{1, -4, -8, -4, 1}, {0, "x"}, {5, "F_4"}}, 
   {{1, -3, -7, -4, 0}, {0, "x"}, {5, "F_4"}}, {{1, -3, -7, -3, 1}, {0, "x"}, 
    {5, "F_4"}}, {{1, -3, -6, -3, 0}, {0, "x"}, {4, "SO(8)"}}, 
   {{1, -3, -6, -3, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{1, -2, -5, -3, 0}, {0, "x"}, {3, "G_2"}}, {{1, -2, -5, -2, 0}, {0, "x"}, 
    {3, "G_2"}}, {{1, -2, -5, -2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{1, -2, -4, -2, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, -2, -4, -2, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, -2, -4, -1, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, -1, -4, -2, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, -1, -4, -1, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, -1, -3, -2, 0}, {0, "x"}, {0, "x"}}, {{1, -1, -3, -1, 0}, {0, "x"}, 
    {0, "x"}}, {{1, -1, -3, -1, 1}, {0, "x"}, {0, "x"}}, 
   {{1, -1, -2, -1, 0}, {0, "x"}, {0, "x"}}, {{1, -1, -2, -1, 1}, {0, "x"}, 
    {0, "x"}}, {{1, -1, -2, 0, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 0, -2, -1, 0}, {0, "x"}, {0, "x"}}, {{1, 0, -2, 0, 1}, {0, "x"}, 
    {0, "x"}}, {{1, 0, -1, -1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 0, -1, 0, 0}, {0, "x"}, {0, "x"}}, {{1, 0, -1, 0, 1}, {0, "x"}, 
    {0, "x"}}, {{1, 0, 0, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 0, 0, 0, 1}, {0, "x"}, {0, "x"}}, {{1, 0, 0, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{1, 1, 0, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 0, 1, 1}, {0, "x"}, {0, "x"}}, {{1, 1, 1, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 1, 1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 1, 1, 1}, {0, "x"}, {0, "x"}}, {{1, 1, 2, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 1, 2, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 2, 2, 1}, {0, "x"}, {0, "x"}}, {{1, 2, 2, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 2, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 3, 1, 0}, {0, "x"}, {0, "x"}}, {{1, 2, 3, 2, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 2, 3, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 4, 2, 0}, {1, "SU(2)"}, {0, "x"}}, {{1, 2, 4, 2, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{1, 2, 4, 3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 3, 4, 2, 0}, {1, "SU(2)"}, {0, "x"}}, {{1, 3, 4, 3, 1}, {2, "SU(3)"}, 
    {0, "x"}}, {{1, 3, 5, 2, 0}, {3, "G_2"}, {0, "x"}}, 
   {{1, 3, 5, 3, 0}, {3, "G_2"}, {0, "x"}}, {{1, 3, 5, 3, 1}, {3, "G_2"}, 
    {0, "x"}}, {{1, 3, 6, 3, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{1, 3, 6, 3, 1}, {4, "SO(8)"}, {0, "x"}}, {{1, 3, 6, 4, 1}, {4, "SO(8)"}, 
    {0, "x"}}, {{1, 4, 6, 3, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{1, 4, 6, 4, 1}, {4, "SO(8)"}, {0, "x"}}, {{1, 4, 7, 4, 0}, {5, "F_4"}, 
    {0, "x"}}, {{1, 4, 7, 4, 1}, {5, "F_4"}, {0, "x"}}, 
   {{1, 5, 8, 4, 0}, {5, "F_4"}, {0, "x"}}, {{1, 5, 8, 5, 1}, {5, "F_4"}, 
    {0, "x"}}, {{1, 5, 9, 5, 0}, {6, "E_6"}, {0, "x"}}, 
   {{1, 5, 9, 5, 1}, {6, "E_6"}, {0, "x"}}, {{1, 6, 10, 5, 0}, {7, "E_7"}, 
    {0, "x"}}, {{1, 6, 10, 6, 1}, {7, "E_7"}, {0, "x"}}, 
   {{1, 6, 11, 6, 0}, {7, "E_7"}, {0, "x"}}, {{1, 6, 11, 6, 1}, {7, "E_7"}, 
    {0, "x"}}, {{1, 7, 12, 6, 0}, {7, "E_7"}, {0, "x"}}, 
   {{1, 7, 12, 7, 1}, {7, "E_7"}, {0, "x"}}, {{2, -4, -10, -5, 0}, {0, "x"}, 
    {7, "E_7"}}, {{2, -4, -10, -5, 1}, {1, "SU(2)"}, {7, "E_7"}}, 
   {{2, -4, -10, -4, 2}, {3, "G_2"}, {7, "E_7"}}, 
   {{2, -4, -9, -5, 0}, {0, "x"}, {6, "E_6"}}, {{2, -4, -9, -4, 1}, 
    {1, "SU(2)"}, {6, "E_6"}}, {{2, -4, -9, -4, 2}, {3, "G_2"}, {6, "E_6"}}, 
   {{2, -3, -8, -4, 0}, {0, "x"}, {5, "F_4"}}, {{2, -3, -8, -4, 1}, 
    {1, "SU(2)"}, {5, "F_4"}}, {{2, -3, -8, -3, 2}, {3, "G_2"}, {5, "F_4"}}, 
   {{2, -3, -7, -4, 0}, {0, "x"}, {5, "F_4"}}, {{2, -3, -7, -3, 1}, 
    {1, "SU(2)"}, {5, "F_4"}}, {{2, -3, -7, -3, 2}, {3, "G_2"}, {5, "F_4"}}, 
   {{2, -2, -6, -3, 0}, {0, "x"}, {4, "SO(8)"}}, 
   {{2, -2, -6, -3, 1}, {1, "SU(2)"}, {4, "SO(8)"}}, 
   {{2, -2, -6, -2, 2}, {3, "G_2"}, {4, "SO(8)"}}, 
   {{2, -2, -5, -3, 0}, {0, "x"}, {3, "G_2"}}, {{2, -2, -5, -2, 0}, {0, "x"}, 
    {3, "G_2"}}, {{2, -2, -5, -2, 1}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{2, -2, -5, -2, 2}, {3, "G_2"}, {3, "G_2"}}, 
   {{2, -1, -4, -2, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{2, -1, -4, -2, 1}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{2, -1, -4, -1, 1}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{2, -1, -4, -1, 2}, {3, "G_2"}, {1, "SU(2)"}}, 
   {{2, -1, -3, -2, 0}, {0, "x"}, {0, "x"}}, {{2, -1, -3, -1, 0}, {0, "x"}, 
    {0, "x"}}, {{2, -1, -3, -1, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, -1, -3, -1, 2}, {3, "G_2"}, {0, "x"}}, {{2, -1, -3, 0, 2}, 
    {3, "G_2"}, {0, "x"}}, {{2, 0, -3, -2, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 0, -3, -1, 0}, {0, "x"}, {0, "x"}}, {{2, 0, -3, -1, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 0, -3, 0, 2}, {3, "G_2"}, {0, "x"}}, 
   {{2, 0, -2, -1, 0}, {0, "x"}, {0, "x"}}, {{2, 0, -2, -1, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 0, -2, 0, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 0, -2, 0, 2}, {3, "G_2"}, {0, "x"}}, {{2, 0, -1, -1, 0}, {0, "x"}, 
    {0, "x"}}, {{2, 0, -1, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 0, -1, 0, 1}, {1, "SU(2)"}, {0, "x"}}, {{2, 0, -1, 0, 2}, {3, "G_2"}, 
    {0, "x"}}, {{2, 0, -1, 1, 2}, {3, "G_2"}, {0, "x"}}, 
   {{2, 1, -1, -1, 0}, {0, "x"}, {0, "x"}}, {{2, 1, -1, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{2, 1, -1, 0, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 1, -1, 1, 2}, {3, "G_2"}, {0, "x"}}, {{2, 1, 0, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{2, 1, 0, 0, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 1, 0, 1, 1}, {1, "SU(2)"}, {0, "x"}}, {{2, 1, 0, 1, 2}, {3, "G_2"}, 
    {0, "x"}}, {{2, 1, 1, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 1, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{2, 1, 1, 1, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 1, 1, 1, 2}, {3, "G_2"}, {0, "x"}}, 
   {{2, 1, 1, 2, 2}, {3, "G_2"}, {0, "x"}}, {{2, 2, 1, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{2, 2, 1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 2, 1, 1, 1}, {1, "SU(2)"}, {0, "x"}}, {{2, 2, 1, 2, 2}, {3, "G_2"}, 
    {0, "x"}}, {{2, 2, 2, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 2, 2, 1, 1}, {1, "SU(2)"}, {0, "x"}}, {{2, 2, 2, 2, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 2, 2, 2, 2}, {3, "G_2"}, {0, "x"}}, 
   {{2, 2, 3, 1, 0}, {1, "SU(2)"}, {0, "x"}}, {{2, 2, 3, 2, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 2, 3, 2, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 2, 3, 2, 2}, {3, "G_2"}, {0, "x"}}, {{2, 2, 3, 3, 2}, {3, "G_2"}, 
    {0, "x"}}, {{2, 3, 3, 1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 3, 3, 2, 0}, {1, "SU(2)"}, {0, "x"}}, {{2, 3, 3, 2, 1}, {2, "SU(3)"}, 
    {0, "x"}}, {{2, 3, 3, 3, 2}, {3, "G_2"}, {0, "x"}}, 
   {{2, 3, 4, 2, 0}, {2, "SU(3)"}, {0, "x"}}, {{2, 3, 4, 2, 1}, {2, "SU(3)"}, 
    {0, "x"}}, {{2, 3, 4, 3, 1}, {3, "G_2"}, {0, "x"}}, 
   {{2, 3, 4, 3, 2}, {3, "G_2"}, {0, "x"}}, {{2, 3, 5, 2, 0}, {3, "G_2"}, 
    {0, "x"}}, {{2, 3, 5, 3, 0}, {3, "G_2"}, {0, "x"}}, 
   {{2, 3, 5, 3, 1}, {3, "G_2"}, {0, "x"}}, {{2, 3, 5, 3, 2}, {3, "G_2"}, 
    {0, "x"}}, {{2, 3, 5, 4, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 4, 5, 2, 0}, {3, "G_2"}, {0, "x"}}, {{2, 4, 5, 3, 0}, {3, "G_2"}, 
    {0, "x"}}, {{2, 4, 5, 3, 1}, {3, "G_2"}, {0, "x"}}, 
   {{2, 4, 5, 4, 2}, {4, "SO(8)"}, {0, "x"}}, {{2, 4, 6, 3, 0}, {4, "SO(8)"}, 
    {0, "x"}}, {{2, 4, 6, 3, 1}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 4, 6, 4, 1}, {4, "SO(8)"}, {0, "x"}}, {{2, 4, 6, 4, 2}, {4, "SO(8)"}, 
    {0, "x"}}, {{2, 4, 7, 4, 0}, {5, "F_4"}, {0, "x"}}, 
   {{2, 4, 7, 4, 1}, {5, "F_4"}, {0, "x"}}, {{2, 4, 7, 4, 2}, {5, "F_4"}, 
    {0, "x"}}, {{2, 4, 7, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{2, 5, 7, 4, 0}, {5, "F_4"}, {0, "x"}}, {{2, 5, 7, 4, 1}, {5, "F_4"}, 
    {0, "x"}}, {{2, 5, 7, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{2, 5, 8, 4, 0}, {5, "F_4"}, {0, "x"}}, {{2, 5, 8, 5, 1}, {5, "F_4"}, 
    {0, "x"}}, {{2, 5, 8, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{2, 6, 9, 5, 0}, {6, "E_6"}, {0, "x"}}, {{2, 6, 9, 5, 1}, {6, "E_6"}, 
    {0, "x"}}, {{2, 6, 9, 6, 2}, {6, "E_6"}, {0, "x"}}, 
   {{2, 6, 10, 5, 0}, {7, "E_7"}, {0, "x"}}, {{2, 6, 10, 6, 1}, {7, "E_7"}, 
    {0, "x"}}, {{2, 6, 10, 6, 2}, {7, "E_7"}, {0, "x"}}, 
   {{2, 7, 11, 6, 0}, {7, "E_7"}, {0, "x"}}, {{2, 7, 11, 6, 1}, {7, "E_7"}, 
    {0, "x"}}, {{2, 7, 11, 7, 2}, {7, "E_7"}, {0, "x"}}, 
   {{2, 7, 12, 6, 0}, {7, "E_7"}, {0, "x"}}, {{2, 7, 12, 7, 1}, {7, "E_7"}, 
    {0, "x"}}, {{2, 7, 12, 7, 2}, {7, "E_7"}, {0, "x"}}, 
   {{3, -3, -9, -5, 0}, {1, "SU(2)"}, {6, "E_6"}}, 
   {{3, -3, -9, -4, 1}, {3, "G_2"}, {6, "E_6"}}, 
   {{3, -3, -9, -4, 2}, {5, "F_4"}, {6, "E_6"}}, 
   {{3, -3, -9, -3, 3}, {5, "F_4"}, {6, "E_6"}}, 
   {{3, -3, -8, -4, 0}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{3, -3, -8, -4, 1}, {3, "G_2"}, {5, "F_4"}}, 
   {{3, -3, -8, -3, 2}, {5, "F_4"}, {5, "F_4"}}, 
   {{3, -3, -8, -3, 3}, {5, "F_4"}, {5, "F_4"}}, 
   {{3, -2, -7, -4, 0}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{3, -2, -7, -3, 1}, {3, "G_2"}, {5, "F_4"}}, 
   {{3, -2, -7, -3, 2}, {5, "F_4"}, {5, "F_4"}}, 
   {{3, -2, -7, -2, 3}, {5, "F_4"}, {5, "F_4"}}, 
   {{3, -2, -6, -3, 0}, {1, "SU(2)"}, {4, "SO(8)"}}, 
   {{3, -2, -6, -3, 1}, {3, "G_2"}, {4, "SO(8)"}}, 
   {{3, -2, -6, -2, 2}, {5, "F_4"}, {4, "SO(8)"}}, 
   {{3, -2, -6, -2, 3}, {5, "F_4"}, {4, "SO(8)"}}, 
   {{3, -1, -5, -3, 0}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{3, -1, -5, -2, 0}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{3, -1, -5, -2, 1}, {3, "G_2"}, {3, "G_2"}}, 
   {{3, -1, -5, -2, 2}, {5, "F_4"}, {3, "G_2"}}, 
   {{3, -1, -5, -1, 3}, {5, "F_4"}, {3, "G_2"}}, 
   {{3, -1, -4, -2, 0}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{3, -1, -4, -2, 1}, {3, "G_2"}, {1, "SU(2)"}}, 
   {{3, -1, -4, -1, 1}, {3, "G_2"}, {1, "SU(2)"}}, 
   {{3, -1, -4, -1, 2}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{3, -1, -4, -1, 3}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{3, 0, -3, -2, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 0, -3, -1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 0, -3, -1, 1}, {3, "G_2"}, {0, "x"}}, {{3, 0, -3, -1, 2}, {5, "F_4"}, 
    {0, "x"}}, {{3, 0, -3, 0, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 0, -3, 0, 3}, {5, "F_4"}, {0, "x"}}, {{3, 0, -2, -1, 0}, 
    {1, "SU(2)"}, {0, "x"}}, {{3, 0, -2, -1, 1}, {3, "G_2"}, {0, "x"}}, 
   {{3, 0, -2, 0, 1}, {3, "G_2"}, {0, "x"}}, {{3, 0, -2, 0, 2}, {5, "F_4"}, 
    {0, "x"}}, {{3, 0, -2, 0, 3}, {5, "F_4"}, {0, "x"}}, 
   {{3, 1, -2, -1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 1, -2, -1, 1}, {3, "G_2"}, {0, "x"}}, {{3, 1, -2, 0, 1}, {3, "G_2"}, 
    {0, "x"}}, {{3, 1, -2, 0, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 1, -2, 1, 3}, {5, "F_4"}, {0, "x"}}, {{3, 1, -1, -1, 0}, 
    {1, "SU(2)"}, {0, "x"}}, {{3, 1, -1, 0, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 1, -1, 0, 1}, {3, "G_2"}, {0, "x"}}, {{3, 1, -1, 0, 2}, {5, "F_4"}, 
    {0, "x"}}, {{3, 1, -1, 1, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 1, -1, 1, 3}, {5, "F_4"}, {0, "x"}}, {{3, 1, 0, 0, 0}, {1, "SU(2)"}, 
    {0, "x"}}, {{3, 1, 0, 0, 1}, {3, "G_2"}, {0, "x"}}, 
   {{3, 1, 0, 1, 1}, {3, "G_2"}, {0, "x"}}, {{3, 1, 0, 1, 2}, {5, "F_4"}, 
    {0, "x"}}, {{3, 1, 0, 1, 3}, {5, "F_4"}, {0, "x"}}, 
   {{3, 2, 0, 0, 0}, {1, "SU(2)"}, {0, "x"}}, {{3, 2, 0, 0, 1}, {3, "G_2"}, 
    {0, "x"}}, {{3, 2, 0, 1, 1}, {3, "G_2"}, {0, "x"}}, 
   {{3, 2, 0, 1, 2}, {5, "F_4"}, {0, "x"}}, {{3, 2, 0, 2, 3}, {5, "F_4"}, 
    {0, "x"}}, {{3, 2, 1, 0, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 2, 1, 1, 0}, {1, "SU(2)"}, {0, "x"}}, {{3, 2, 1, 1, 1}, {3, "G_2"}, 
    {0, "x"}}, {{3, 2, 1, 1, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 2, 1, 2, 2}, {5, "F_4"}, {0, "x"}}, {{3, 2, 1, 2, 3}, {5, "F_4"}, 
    {0, "x"}}, {{3, 2, 2, 1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 2, 2, 1, 1}, {3, "G_2"}, {0, "x"}}, {{3, 2, 2, 2, 1}, {3, "G_2"}, 
    {0, "x"}}, {{3, 2, 2, 2, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 2, 2, 2, 3}, {5, "F_4"}, {0, "x"}}, {{3, 3, 2, 1, 0}, {2, "SU(3)"}, 
    {0, "x"}}, {{3, 3, 2, 1, 1}, {3, "G_2"}, {0, "x"}}, 
   {{3, 3, 2, 2, 1}, {3, "G_2"}, {0, "x"}}, {{3, 3, 2, 2, 2}, {5, "F_4"}, 
    {0, "x"}}, {{3, 3, 2, 3, 3}, {5, "F_4"}, {0, "x"}}, 
   {{3, 3, 3, 1, 0}, {2, "SU(3)"}, {0, "x"}}, {{3, 3, 3, 2, 0}, {3, "G_2"}, 
    {0, "x"}}, {{3, 3, 3, 2, 1}, {3, "G_2"}, {0, "x"}}, 
   {{3, 3, 3, 2, 2}, {5, "F_4"}, {0, "x"}}, {{3, 3, 3, 3, 2}, {5, "F_4"}, 
    {0, "x"}}, {{3, 3, 3, 3, 3}, {5, "F_4"}, {0, "x"}}, 
   {{3, 3, 4, 2, 0}, {3, "G_2"}, {0, "x"}}, {{3, 3, 4, 2, 1}, {3, "G_2"}, 
    {0, "x"}}, {{3, 3, 4, 3, 1}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 3, 4, 3, 2}, {5, "F_4"}, {0, "x"}}, {{3, 3, 4, 3, 3}, {5, "F_4"}, 
    {0, "x"}}, {{3, 4, 4, 2, 0}, {3, "G_2"}, {0, "x"}}, 
   {{3, 4, 4, 2, 1}, {4, "SO(8)"}, {0, "x"}}, {{3, 4, 4, 3, 1}, {4, "SO(8)"}, 
    {0, "x"}}, {{3, 4, 4, 3, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 4, 4, 4, 3}, {5, "F_4"}, {0, "x"}}, {{3, 4, 5, 2, 0}, {4, "SO(8)"}, 
    {0, "x"}}, {{3, 4, 5, 3, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 4, 5, 3, 1}, {4, "SO(8)"}, {0, "x"}}, {{3, 4, 5, 3, 2}, {5, "F_4"}, 
    {0, "x"}}, {{3, 4, 5, 4, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 4, 5, 4, 3}, {5, "F_4"}, {0, "x"}}, {{3, 4, 6, 3, 0}, {5, "F_4"}, 
    {0, "x"}}, {{3, 4, 6, 3, 1}, {5, "F_4"}, {0, "x"}}, 
   {{3, 4, 6, 4, 1}, {5, "F_4"}, {0, "x"}}, {{3, 4, 6, 4, 2}, {5, "F_4"}, 
    {0, "x"}}, {{3, 4, 6, 4, 3}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 6, 3, 0}, {5, "F_4"}, {0, "x"}}, {{3, 5, 6, 3, 1}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 6, 4, 1}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 6, 4, 2}, {5, "F_4"}, {0, "x"}}, {{3, 5, 6, 5, 3}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 7, 4, 0}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 7, 4, 1}, {5, "F_4"}, {0, "x"}}, {{3, 5, 7, 4, 2}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 7, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 7, 5, 3}, {5, "F_4"}, {0, "x"}}, {{3, 5, 8, 4, 0}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 8, 5, 1}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 8, 5, 2}, {5, "F_4"}, {0, "x"}}, {{3, 5, 8, 5, 3}, {5, "F_4"}, 
    {0, "x"}}, {{3, 6, 8, 4, 0}, {5, "F_4"}, {0, "x"}}, 
   {{3, 6, 8, 5, 1}, {5, "F_4"}, {0, "x"}}, {{3, 6, 8, 5, 2}, {5, "F_4"}, 
    {0, "x"}}, {{3, 6, 8, 6, 3}, {6, "E_6"}, {0, "x"}}, 
   {{3, 6, 9, 5, 0}, {6, "E_6"}, {0, "x"}}, {{3, 6, 9, 5, 1}, {6, "E_6"}, 
    {0, "x"}}, {{3, 6, 9, 6, 2}, {6, "E_6"}, {0, "x"}}, 
   {{3, 6, 9, 6, 3}, {6, "E_6"}, {0, "x"}}, {{3, 7, 10, 5, 0}, {7, "E_7"}, 
    {0, "x"}}, {{3, 7, 10, 6, 1}, {7, "E_7"}, {0, "x"}}, 
   {{3, 7, 10, 6, 2}, {7, "E_7"}, {0, "x"}}, {{3, 7, 10, 7, 3}, {7, "E_7"}, 
    {0, "x"}}, {{3, 7, 11, 6, 0}, {7, "E_7"}, {0, "x"}}, 
   {{3, 7, 11, 6, 1}, {7, "E_7"}, {0, "x"}}, {{3, 7, 11, 7, 2}, {7, "E_7"}, 
    {0, "x"}}, {{3, 7, 11, 7, 3}, {7, "E_7"}, {0, "x"}}, 
   {{3, 8, 12, 6, 0}, {7, "E_7"}, {0, "x"}}, {{3, 8, 12, 7, 1}, {7, "E_7"}, 
    {0, "x"}}, {{3, 8, 12, 7, 2}, {7, "E_7"}, {0, "x"}}, 
   {{3, 8, 12, 8, 3}, {7, "E_7"}, {0, "x"}}, {{4, -2, -8, -4, 0}, {3, "G_2"}, 
    {5, "F_4"}}, {{4, -2, -8, -4, 1}, {5, "F_4"}, {5, "F_4"}}, 
   {{4, -2, -8, -3, 2}, {5, "F_4"}, {5, "F_4"}}, 
   {{4, -2, -8, -2, 4}, {7, "E_7"}, {5, "F_4"}}, 
   {{4, -2, -7, -4, 0}, {3, "G_2"}, {5, "F_4"}}, 
   {{4, -2, -7, -3, 1}, {5, "F_4"}, {5, "F_4"}}, 
   {{4, -2, -7, -3, 2}, {5, "F_4"}, {5, "F_4"}}, 
   {{4, -1, -6, -3, 0}, {3, "G_2"}, {4, "SO(8)"}}, 
   {{4, -1, -6, -3, 1}, {5, "F_4"}, {4, "SO(8)"}}, 
   {{4, -1, -6, -2, 2}, {5, "F_4"}, {4, "SO(8)"}}, 
   {{4, -1, -6, -1, 4}, {7, "E_7"}, {4, "SO(8)"}}, 
   {{4, -1, -5, -3, 0}, {3, "G_2"}, {3, "G_2"}}, 
   {{4, -1, -5, -2, 0}, {3, "G_2"}, {3, "G_2"}}, 
   {{4, -1, -5, -2, 1}, {5, "F_4"}, {3, "G_2"}}, 
   {{4, -1, -5, -2, 2}, {5, "F_4"}, {3, "G_2"}}, 
   {{4, 0, -4, -2, 0}, {3, "G_2"}, {1, "SU(2)"}}, 
   {{4, 0, -4, -2, 1}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{4, 0, -4, -1, 1}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{4, 0, -4, -1, 2}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{4, 0, -4, 0, 4}, {7, "E_7"}, {1, "SU(2)"}}, 
   {{4, 0, -3, -2, 0}, {3, "G_2"}, {0, "x"}}, {{4, 0, -3, -1, 0}, {3, "G_2"}, 
    {0, "x"}}, {{4, 0, -3, -1, 1}, {5, "F_4"}, {0, "x"}}, 
   {{4, 0, -3, -1, 2}, {5, "F_4"}, {0, "x"}}, {{4, 1, -2, -1, 0}, {3, "G_2"}, 
    {0, "x"}}, {{4, 1, -2, -1, 1}, {5, "F_4"}, {0, "x"}}, 
   {{4, 1, -2, 0, 1}, {5, "F_4"}, {0, "x"}}, {{4, 1, -2, 0, 2}, {5, "F_4"}, 
    {0, "x"}}, {{4, 1, -2, 1, 3}, {7, "E_7"}, {0, "x"}}, 
   {{4, 1, -2, 1, 4}, {7, "E_7"}, {0, "x"}}, {{4, 1, -1, -1, 0}, {3, "G_2"}, 
    {0, "x"}}, {{4, 1, -1, 0, 0}, {3, "G_2"}, {0, "x"}}, 
   {{4, 1, -1, 0, 1}, {5, "F_4"}, {0, "x"}}, {{4, 1, -1, 0, 2}, {5, "F_4"}, 
    {0, "x"}}, {{4, 2, -1, -1, 0}, {3, "G_2"}, {0, "x"}}, 
   {{4, 2, -1, 0, 0}, {3, "G_2"}, {0, "x"}}, {{4, 2, -1, 0, 1}, {5, "F_4"}, 
    {0, "x"}}, {{4, 2, -1, 1, 2}, {5, "F_4"}, {0, "x"}}, 
   {{4, 2, -1, 1, 3}, {7, "E_7"}, {0, "x"}}, {{4, 2, -1, 2, 4}, {7, "E_7"}, 
    {0, "x"}}, {{4, 2, 0, 0, 0}, {3, "G_2"}, {0, "x"}}, 
   {{4, 2, 0, 0, 1}, {5, "F_4"}, {0, "x"}}, {{4, 2, 0, 1, 1}, {5, "F_4"}, 
    {0, "x"}}, {{4, 2, 0, 1, 2}, {5, "F_4"}, {0, "x"}}, 
   {{4, 2, 0, 2, 3}, {7, "E_7"}, {0, "x"}}, {{4, 2, 0, 2, 4}, {7, "E_7"}, 
    {0, "x"}}, {{4, 2, 1, 0, 0}, {3, "G_2"}, {0, "x"}}, 
   {{4, 2, 1, 1, 0}, {3, "G_2"}, {0, "x"}}, {{4, 2, 1, 1, 1}, {5, "F_4"}, 
    {0, "x"}}, {{4, 2, 1, 1, 2}, {5, "F_4"}, {0, "x"}}, 
   {{4, 3, 1, 0, 0}, {3, "G_2"}, {0, "x"}}, {{4, 3, 1, 1, 0}, {3, "G_2"}, 
    {0, "x"}}, {{4, 3, 1, 1, 1}, {5, "F_4"}, {0, "x"}}, 
   {{4, 3, 1, 2, 2}, {5, "F_4"}, {0, "x"}}, {{4, 3, 1, 2, 3}, {7, "E_7"}, 
    {0, "x"}}, {{4, 3, 1, 3, 4}, {7, "E_7"}, {0, "x"}}, 
   {{4, 3, 2, 1, 0}, {3, "G_2"}, {0, "x"}}, {{4, 3, 2, 1, 1}, {5, "F_4"}, 
    {0, "x"}}, {{4, 3, 2, 2, 1}, {5, "F_4"}, {0, "x"}}, 
   {{4, 3, 2, 2, 2}, {5, "F_4"}, {0, "x"}}, {{4, 3, 2, 3, 3}, {7, "E_7"}, 
    {0, "x"}}, {{4, 3, 2, 3, 4}, {7, "E_7"}, {0, "x"}}, 
   {{4, 3, 3, 1, 0}, {3, "G_2"}, {0, "x"}}, {{4, 3, 3, 2, 0}, {4, "SO(8)"}, 
    {0, "x"}}, {{4, 3, 3, 2, 1}, {5, "F_4"}, {0, "x"}}, 
   {{4, 3, 3, 2, 2}, {5, "F_4"}, {0, "x"}}, {{4, 4, 3, 1, 0}, {4, "SO(8)"}, 
    {0, "x"}}, {{4, 4, 3, 2, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 4, 3, 2, 1}, {5, "F_4"}, {0, "x"}}, {{4, 4, 3, 3, 2}, {5, "F_4"}, 
    {0, "x"}}, {{4, 4, 3, 3, 3}, {7, "E_7"}, {0, "x"}}, 
   {{4, 4, 3, 4, 4}, {7, "E_7"}, {0, "x"}}, {{4, 4, 4, 2, 0}, {4, "SO(8)"}, 
    {0, "x"}}, {{4, 4, 4, 2, 1}, {5, "F_4"}, {0, "x"}}, 
   {{4, 4, 4, 3, 1}, {5, "F_4"}, {0, "x"}}, {{4, 4, 4, 3, 2}, {5, "F_4"}, 
    {0, "x"}}, {{4, 4, 4, 4, 3}, {7, "E_7"}, {0, "x"}}, 
   {{4, 4, 4, 4, 4}, {7, "E_7"}, {0, "x"}}, {{4, 4, 5, 2, 0}, {5, "F_4"}, 
    {0, "x"}}, {{4, 4, 5, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{4, 4, 5, 3, 1}, {5, "F_4"}, {0, "x"}}, {{4, 4, 5, 3, 2}, {5, "F_4"}, 
    {0, "x"}}, {{4, 5, 5, 2, 0}, {5, "F_4"}, {0, "x"}}, 
   {{4, 5, 5, 3, 0}, {5, "F_4"}, {0, "x"}}, {{4, 5, 5, 3, 1}, {5, "F_4"}, 
    {0, "x"}}, {{4, 5, 5, 4, 2}, {5, "F_4"}, {0, "x"}}, 
   {{4, 5, 5, 4, 3}, {7, "E_7"}, {0, "x"}}, {{4, 5, 5, 5, 4}, {7, "E_7"}, 
    {0, "x"}}, {{4, 5, 6, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{4, 5, 6, 3, 1}, {5, "F_4"}, {0, "x"}}, {{4, 5, 6, 4, 1}, {5, "F_4"}, 
    {0, "x"}}, {{4, 5, 6, 4, 2}, {5, "F_4"}, {0, "x"}}, 
   {{4, 5, 6, 5, 3}, {7, "E_7"}, {0, "x"}}, {{4, 5, 6, 5, 4}, {7, "E_7"}, 
    {0, "x"}}, {{4, 5, 7, 4, 0}, {5, "F_4"}, {0, "x"}}, 
   {{4, 5, 7, 4, 1}, {5, "F_4"}, {0, "x"}}, {{4, 5, 7, 4, 2}, {5, "F_4"}, 
    {0, "x"}}, {{4, 6, 7, 4, 0}, {5, "F_4"}, {0, "x"}}, 
   {{4, 6, 7, 4, 1}, {5, "F_4"}, {0, "x"}}, {{4, 6, 7, 5, 2}, {6, "E_6"}, 
    {0, "x"}}, {{4, 6, 7, 5, 3}, {7, "E_7"}, {0, "x"}}, 
   {{4, 6, 7, 6, 4}, {7, "E_7"}, {0, "x"}}, {{4, 6, 8, 4, 0}, {6, "E_6"}, 
    {0, "x"}}, {{4, 6, 8, 5, 1}, {6, "E_6"}, {0, "x"}}, 
   {{4, 6, 8, 5, 2}, {6, "E_6"}, {0, "x"}}, {{4, 6, 8, 6, 3}, {7, "E_7"}, 
    {0, "x"}}, {{4, 6, 8, 6, 4}, {7, "E_7"}, {0, "x"}}, 
   {{4, 7, 9, 5, 0}, {7, "E_7"}, {0, "x"}}, {{4, 7, 9, 5, 1}, {7, "E_7"}, 
    {0, "x"}}, {{4, 7, 9, 6, 2}, {7, "E_7"}, {0, "x"}}, 
   {{4, 7, 9, 6, 3}, {7, "E_7"}, {0, "x"}}, {{4, 7, 9, 7, 4}, {7, "E_7"}, 
    {0, "x"}}, {{4, 7, 10, 5, 0}, {7, "E_7"}, {0, "x"}}, 
   {{4, 7, 10, 6, 1}, {7, "E_7"}, {0, "x"}}, {{4, 7, 10, 6, 2}, {7, "E_7"}, 
    {0, "x"}}, {{4, 7, 10, 7, 3}, {7, "E_7"}, {0, "x"}}, 
   {{4, 7, 10, 7, 4}, {7, "E_7"}, {0, "x"}}, {{4, 8, 11, 6, 0}, {7, "E_7"}, 
    {0, "x"}}, {{4, 8, 11, 6, 1}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 11, 7, 2}, {7, "E_7"}, {0, "x"}}, {{4, 8, 11, 7, 3}, {7, "E_7"}, 
    {0, "x"}}, {{4, 8, 11, 8, 4}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 12, 6, 0}, {7, "E_7"}, {0, "x"}}, {{4, 8, 12, 7, 1}, {7, "E_7"}, 
    {0, "x"}}, {{4, 8, 12, 7, 2}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 12, 8, 3}, {7, "E_7"}, {0, "x"}}, {{4, 8, 12, 8, 4}, {7, "E_7"}, 
    {0, "x"}}, {{5, -1, -7, -4, 0}, {5, "F_4"}, {5, "F_4"}}, 
   {{5, -1, -7, -3, 1}, {5, "F_4"}, {5, "F_4"}}, 
   {{5, -1, -7, -2, 3}, {7, "E_7"}, {5, "F_4"}}, 
   {{5, -1, -6, -3, 0}, {5, "F_4"}, {4, "SO(8)"}}, 
   {{5, -1, -6, -3, 1}, {5, "F_4"}, {4, "SO(8)"}}, 
   {{5, 0, -5, -3, 0}, {5, "F_4"}, {3, "G_2"}}, 
   {{5, 0, -5, -2, 0}, {5, "F_4"}, {3, "G_2"}}, 
   {{5, 0, -5, -2, 1}, {5, "F_4"}, {3, "G_2"}}, 
   {{5, 0, -5, -1, 3}, {7, "E_7"}, {3, "G_2"}}, 
   {{5, 0, -4, -2, 0}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{5, 0, -4, -2, 1}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{5, 1, -3, -2, 0}, {5, "F_4"}, {0, "x"}}, {{5, 1, -3, -1, 0}, {5, "F_4"}, 
    {0, "x"}}, {{5, 1, -3, -1, 1}, {5, "F_4"}, {0, "x"}}, 
   {{5, 1, -3, 0, 2}, {7, "E_7"}, {0, "x"}}, {{5, 1, -3, 0, 3}, {7, "E_7"}, 
    {0, "x"}}, {{5, 1, -2, -1, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 1, -2, -1, 1}, {5, "F_4"}, {0, "x"}}, {{5, 2, -1, -1, 0}, {5, "F_4"}, 
    {0, "x"}}, {{5, 2, -1, 0, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 2, -1, 0, 1}, {5, "F_4"}, {0, "x"}}, {{5, 2, -1, 1, 2}, {7, "E_7"}, 
    {0, "x"}}, {{5, 2, -1, 1, 3}, {7, "E_7"}, {0, "x"}}, 
   {{5, 2, 0, 0, 0}, {5, "F_4"}, {0, "x"}}, {{5, 2, 0, 0, 1}, {5, "F_4"}, 
    {0, "x"}}, {{5, 3, 0, 0, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 3, 0, 1, 1}, {5, "F_4"}, {0, "x"}}, {{5, 3, 0, 1, 2}, {7, "E_7"}, 
    {0, "x"}}, {{5, 3, 0, 2, 3}, {7, "E_7"}, {0, "x"}}, 
   {{5, 3, 1, 0, 0}, {5, "F_4"}, {0, "x"}}, {{5, 3, 1, 1, 0}, {5, "F_4"}, 
    {0, "x"}}, {{5, 3, 1, 1, 1}, {5, "F_4"}, {0, "x"}}, 
   {{5, 3, 1, 2, 2}, {7, "E_7"}, {0, "x"}}, {{5, 3, 1, 2, 3}, {7, "E_7"}, 
    {0, "x"}}, {{5, 3, 2, 1, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 3, 2, 1, 1}, {5, "F_4"}, {0, "x"}}, {{5, 4, 2, 1, 0}, {5, "F_4"}, 
    {0, "x"}}, {{5, 4, 2, 2, 1}, {5, "F_4"}, {0, "x"}}, 
   {{5, 4, 2, 2, 2}, {7, "E_7"}, {0, "x"}}, {{5, 4, 2, 3, 3}, {7, "E_7"}, 
    {0, "x"}}, {{5, 4, 3, 1, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 4, 3, 2, 0}, {5, "F_4"}, {0, "x"}}, {{5, 4, 3, 2, 1}, {5, "F_4"}, 
    {0, "x"}}, {{5, 4, 3, 3, 2}, {7, "E_7"}, {0, "x"}}, 
   {{5, 4, 3, 3, 3}, {7, "E_7"}, {0, "x"}}, {{5, 4, 4, 2, 0}, {5, "F_4"}, 
    {0, "x"}}, {{5, 4, 4, 2, 1}, {5, "F_4"}, {0, "x"}}, 
   {{5, 5, 4, 2, 0}, {5, "F_4"}, {0, "x"}}, {{5, 5, 4, 3, 1}, {5, "F_4"}, 
    {0, "x"}}, {{5, 5, 4, 3, 2}, {7, "E_7"}, {0, "x"}}, 
   {{5, 5, 4, 4, 3}, {7, "E_7"}, {0, "x"}}, {{5, 5, 5, 2, 0}, {5, "F_4"}, 
    {0, "x"}}, {{5, 5, 5, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 5, 5, 3, 1}, {5, "F_4"}, {0, "x"}}, {{5, 5, 5, 4, 2}, {7, "E_7"}, 
    {0, "x"}}, {{5, 5, 5, 4, 3}, {7, "E_7"}, {0, "x"}}, 
   {{5, 5, 6, 3, 0}, {5, "F_4"}, {0, "x"}}, {{5, 5, 6, 3, 1}, {5, "F_4"}, 
    {0, "x"}}, {{5, 6, 6, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{5, 6, 6, 4, 1}, {6, "E_6"}, {0, "x"}}, {{5, 6, 6, 4, 2}, {7, "E_7"}, 
    {0, "x"}}, {{5, 6, 6, 5, 3}, {7, "E_7"}, {0, "x"}}, 
   {{5, 6, 7, 4, 0}, {6, "E_6"}, {0, "x"}}, {{5, 6, 7, 4, 1}, {6, "E_6"}, 
    {0, "x"}}, {{5, 6, 7, 5, 2}, {7, "E_7"}, {0, "x"}}, 
   {{5, 6, 7, 5, 3}, {7, "E_7"}, {0, "x"}}, {{5, 7, 8, 4, 0}, {7, "E_7"}, 
    {0, "x"}}, {{5, 7, 8, 5, 1}, {7, "E_7"}, {0, "x"}}, 
   {{5, 7, 8, 5, 2}, {7, "E_7"}, {0, "x"}}, {{5, 7, 8, 6, 3}, {7, "E_7"}, 
    {0, "x"}}, {{5, 7, 9, 5, 0}, {7, "E_7"}, {0, "x"}}, 
   {{5, 7, 9, 5, 1}, {7, "E_7"}, {0, "x"}}, {{5, 7, 9, 6, 2}, {7, "E_7"}, 
    {0, "x"}}, {{5, 7, 9, 6, 3}, {7, "E_7"}, {0, "x"}}, 
   {{5, 8, 10, 5, 0}, {7, "E_7"}, {0, "x"}}, {{5, 8, 10, 6, 1}, {7, "E_7"}, 
    {0, "x"}}, {{5, 8, 10, 6, 2}, {7, "E_7"}, {0, "x"}}, 
   {{5, 8, 10, 7, 3}, {7, "E_7"}, {0, "x"}}, {{5, 8, 11, 6, 0}, {7, "E_7"}, 
    {0, "x"}}, {{5, 8, 11, 6, 1}, {7, "E_7"}, {0, "x"}}, 
   {{5, 8, 11, 7, 2}, {7, "E_7"}, {0, "x"}}, {{5, 8, 11, 7, 3}, {7, "E_7"}, 
    {0, "x"}}, {{6, 0, -6, -3, 0}, {5, "F_4"}, {4, "SO(8)"}}, 
   {{6, 0, -6, -2, 2}, {7, "E_7"}, {4, "SO(8)"}}, 
   {{6, 0, -5, -3, 0}, {5, "F_4"}, {3, "G_2"}}, 
   {{6, 1, -4, -2, 0}, {5, "F_4"}, {1, "SU(2)"}}, 
   {{6, 1, -4, -1, 1}, {7, "E_7"}, {1, "SU(2)"}}, 
   {{6, 1, -4, -1, 2}, {7, "E_7"}, {1, "SU(2)"}}, 
   {{6, 1, -3, -2, 0}, {5, "F_4"}, {0, "x"}}, {{6, 2, -2, -1, 0}, {5, "F_4"}, 
    {0, "x"}}, {{6, 2, -2, 0, 1}, {7, "E_7"}, {0, "x"}}, 
   {{6, 2, -2, 0, 2}, {7, "E_7"}, {0, "x"}}, {{6, 2, -1, -1, 0}, {5, "F_4"}, 
    {0, "x"}}, {{6, 3, 0, 0, 0}, {5, "F_4"}, {0, "x"}}, 
   {{6, 3, 0, 1, 1}, {7, "E_7"}, {0, "x"}}, {{6, 3, 0, 1, 2}, {7, "E_7"}, 
    {0, "x"}}, {{6, 3, 1, 0, 0}, {5, "F_4"}, {0, "x"}}, 
   {{6, 4, 1, 1, 0}, {5, "F_4"}, {0, "x"}}, {{6, 4, 1, 1, 1}, {7, "E_7"}, 
    {0, "x"}}, {{6, 4, 1, 2, 2}, {7, "E_7"}, {0, "x"}}, 
   {{6, 4, 2, 1, 0}, {5, "F_4"}, {0, "x"}}, {{6, 4, 2, 2, 1}, {7, "E_7"}, 
    {0, "x"}}, {{6, 4, 2, 2, 2}, {7, "E_7"}, {0, "x"}}, 
   {{6, 4, 3, 1, 0}, {5, "F_4"}, {0, "x"}}, {{6, 5, 3, 2, 0}, {5, "F_4"}, 
    {0, "x"}}, {{6, 5, 3, 2, 1}, {7, "E_7"}, {0, "x"}}, 
   {{6, 5, 3, 3, 2}, {7, "E_7"}, {0, "x"}}, {{6, 5, 4, 2, 0}, {5, "F_4"}, 
    {0, "x"}}, {{6, 5, 4, 3, 1}, {7, "E_7"}, {0, "x"}}, 
   {{6, 5, 4, 3, 2}, {7, "E_7"}, {0, "x"}}, {{6, 5, 5, 2, 0}, {5, "F_4"}, 
    {0, "x"}}, {{6, 6, 5, 3, 0}, {6, "E_6"}, {0, "x"}}, 
   {{6, 6, 5, 3, 1}, {7, "E_7"}, {0, "x"}}, {{6, 6, 5, 4, 2}, {7, "E_7"}, 
    {0, "x"}}, {{6, 6, 6, 3, 0}, {6, "E_6"}, {0, "x"}}, 
   {{6, 6, 6, 4, 1}, {7, "E_7"}, {0, "x"}}, {{6, 6, 6, 4, 2}, {7, "E_7"}, 
    {0, "x"}}, {{6, 7, 7, 4, 0}, {7, "E_7"}, {0, "x"}}, 
   {{6, 7, 7, 4, 1}, {7, "E_7"}, {0, "x"}}, {{6, 7, 7, 5, 2}, {7, "E_7"}, 
    {0, "x"}}, {{6, 7, 8, 4, 0}, {7, "E_7"}, {0, "x"}}, 
   {{6, 7, 8, 5, 1}, {7, "E_7"}, {0, "x"}}, {{6, 7, 8, 5, 2}, {7, "E_7"}, 
    {0, "x"}}, {{6, 8, 9, 5, 0}, {7, "E_7"}, {0, "x"}}, 
   {{6, 8, 9, 5, 1}, {7, "E_7"}, {0, "x"}}, {{6, 8, 9, 6, 2}, {7, "E_7"}, 
    {0, "x"}}, {{6, 8, 10, 5, 0}, {7, "E_7"}, {0, "x"}}, 
   {{6, 8, 10, 6, 1}, {7, "E_7"}, {0, "x"}}, {{6, 8, 10, 6, 2}, {7, "E_7"}, 
    {0, "x"}}, {{6, 12, 18, 12, 6}, {8, "E_8"}, {0, "x"}}}}, 
 {{{0, 1}, {1, 0}, {1, -1}, {0, -1}, {-1, -1}, {-2, -1}, {-1, 0}}, 
  {{{-6, -4, -1, 1, 1}, {0, "x"}, {3, "G_2"}}, {{-6, -3, -1, 1, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-6, -3, -1, 2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-6, -3, 0, 2, 1}, {0, "x"}, {3, "G_2"}}, {{-6, -3, 0, 3, 1}, {0, "x"}, 
    {3, "G_2"}}, {{-6, -3, 0, 3, 2}, {0, "x"}, {2, "SU(3)"}}, 
   {{-6, -2, 1, 4, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-6, -2, 2, 5, 2}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-6, -2, 2, 5, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-6, -2, 2, 6, 3}, {2, "SU(3)"}, {0, "x"}}, 
   {{-6, -1, 3, 7, 3}, {3, "G_2"}, {0, "x"}}, {{-6, -1, 3, 7, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-6, -1, 4, 8, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{-6, -1, 4, 9, 4}, {5, "F_4"}, {0, "x"}}, {{-6, -1, 4, 9, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-6, 0, 5, 10, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-6, 0, 6, 11, 5}, {5, "F_4"}, {0, "x"}}, {{-6, 0, 6, 11, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-6, 0, 6, 12, 6}, {6, "E_6"}, {0, "x"}}, 
   {{-5, -3, -1, 1, 1}, {0, "x"}, {2, "SU(3)"}}, 
   {{-5, -3, 0, 2, 1}, {0, "x"}, {1, "SU(2)"}}, {{-5, -2, 0, 2, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-5, -2, 0, 3, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-5, -2, 0, 3, 2}, {0, "x"}, {1, "SU(2)"}}, {{-5, -2, 1, 3, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-5, -2, 1, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{-5, -2, 1, 4, 2}, {0, "x"}, {0, "x"}}, {{-5, -1, 2, 5, 2}, {1, "SU(2)"}, 
    {0, "x"}}, {{-5, -1, 2, 5, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-5, -1, 3, 6, 3}, {2, "SU(3)"}, {0, "x"}}, 
   {{-5, -1, 3, 7, 3}, {3, "G_2"}, {0, "x"}}, {{-5, -1, 3, 7, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-5, 0, 4, 8, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{-5, 0, 5, 9, 4}, {5, "F_4"}, {0, "x"}}, {{-5, 0, 5, 9, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-5, 0, 5, 10, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-5, 1, 6, 11, 5}, {5, "F_4"}, {0, "x"}}, {{-5, 1, 6, 11, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-5, 1, 7, 12, 6}, {6, "E_6"}, {0, "x"}}, 
   {{-5, 1, 7, 13, 7}, {7, "E_7"}, {0, "x"}}, {{-4, -3, -1, 1, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-4, -2, -1, 1, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -2, 0, 1, 1}, {0, "x"}, {0, "x"}}, {{-4, -2, 0, 2, 1}, {0, "x"}, 
    {0, "x"}}, {{-4, -2, 1, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{-4, -2, 1, 3, 2}, {0, "x"}, {0, "x"}}, {{-4, -1, 1, 3, 1}, {0, "x"}, 
    {0, "x"}}, {{-4, -1, 1, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{-4, -1, 1, 4, 2}, {0, "x"}, {0, "x"}}, {{-4, -1, 2, 4, 2}, {0, "x"}, 
    {0, "x"}}, {{-4, -1, 2, 5, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-4, -1, 2, 5, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-4, 0, 3, 6, 3}, {2, "SU(3)"}, {0, "x"}}, {{-4, 0, 4, 7, 3}, {3, "G_2"}, 
    {0, "x"}}, {{-4, 0, 4, 7, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-4, 0, 4, 8, 4}, {4, "SO(8)"}, {0, "x"}}, {{-4, 1, 5, 9, 4}, {5, "F_4"}, 
    {0, "x"}}, {{-4, 1, 5, 9, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-4, 1, 6, 10, 5}, {5, "F_4"}, {0, "x"}}, {{-4, 1, 6, 11, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-4, 1, 6, 11, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-4, 2, 7, 12, 6}, {6, "E_6"}, {0, "x"}}, {{-4, 2, 8, 13, 7}, {7, "E_7"}, 
    {0, "x"}}, {{-4, 2, 8, 14, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-3, -2, -1, 1, 1}, {0, "x"}, {0, "x"}}, {{-3, -2, 0, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, -2, 0, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-3, -1, 0, 1, 1}, {0, "x"}, {0, "x"}}, {{-3, -1, 0, 2, 1}, {0, "x"}, 
    {0, "x"}}, {{-3, -1, 1, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-3, -1, 1, 3, 1}, {0, "x"}, {0, "x"}}, {{-3, -1, 1, 3, 2}, {0, "x"}, 
    {0, "x"}}, {{-3, -1, 2, 4, 2}, {0, "x"}, {0, "x"}}, 
   {{-3, 0, 2, 4, 2}, {0, "x"}, {0, "x"}}, {{-3, 0, 2, 5, 2}, {1, "SU(2)"}, 
    {0, "x"}}, {{-3, 0, 2, 5, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-3, 0, 3, 5, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-3, 0, 3, 5, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-3, 0, 3, 6, 3}, {2, "SU(3)"}, {0, "x"}}, {{-3, 1, 4, 7, 3}, {3, "G_2"}, 
    {0, "x"}}, {{-3, 1, 4, 7, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-3, 1, 5, 8, 4}, {4, "SO(8)"}, {0, "x"}}, {{-3, 1, 5, 9, 4}, {5, "F_4"}, 
    {0, "x"}}, {{-3, 1, 5, 9, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-3, 2, 6, 10, 5}, {5, "F_4"}, {0, "x"}}, {{-3, 2, 7, 11, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-3, 2, 7, 11, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-3, 2, 7, 12, 6}, {6, "E_6"}, {0, "x"}}, {{-3, 3, 8, 13, 7}, {7, "E_7"}, 
    {0, "x"}}, {{-3, 3, 9, 14, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-3, 3, 9, 15, 8}, {7, "E_7"}, {0, "x"}}, {{-2, -1, 0, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{-2, -1, 0, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -1, 1, 2, 1}, {0, "x"}, {0, "x"}}, {{-2, -1, 1, 3, 1}, {0, "x"}, 
    {0, "x"}}, {{-2, -1, 1, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, 0, 1, 2, 1}, {0, "x"}, {0, "x"}}, {{-2, 0, 1, 3, 1}, {0, "x"}, 
    {0, "x"}}, {{-2, 0, 1, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, 0, 2, 3, 1}, {0, "x"}, {0, "x"}}, {{-2, 0, 2, 3, 2}, {0, "x"}, 
    {0, "x"}}, {{-2, 0, 2, 4, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, 0, 3, 5, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-2, 0, 3, 5, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-2, 1, 3, 5, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-2, 1, 3, 5, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-2, 1, 3, 6, 3}, {2, "SU(3)"}, {0, "x"}}, 
   {{-2, 1, 4, 6, 3}, {2, "SU(3)"}, {0, "x"}}, {{-2, 1, 4, 7, 3}, {3, "G_2"}, 
    {0, "x"}}, {{-2, 1, 4, 7, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-2, 2, 5, 8, 4}, {4, "SO(8)"}, {0, "x"}}, {{-2, 2, 6, 9, 4}, {5, "F_4"}, 
    {0, "x"}}, {{-2, 2, 6, 9, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-2, 2, 6, 10, 5}, {5, "F_4"}, {0, "x"}}, {{-2, 3, 7, 11, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-2, 3, 7, 11, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-2, 3, 8, 12, 6}, {6, "E_6"}, {0, "x"}}, {{-2, 3, 8, 13, 7}, {7, "E_7"}, 
    {0, "x"}}, {{-2, 4, 9, 14, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-2, 4, 10, 15, 8}, {7, "E_7"}, {0, "x"}}, {{-2, 4, 10, 16, 8}, 
    {7, "E_7"}, {0, "x"}}, {{-1, -1, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, 0, 0, 1, 1}, {0, "x"}, {0, "x"}}, {{-1, 0, 1, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{-1, 0, 1, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, 0, 1, 3, 1}, {0, "x"}, {0, "x"}}, {{-1, 0, 1, 3, 2}, {0, "x"}, 
    {0, "x"}}, {{-1, 0, 2, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, 0, 2, 3, 2}, {0, "x"}, {0, "x"}}, {{-1, 0, 2, 4, 2}, {0, "x"}, 
    {0, "x"}}, {{-1, 1, 2, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, 1, 2, 3, 2}, {0, "x"}, {0, "x"}}, {{-1, 1, 2, 4, 2}, {0, "x"}, 
    {0, "x"}}, {{-1, 1, 3, 4, 2}, {0, "x"}, {0, "x"}}, 
   {{-1, 1, 3, 5, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-1, 1, 3, 5, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-1, 1, 4, 6, 3}, {2, "SU(3)"}, {0, "x"}}, 
   {{-1, 2, 4, 6, 3}, {2, "SU(3)"}, {0, "x"}}, {{-1, 2, 4, 7, 3}, {3, "G_2"}, 
    {0, "x"}}, {{-1, 2, 4, 7, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-1, 2, 5, 7, 3}, {3, "G_2"}, {0, "x"}}, {{-1, 2, 5, 7, 4}, {3, "G_2"}, 
    {0, "x"}}, {{-1, 2, 5, 8, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{-1, 3, 6, 9, 4}, {5, "F_4"}, {0, "x"}}, {{-1, 3, 6, 9, 5}, {5, "F_4"}, 
    {0, "x"}}, {{-1, 3, 7, 10, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-1, 3, 7, 11, 5}, {5, "F_4"}, {0, "x"}}, {{-1, 3, 7, 11, 6}, {5, "F_4"}, 
    {0, "x"}}, {{-1, 4, 8, 12, 6}, {6, "E_6"}, {0, "x"}}, 
   {{-1, 4, 9, 13, 7}, {7, "E_7"}, {0, "x"}}, {{-1, 4, 9, 14, 7}, {7, "E_7"}, 
    {0, "x"}}, {{-1, 5, 10, 15, 8}, {7, "E_7"}, {0, "x"}}, 
   {{-1, 5, 11, 16, 8}, {7, "E_7"}, {0, "x"}}, {{0, 0, 0, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 0, 0, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 0, 1, 1}, {0, "x"}, {0, "x"}}, {{0, 0, 1, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 0, 1, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 1, 2, 1}, {0, "x"}, {0, "x"}}, {{0, 1, 1, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 1, 1, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 1, 2, 1}, {0, "x"}, {0, "x"}}, {{0, 1, 2, 2, 1}, {0, "x"}, 
    {0, "x"}}, {{0, 1, 2, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 2, 3, 2}, {0, "x"}, {0, "x"}}, {{0, 1, 2, 4, 2}, {0, "x"}, 
    {0, "x"}}, {{0, 1, 3, 4, 2}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 3, 5, 2}, {1, "SU(2)"}, {0, "x"}}, {{0, 1, 3, 5, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{0, 2, 3, 4, 2}, {0, "x"}, {0, "x"}}, 
   {{0, 2, 3, 5, 2}, {1, "SU(2)"}, {0, "x"}}, {{0, 2, 3, 5, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{0, 2, 4, 5, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{0, 2, 4, 5, 3}, {1, "SU(2)"}, {0, "x"}}, {{0, 2, 4, 6, 3}, {2, "SU(3)"}, 
    {0, "x"}}, {{0, 2, 5, 7, 3}, {3, "G_2"}, {0, "x"}}, 
   {{0, 2, 5, 7, 4}, {3, "G_2"}, {0, "x"}}, {{0, 3, 5, 7, 3}, {3, "G_2"}, 
    {0, "x"}}, {{0, 3, 5, 7, 4}, {3, "G_2"}, {0, "x"}}, 
   {{0, 3, 5, 8, 4}, {4, "SO(8)"}, {0, "x"}}, {{0, 3, 6, 8, 4}, {4, "SO(8)"}, 
    {0, "x"}}, {{0, 3, 6, 9, 4}, {5, "F_4"}, {0, "x"}}, 
   {{0, 3, 6, 9, 5}, {5, "F_4"}, {0, "x"}}, {{0, 4, 7, 10, 5}, {5, "F_4"}, 
    {0, "x"}}, {{0, 4, 8, 11, 5}, {5, "F_4"}, {0, "x"}}, 
   {{0, 4, 8, 11, 6}, {5, "F_4"}, {0, "x"}}, {{0, 4, 8, 12, 6}, {6, "E_6"}, 
    {0, "x"}}, {{0, 5, 9, 13, 7}, {7, "E_7"}, {0, "x"}}, 
   {{0, 5, 10, 14, 7}, {7, "E_7"}, {0, "x"}}, {{0, 5, 10, 15, 8}, {7, "E_7"}, 
    {0, "x"}}, {{0, 6, 11, 16, 8}, {7, "E_7"}, {0, "x"}}, 
   {{1, 0, -1, -1, 0}, {0, "x"}, {0, "x"}}, {{1, 0, 0, -1, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 0, 0, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 0, -1, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 0, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 1, 1, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 1, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{1, 1, 1, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 2, 2, 1}, {0, "x"}, {0, "x"}}, {{1, 1, 2, 3, 1}, {0, "x"}, 
    {0, "x"}}, {{1, 1, 2, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 2, 2, 1}, {0, "x"}, {0, "x"}}, {{1, 2, 2, 3, 1}, {0, "x"}, 
    {0, "x"}}, {{1, 2, 2, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 3, 3, 1}, {0, "x"}, {0, "x"}}, {{1, 2, 3, 3, 2}, {0, "x"}, 
    {0, "x"}}, {{1, 2, 3, 4, 2}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 3, 5, 2}, {1, "SU(2)"}, {0, "x"}}, {{1, 2, 3, 5, 3}, {1, "SU(2)"}, 
    {0, "x"}}, {{1, 2, 4, 5, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 2, 4, 5, 3}, {1, "SU(2)"}, {0, "x"}}, {{1, 2, 4, 6, 3}, {2, "SU(3)"}, 
    {0, "x"}}, {{1, 3, 4, 5, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 3, 4, 5, 3}, {2, "SU(3)"}, {0, "x"}}, {{1, 3, 4, 6, 3}, {2, "SU(3)"}, 
    {0, "x"}}, {{1, 3, 5, 6, 3}, {3, "G_2"}, {0, "x"}}, 
   {{1, 3, 5, 7, 3}, {3, "G_2"}, {0, "x"}}, {{1, 3, 5, 7, 4}, {3, "G_2"}, 
    {0, "x"}}, {{1, 3, 6, 8, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{1, 4, 6, 8, 4}, {4, "SO(8)"}, {0, "x"}}, {{1, 4, 6, 9, 4}, {5, "F_4"}, 
    {0, "x"}}, {{1, 4, 6, 9, 5}, {5, "F_4"}, {0, "x"}}, 
   {{1, 4, 7, 9, 4}, {5, "F_4"}, {0, "x"}}, {{1, 4, 7, 9, 5}, {5, "F_4"}, 
    {0, "x"}}, {{1, 4, 7, 10, 5}, {5, "F_4"}, {0, "x"}}, 
   {{1, 5, 8, 11, 5}, {5, "F_4"}, {0, "x"}}, {{1, 5, 8, 11, 6}, {5, "F_4"}, 
    {0, "x"}}, {{1, 5, 9, 12, 6}, {6, "E_6"}, {0, "x"}}, 
   {{1, 5, 9, 13, 7}, {7, "E_7"}, {0, "x"}}, {{1, 6, 10, 14, 7}, {7, "E_7"}, 
    {0, "x"}}, {{1, 6, 11, 15, 8}, {7, "E_7"}, {0, "x"}}, 
   {{1, 6, 11, 16, 8}, {7, "E_7"}, {0, "x"}}, {{2, 1, 0, -1, 0}, {0, "x"}, 
    {0, "x"}}, {{2, 1, 0, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 1, 1, 0, 0}, {0, "x"}, {0, "x"}}, {{2, 1, 1, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{2, 1, 1, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{2, 2, 1, 0, 0}, {0, "x"}, {0, "x"}}, {{2, 2, 1, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{2, 2, 1, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{2, 2, 2, 1, 0}, {0, "x"}, {0, "x"}}, {{2, 2, 2, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{2, 2, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{2, 2, 2, 3, 1}, {0, "x"}, {0, "x"}}, {{2, 2, 2, 3, 2}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 2, 3, 3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 2, 3, 3, 2}, {1, "SU(2)"}, {0, "x"}}, {{2, 2, 3, 4, 2}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 3, 3, 3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 3, 3, 3, 2}, {1, "SU(2)"}, {0, "x"}}, {{2, 3, 3, 4, 2}, {1, "SU(2)"}, 
    {0, "x"}}, {{2, 3, 4, 4, 2}, {2, "SU(3)"}, {0, "x"}}, 
   {{2, 3, 4, 5, 2}, {2, "SU(3)"}, {0, "x"}}, {{2, 3, 4, 5, 3}, {3, "G_2"}, 
    {0, "x"}}, {{2, 3, 4, 6, 3}, {3, "G_2"}, {0, "x"}}, 
   {{2, 3, 5, 6, 3}, {3, "G_2"}, {0, "x"}}, {{2, 3, 5, 7, 3}, {3, "G_2"}, 
    {0, "x"}}, {{2, 4, 5, 6, 3}, {3, "G_2"}, {0, "x"}}, 
   {{2, 4, 5, 7, 3}, {3, "G_2"}, {0, "x"}}, {{2, 4, 5, 7, 4}, {4, "SO(8)"}, 
    {0, "x"}}, {{2, 4, 6, 7, 3}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 4, 6, 7, 4}, {4, "SO(8)"}, {0, "x"}}, {{2, 4, 6, 8, 4}, {4, "SO(8)"}, 
    {0, "x"}}, {{2, 4, 7, 9, 4}, {5, "F_4"}, {0, "x"}}, 
   {{2, 4, 7, 9, 5}, {5, "F_4"}, {0, "x"}}, {{2, 5, 7, 9, 4}, {5, "F_4"}, 
    {0, "x"}}, {{2, 5, 7, 9, 5}, {5, "F_4"}, {0, "x"}}, 
   {{2, 5, 7, 10, 5}, {5, "F_4"}, {0, "x"}}, {{2, 5, 8, 10, 5}, {5, "F_4"}, 
    {0, "x"}}, {{2, 5, 8, 11, 5}, {5, "F_4"}, {0, "x"}}, 
   {{2, 5, 8, 11, 6}, {5, "F_4"}, {0, "x"}}, {{2, 6, 9, 12, 6}, {6, "E_6"}, 
    {0, "x"}}, {{2, 6, 10, 13, 7}, {7, "E_7"}, {0, "x"}}, 
   {{2, 6, 10, 14, 7}, {7, "E_7"}, {0, "x"}}, {{2, 7, 11, 15, 8}, {7, "E_7"}, 
    {0, "x"}}, {{2, 7, 12, 16, 8}, {7, "E_7"}, {0, "x"}}, 
   {{3, 1, 0, -1, 0}, {0, "x"}, {0, "x"}}, {{3, 2, 0, -1, 0}, {0, "x"}, 
    {0, "x"}}, {{3, 2, 1, -1, 0}, {0, "x"}, {0, "x"}}, 
   {{3, 2, 1, 0, 0}, {0, "x"}, {0, "x"}}, {{3, 2, 1, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{3, 2, 1, 1, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 2, 2, 1, 0}, {1, "SU(2)"}, {0, "x"}}, {{3, 2, 2, 1, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{3, 2, 2, 2, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 3, 2, 1, 0}, {1, "SU(2)"}, {0, "x"}}, {{3, 3, 2, 1, 1}, {1, "SU(2)"}, 
    {0, "x"}}, {{3, 3, 2, 2, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{3, 3, 3, 2, 1}, {2, "SU(3)"}, {0, "x"}}, {{3, 3, 3, 3, 1}, {2, "SU(3)"}, 
    {0, "x"}}, {{3, 3, 3, 3, 2}, {3, "G_2"}, {0, "x"}}, 
   {{3, 3, 3, 4, 2}, {3, "G_2"}, {0, "x"}}, {{3, 3, 4, 4, 2}, {3, "G_2"}, 
    {0, "x"}}, {{3, 3, 4, 5, 2}, {3, "G_2"}, {0, "x"}}, 
   {{3, 4, 4, 4, 2}, {3, "G_2"}, {0, "x"}}, {{3, 4, 4, 5, 2}, {3, "G_2"}, 
    {0, "x"}}, {{3, 4, 4, 5, 3}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 4, 5, 5, 2}, {4, "SO(8)"}, {0, "x"}}, {{3, 4, 5, 5, 3}, {4, "SO(8)"}, 
    {0, "x"}}, {{3, 4, 5, 6, 3}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 4, 6, 7, 3}, {5, "F_4"}, {0, "x"}}, {{3, 4, 6, 7, 4}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 6, 7, 3}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 6, 7, 4}, {5, "F_4"}, {0, "x"}}, {{3, 5, 6, 8, 4}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 7, 8, 4}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 7, 9, 4}, {5, "F_4"}, {0, "x"}}, {{3, 5, 7, 9, 5}, {5, "F_4"}, 
    {0, "x"}}, {{3, 5, 8, 10, 5}, {5, "F_4"}, {0, "x"}}, 
   {{3, 6, 8, 10, 5}, {5, "F_4"}, {0, "x"}}, {{3, 6, 8, 11, 5}, {5, "F_4"}, 
    {0, "x"}}, {{3, 6, 9, 11, 6}, {6, "E_6"}, {0, "x"}}, 
   {{3, 6, 9, 12, 6}, {6, "E_6"}, {0, "x"}}, {{3, 7, 10, 13, 7}, {7, "E_7"}, 
    {0, "x"}}, {{3, 7, 11, 14, 7}, {7, "E_7"}, {0, "x"}}, 
   {{3, 7, 11, 15, 8}, {7, "E_7"}, {0, "x"}}, {{3, 8, 12, 16, 8}, {7, "E_7"}, 
    {0, "x"}}, {{4, 2, 0, -1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{4, 2, 1, -1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{4, 2, 1, 0, 0}, {1, "SU(2)"}, {0, "x"}}, {{4, 3, 1, -1, 0}, 
    {1, "SU(2)"}, {0, "x"}}, {{4, 3, 1, 0, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{4, 3, 2, 0, 0}, {2, "SU(3)"}, {0, "x"}}, {{4, 3, 2, 1, 0}, {2, "SU(3)"}, 
    {0, "x"}}, {{4, 3, 2, 1, 1}, {3, "G_2"}, {0, "x"}}, 
   {{4, 3, 2, 2, 1}, {3, "G_2"}, {0, "x"}}, {{4, 3, 3, 2, 1}, {3, "G_2"}, 
    {0, "x"}}, {{4, 3, 3, 3, 1}, {3, "G_2"}, {0, "x"}}, 
   {{4, 4, 3, 2, 1}, {3, "G_2"}, {0, "x"}}, {{4, 4, 3, 3, 1}, {3, "G_2"}, 
    {0, "x"}}, {{4, 4, 3, 3, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 4, 4, 3, 1}, {4, "SO(8)"}, {0, "x"}}, {{4, 4, 4, 3, 2}, {4, "SO(8)"}, 
    {0, "x"}}, {{4, 4, 4, 4, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{4, 4, 5, 5, 2}, {5, "F_4"}, {0, "x"}}, {{4, 4, 5, 5, 3}, {5, "F_4"}, 
    {0, "x"}}, {{4, 5, 5, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{4, 5, 5, 5, 3}, {5, "F_4"}, {0, "x"}}, {{4, 5, 5, 6, 3}, {5, "F_4"}, 
    {0, "x"}}, {{4, 5, 6, 6, 3}, {5, "F_4"}, {0, "x"}}, 
   {{4, 5, 6, 7, 3}, {5, "F_4"}, {0, "x"}}, {{4, 5, 6, 7, 4}, {5, "F_4"}, 
    {0, "x"}}, {{4, 5, 7, 8, 4}, {5, "F_4"}, {0, "x"}}, 
   {{4, 6, 7, 8, 4}, {5, "F_4"}, {0, "x"}}, {{4, 6, 7, 9, 4}, {5, "F_4"}, 
    {0, "x"}}, {{4, 6, 8, 9, 5}, {6, "E_6"}, {0, "x"}}, 
   {{4, 6, 8, 10, 5}, {6, "E_6"}, {0, "x"}}, {{4, 7, 9, 11, 6}, {7, "E_7"}, 
    {0, "x"}}, {{4, 7, 10, 12, 6}, {7, "E_7"}, {0, "x"}}, 
   {{4, 7, 10, 13, 7}, {7, "E_7"}, {0, "x"}}, {{4, 8, 11, 14, 7}, {7, "E_7"}, 
    {0, "x"}}, {{4, 8, 12, 15, 8}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 12, 16, 8}, {7, "E_7"}, {0, "x"}}, {{5, 3, 1, -1, 0}, {3, "G_2"}, 
    {0, "x"}}, {{5, 3, 1, 0, 0}, {3, "G_2"}, {0, "x"}}, 
   {{5, 3, 2, 0, 0}, {3, "G_2"}, {0, "x"}}, {{5, 3, 2, 1, 0}, {3, "G_2"}, 
    {0, "x"}}, {{5, 4, 2, 0, 0}, {3, "G_2"}, {0, "x"}}, 
   {{5, 4, 2, 1, 0}, {3, "G_2"}, {0, "x"}}, {{5, 4, 2, 1, 1}, {4, "SO(8)"}, 
    {0, "x"}}, {{5, 4, 3, 1, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{5, 4, 3, 1, 1}, {4, "SO(8)"}, {0, "x"}}, {{5, 4, 3, 2, 1}, {4, "SO(8)"}, 
    {0, "x"}}, {{5, 4, 4, 3, 1}, {5, "F_4"}, {0, "x"}}, 
   {{5, 4, 4, 3, 2}, {5, "F_4"}, {0, "x"}}, {{5, 5, 4, 3, 1}, {5, "F_4"}, 
    {0, "x"}}, {{5, 5, 4, 3, 2}, {5, "F_4"}, {0, "x"}}, 
   {{5, 5, 4, 4, 2}, {5, "F_4"}, {0, "x"}}, {{5, 5, 5, 4, 2}, {5, "F_4"}, 
    {0, "x"}}, {{5, 5, 5, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{5, 5, 5, 5, 3}, {5, "F_4"}, {0, "x"}}, {{5, 5, 6, 6, 3}, {5, "F_4"}, 
    {0, "x"}}, {{5, 6, 6, 6, 3}, {5, "F_4"}, {0, "x"}}, 
   {{5, 6, 6, 7, 3}, {5, "F_4"}, {0, "x"}}, {{5, 6, 7, 7, 4}, {6, "E_6"}, 
    {0, "x"}}, {{5, 6, 7, 8, 4}, {6, "E_6"}, {0, "x"}}, 
   {{5, 7, 8, 9, 5}, {7, "E_7"}, {0, "x"}}, {{5, 7, 9, 10, 5}, {7, "E_7"}, 
    {0, "x"}}, {{5, 7, 9, 11, 6}, {7, "E_7"}, {0, "x"}}, 
   {{5, 8, 10, 12, 6}, {7, "E_7"}, {0, "x"}}, {{5, 8, 11, 13, 7}, {7, "E_7"}, 
    {0, "x"}}, {{5, 8, 11, 14, 7}, {7, "E_7"}, {0, "x"}}, 
   {{6, 4, 1, -1, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{6, 4, 2, 0, 0}, {4, "SO(8)"}, {0, "x"}}, {{6, 4, 3, 1, 0}, {5, "F_4"}, 
    {0, "x"}}, {{6, 4, 3, 1, 1}, {5, "F_4"}, {0, "x"}}, 
   {{6, 5, 3, 1, 0}, {5, "F_4"}, {0, "x"}}, {{6, 5, 3, 1, 1}, {5, "F_4"}, 
    {0, "x"}}, {{6, 5, 3, 2, 1}, {5, "F_4"}, {0, "x"}}, 
   {{6, 5, 4, 2, 1}, {5, "F_4"}, {0, "x"}}, {{6, 5, 4, 3, 1}, {5, "F_4"}, 
    {0, "x"}}, {{6, 5, 4, 3, 2}, {5, "F_4"}, {0, "x"}}, 
   {{6, 5, 5, 4, 2}, {5, "F_4"}, {0, "x"}}, {{6, 6, 5, 4, 2}, {5, "F_4"}, 
    {0, "x"}}, {{6, 6, 5, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{6, 6, 6, 5, 3}, {6, "E_6"}, {0, "x"}}, {{6, 6, 6, 6, 3}, {6, "E_6"}, 
    {0, "x"}}, {{6, 7, 7, 7, 4}, {7, "E_7"}, {0, "x"}}, 
   {{6, 7, 8, 8, 4}, {7, "E_7"}, {0, "x"}}, {{6, 7, 8, 9, 5}, {7, "E_7"}, 
    {0, "x"}}, {{6, 8, 9, 10, 5}, {7, "E_7"}, {0, "x"}}, 
   {{6, 8, 10, 11, 6}, {7, "E_7"}, {0, "x"}}, {{6, 8, 10, 12, 6}, {7, "E_7"}, 
    {0, "x"}}, {{6, 12, 18, 24, 12}, {8, "E_8"}, {0, "x"}}}}, 
 {{{0, 1}, {1, 0}, {1, -1}, {1, -2}, {0, -1}, {-1, 0}, {-2, 1}, {-1, 1}}, 
  {{{-6, -12, -8, -3, 2, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -12, -7, -2, 3, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -12, -7, -2, 4, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -12, -7, -1, 5, 2}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -12, -6, 0, 6, 3}, {0, "x"}, {6, "E_6"}}, 
   {{-6, -12, -6, 1, 7, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -12, -6, 1, 8, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -12, -5, 1, 8, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -12, -5, 2, 9, 5}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -12, -5, 2, 10, 5}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{-6, -12, -5, 3, 10, 5}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{-6, -12, -5, 3, 11, 6}, {3, "G_2"}, {5, "F_4"}}, 
   {{-6, -12, -4, 3, 11, 6}, {3, "G_2"}, {5, "F_4"}}, 
   {{-6, -12, -4, 4, 12, 6}, {4, "SO(8)"}, {4, "SO(8)"}}, 
   {{-6, -11, -7, -3, 2, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -11, -7, -2, 3, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-6, -11, -6, -1, 4, 2}, {0, "x"}, {6, "E_6"}}, 
   {{-6, -11, -6, -1, 5, 2}, {0, "x"}, {6, "E_6"}}, 
   {{-6, -11, -6, 0, 5, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -11, -6, 0, 6, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -11, -5, 0, 6, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -11, -5, 1, 7, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -11, -5, 1, 8, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -11, -5, 2, 8, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -11, -5, 2, 9, 5}, {0, "x"}, {5, "F_4"}}, 
   {{-6, -11, -4, 2, 9, 5}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{-6, -11, -4, 3, 10, 5}, {2, "SU(3)"}, {4, "SO(8)"}}, 
   {{-6, -11, -4, 3, 11, 6}, {3, "G_2"}, {4, "SO(8)"}}, 
   {{-6, -11, -4, 4, 11, 6}, {3, "G_2"}, {3, "G_2"}}, 
   {{-5, -10, -6, -2, 2, 1}, {0, "x"}, {6, "E_6"}}, 
   {{-5, -10, -6, -2, 3, 1}, {0, "x"}, {6, "E_6"}}, 
   {{-5, -10, -6, -1, 3, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -10, -6, -1, 4, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -10, -5, -1, 4, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -10, -5, 0, 5, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -10, -5, 0, 5, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -10, -5, 0, 6, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -10, -5, 1, 6, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -10, -5, 1, 7, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -10, -4, 1, 7, 4}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -10, -4, 2, 8, 4}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -10, -4, 2, 9, 5}, {1, "SU(2)"}, {4, "SO(8)"}}, 
   {{-5, -10, -4, 3, 9, 5}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{-5, -10, -4, 3, 10, 5}, {3, "G_2"}, {3, "G_2"}}, 
   {{-5, -10, -3, 3, 9, 5}, {2, "SU(3)"}, {3, "G_2"}}, 
   {{-5, -10, -3, 3, 10, 5}, {3, "G_2"}, {3, "G_2"}}, 
   {{-5, -9, -6, -2, 1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -9, -6, -2, 2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -9, -5, -2, 2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -9, -5, -1, 3, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -9, -5, -1, 3, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -9, -5, -1, 4, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -9, -5, 0, 4, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -9, -5, 0, 5, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -9, -5, 0, 5, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -9, -4, 0, 5, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -9, -4, 0, 5, 3}, {0, "x"}, {5, "F_4"}}, 
   {{-5, -9, -4, 1, 6, 3}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -9, -4, 1, 7, 4}, {0, "x"}, {4, "SO(8)"}}, 
   {{-5, -9, -4, 2, 7, 4}, {0, "x"}, {3, "G_2"}}, 
   {{-5, -9, -4, 2, 8, 4}, {0, "x"}, {3, "G_2"}}, 
   {{-5, -9, -3, 2, 7, 4}, {0, "x"}, {3, "G_2"}}, 
   {{-5, -9, -3, 2, 8, 4}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{-5, -9, -3, 3, 8, 4}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{-5, -9, -3, 3, 9, 5}, {2, "SU(3)"}, {2, "SU(3)"}}, 
   {{-4, -8, -5, -2, 1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -8, -5, -2, 2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -8, -5, -1, 2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -8, -5, -1, 3, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -8, -5, -1, 3, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -8, -4, -1, 3, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -8, -4, -1, 3, 2}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -8, -4, 0, 4, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -8, -4, 0, 5, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -8, -4, 0, 5, 3}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -8, -4, 1, 5, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -8, -4, 1, 5, 3}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -8, -4, 1, 6, 3}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -8, -3, 1, 5, 3}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -8, -3, 1, 6, 3}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -8, -3, 2, 6, 3}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -8, -3, 2, 7, 4}, {0, "x"}, {2, "SU(3)"}}, 
   {{-4, -8, -3, 2, 8, 4}, {1, "SU(2)"}, {2, "SU(3)"}}, 
   {{-4, -8, -3, 3, 8, 4}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-4, -7, -5, -2, 1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -7, -4, -2, 1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -7, -4, -1, 2, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -7, -4, -1, 3, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -7, -4, -1, 3, 2}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -7, -4, 0, 3, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-4, -7, -4, 0, 3, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -7, -4, 0, 4, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -7, -3, 0, 3, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -7, -3, 0, 4, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -7, -3, 1, 4, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -7, -3, 1, 5, 2}, {0, "x"}, {3, "G_2"}}, 
   {{-4, -7, -3, 1, 5, 3}, {0, "x"}, {2, "SU(3)"}}, 
   {{-4, -7, -3, 1, 6, 3}, {0, "x"}, {2, "SU(3)"}}, 
   {{-4, -7, -3, 2, 6, 3}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -7, -3, 2, 7, 4}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -7, -2, 2, 6, 3}, {0, "x"}, {1, "SU(2)"}}, 
   {{-4, -7, -2, 2, 7, 4}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{-3, -6, -4, -2, 1, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-3, -6, -4, -1, 1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -6, -4, -1, 2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -6, -3, -1, 1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -6, -3, -1, 2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -6, -3, 0, 2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -6, -3, 0, 3, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -6, -3, 0, 3, 2}, {0, "x"}, {2, "SU(3)"}}, 
   {{-3, -6, -3, 0, 4, 2}, {0, "x"}, {2, "SU(3)"}}, 
   {{-3, -6, -3, 1, 4, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -6, -3, 1, 5, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -6, -3, 1, 5, 3}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -6, -2, 1, 4, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -6, -2, 1, 5, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -6, -2, 1, 5, 3}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -6, -2, 2, 5, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -6, -2, 2, 5, 3}, {0, "x"}, {0, "x"}}, {{-3, -6, -2, 2, 6, 3}, 
    {0, "x"}, {0, "x"}}, {{-3, -5, -3, -1, 1, 1}, {0, "x"}, {2, "SU(3)"}}, 
   {{-3, -5, -3, -1, 2, 1}, {0, "x"}, {2, "SU(3)"}}, 
   {{-3, -5, -3, 0, 2, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -5, -3, 0, 3, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -5, -3, 0, 3, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -5, -2, 0, 2, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -5, -2, 0, 3, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -5, -2, 0, 3, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -5, -2, 1, 3, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-3, -5, -2, 1, 3, 2}, {0, "x"}, {0, "x"}}, {{-3, -5, -2, 1, 4, 2}, 
    {0, "x"}, {0, "x"}}, {{-3, -5, -2, 1, 5, 2}, {0, "x"}, {0, "x"}}, 
   {{-3, -5, -2, 1, 5, 3}, {0, "x"}, {0, "x"}}, {{-3, -5, -2, 2, 5, 2}, 
    {0, "x"}, {0, "x"}}, {{-3, -5, -2, 2, 5, 3}, {0, "x"}, {0, "x"}}, 
   {{-3, -5, -1, 2, 5, 2}, {0, "x"}, {0, "x"}}, {{-2, -5, -3, -1, 1, 1}, 
    {0, "x"}, {2, "SU(3)"}}, {{-2, -5, -3, -1, 2, 1}, {0, "x"}, 
    {2, "SU(3)"}}, {{-2, -5, -3, 0, 2, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -5, -3, 0, 3, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -5, -3, 0, 3, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -5, -2, 0, 2, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -5, -2, 0, 3, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -5, -2, 0, 3, 2}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -5, -2, 1, 3, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -5, -2, 1, 3, 2}, {0, "x"}, {0, "x"}}, {{-2, -5, -2, 1, 4, 2}, 
    {0, "x"}, {0, "x"}}, {{-2, -5, -2, 1, 5, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, -5, -2, 2, 5, 2}, {0, "x"}, {0, "x"}}, {{-2, -4, -3, -1, 1, 1}, 
    {0, "x"}, {1, "SU(2)"}}, {{-2, -4, -2, -1, 1, 1}, {0, "x"}, 
    {1, "SU(2)"}}, {{-2, -4, -2, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -4, -2, 0, 2, 1}, {0, "x"}, {0, "x"}}, {{-2, -4, -2, 0, 3, 1}, 
    {0, "x"}, {0, "x"}}, {{-2, -4, -2, 0, 3, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, -4, -2, 1, 3, 1}, {0, "x"}, {0, "x"}}, {{-2, -4, -2, 1, 3, 2}, 
    {0, "x"}, {0, "x"}}, {{-2, -4, -2, 1, 4, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, -4, -1, 1, 3, 1}, {0, "x"}, {0, "x"}}, {{-2, -4, -1, 1, 3, 2}, 
    {0, "x"}, {0, "x"}}, {{-2, -4, -1, 1, 4, 2}, {0, "x"}, {0, "x"}}, 
   {{-2, -3, -2, -1, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -3, -2, 0, 1, 1}, {0, "x"}, {0, "x"}}, {{-2, -3, -2, 0, 2, 1}, 
    {0, "x"}, {0, "x"}}, {{-2, -3, -1, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -3, -1, 0, 2, 1}, {0, "x"}, {0, "x"}}, {{-2, -3, -1, 1, 2, 1}, 
    {0, "x"}, {0, "x"}}, {{-2, -3, -1, 1, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -3, -1, 1, 3, 2}, {0, "x"}, {0, "x"}}, {{-1, -3, -2, -1, 1, 1}, 
    {0, "x"}, {0, "x"}}, {{-1, -3, -2, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -3, -2, 0, 2, 1}, {0, "x"}, {0, "x"}}, {{-1, -3, -1, 0, 1, 1}, 
    {0, "x"}, {0, "x"}}, {{-1, -3, -1, 0, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -3, -1, 1, 2, 1}, {0, "x"}, {0, "x"}}, {{-1, -3, -1, 1, 3, 1}, 
    {0, "x"}, {0, "x"}}, {{-1, -2, -1, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -2, -1, 0, 2, 1}, {0, "x"}, {0, "x"}}, {{-1, -2, -1, 1, 2, 1}, 
    {0, "x"}, {0, "x"}}, {{-1, -1, -1, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -1, 0, 0, 1, 1}, {0, "x"}, {0, "x"}}, {{0, 0, 0, 0, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 0, 0, 0, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 0, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{0, 0, 1, 1, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 1, 0, -1, -1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 0, 0, -1, 0}, {0, "x"}, {0, "x"}}, {{0, 1, 1, 1, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 1, 0, -1, -1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 0, 0, -1, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 0, 0, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 1, 1, 0, -1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 1, 0, 0, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 1, 1, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 1, 1, 1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 1, 1, 1, 1}, {0, "x"}, {0, "x"}}, {{1, 1, 1, 1, 2, 1}, {0, "x"}, 
    {0, "x"}}, {{1, 1, 1, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 1, 2, 3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 1, 2, 2, 2, 1}, {0, "x"}, {0, "x"}}, {{1, 1, 2, 2, 3, 1}, 
    {1, "SU(2)"}, {0, "x"}}, {{1, 1, 2, 3, 3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 2, 1, 0, -1, 0}, {0, "x"}, {0, "x"}}, {{1, 2, 1, 0, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 2, 1, 1, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 1, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{1, 2, 2, 1, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 2, 2, 1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 2, 2, 1, 0}, {0, "x"}, {0, "x"}}, {{1, 2, 2, 2, 2, 1}, {0, "x"}, 
    {0, "x"}}, {{1, 2, 2, 2, 3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 2, 2, 3, 3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 2, 3, 3, 3, 1}, {2, "SU(3)"}, {0, "x"}}, 
   {{1, 3, 1, 0, -1, 0}, {0, "x"}, {0, "x"}}, {{1, 3, 2, 0, -1, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 3, 2, 1, -1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 3, 2, 1, 0, 0}, {0, "x"}, {0, "x"}}, {{1, 3, 2, 1, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 3, 2, 2, 1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 3, 3, 2, 1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 3, 3, 3, 3, 1}, {2, "SU(3)"}, {0, "x"}}, 
   {{2, 3, 1, 0, -1, 0}, {0, "x"}, {0, "x"}}, {{2, 3, 2, 0, -1, 0}, {0, "x"}, 
    {0, "x"}}, {{2, 3, 2, 1, -1, 0}, {0, "x"}, {0, "x"}}, 
   {{2, 3, 2, 1, 0, 0}, {0, "x"}, {0, "x"}}, {{2, 3, 2, 1, 1, 0}, 
    {1, "SU(2)"}, {0, "x"}}, {{2, 3, 2, 1, 1, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 3, 2, 2, 1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 3, 2, 2, 1, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 3, 2, 2, 2, 1}, {2, "SU(3)"}, {0, "x"}}, 
   {{2, 3, 3, 2, 1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 3, 3, 2, 1, 1}, {2, "SU(3)"}, {0, "x"}}, 
   {{2, 3, 3, 2, 2, 1}, {2, "SU(3)"}, {0, "x"}}, 
   {{2, 3, 3, 3, 2, 1}, {3, "G_2"}, {0, "x"}}, {{2, 3, 3, 3, 3, 1}, 
    {3, "G_2"}, {0, "x"}}, {{2, 3, 3, 3, 3, 2}, {3, "G_2"}, {0, "x"}}, 
   {{2, 3, 3, 4, 4, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 3, 4, 4, 4, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 3, 4, 4, 5, 2}, {5, "F_4"}, {0, "x"}}, {{2, 3, 4, 5, 5, 2}, 
    {5, "F_4"}, {0, "x"}}, {{2, 4, 2, 0, -1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 4, 2, 1, -1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 4, 2, 1, 0, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 4, 3, 1, -1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 4, 3, 1, 0, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{2, 4, 3, 2, 0, 0}, {2, "SU(3)"}, {0, "x"}}, 
   {{2, 4, 3, 2, 1, 0}, {2, "SU(3)"}, {0, "x"}}, 
   {{2, 4, 3, 2, 1, 1}, {3, "G_2"}, {0, "x"}}, {{2, 4, 3, 2, 2, 1}, 
    {3, "G_2"}, {0, "x"}}, {{2, 4, 3, 3, 2, 1}, {3, "G_2"}, {0, "x"}}, 
   {{2, 4, 3, 3, 3, 1}, {3, "G_2"}, {0, "x"}}, {{2, 4, 4, 3, 2, 1}, 
    {3, "G_2"}, {0, "x"}}, {{2, 4, 4, 3, 3, 1}, {3, "G_2"}, {0, "x"}}, 
   {{2, 4, 4, 4, 3, 1}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 4, 4, 4, 4, 2}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 4, 4, 5, 5, 2}, {5, "F_4"}, {0, "x"}}, {{2, 4, 5, 5, 5, 2}, 
    {5, "F_4"}, {0, "x"}}, {{2, 5, 3, 1, -1, 0}, {3, "G_2"}, {0, "x"}}, 
   {{2, 5, 3, 1, 0, 0}, {3, "G_2"}, {0, "x"}}, {{2, 5, 3, 2, 0, 0}, 
    {3, "G_2"}, {0, "x"}}, {{2, 5, 3, 2, 1, 0}, {3, "G_2"}, {0, "x"}}, 
   {{2, 5, 4, 2, 0, 0}, {3, "G_2"}, {0, "x"}}, {{2, 5, 4, 2, 1, 0}, 
    {3, "G_2"}, {0, "x"}}, {{2, 5, 4, 2, 1, 1}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 5, 4, 3, 1, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 5, 4, 3, 1, 1}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 5, 4, 3, 2, 1}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 5, 4, 4, 3, 1}, {5, "F_4"}, {0, "x"}}, {{2, 5, 5, 4, 3, 1}, 
    {5, "F_4"}, {0, "x"}}, {{2, 5, 5, 5, 5, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 3, 1, -1, 0}, {3, "G_2"}, {0, "x"}}, 
   {{3, 5, 3, 1, 0, 0}, {3, "G_2"}, {0, "x"}}, {{3, 5, 3, 2, 0, 0}, 
    {3, "G_2"}, {0, "x"}}, {{3, 5, 3, 2, 1, 0}, {3, "G_2"}, {0, "x"}}, 
   {{3, 5, 4, 2, 0, 0}, {3, "G_2"}, {0, "x"}}, {{3, 5, 4, 2, 1, 0}, 
    {3, "G_2"}, {0, "x"}}, {{3, 5, 4, 2, 1, 1}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 5, 4, 3, 1, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 5, 4, 3, 1, 1}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 5, 4, 3, 2, 1}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 5, 4, 4, 3, 1}, {5, "F_4"}, {0, "x"}}, {{3, 5, 4, 4, 3, 2}, 
    {5, "F_4"}, {0, "x"}}, {{3, 5, 5, 4, 3, 1}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 5, 4, 3, 2}, {5, "F_4"}, {0, "x"}}, {{3, 5, 5, 4, 4, 2}, 
    {5, "F_4"}, {0, "x"}}, {{3, 5, 5, 5, 4, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 5, 5, 5, 2}, {5, "F_4"}, {0, "x"}}, {{3, 5, 5, 5, 5, 3}, 
    {5, "F_4"}, {0, "x"}}, {{3, 5, 6, 6, 6, 3}, {6, "E_6"}, {0, "x"}}, 
   {{3, 6, 4, 1, -1, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 6, 4, 2, -1, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 6, 4, 2, 0, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{3, 6, 4, 3, 1, 0}, {5, "F_4"}, {0, "x"}}, {{3, 6, 4, 3, 1, 1}, 
    {5, "F_4"}, {0, "x"}}, {{3, 6, 5, 3, 1, 0}, {5, "F_4"}, {0, "x"}}, 
   {{3, 6, 5, 3, 1, 1}, {5, "F_4"}, {0, "x"}}, {{3, 6, 5, 3, 2, 1}, 
    {5, "F_4"}, {0, "x"}}, {{3, 6, 5, 4, 2, 1}, {5, "F_4"}, {0, "x"}}, 
   {{3, 6, 5, 4, 3, 1}, {5, "F_4"}, {0, "x"}}, {{3, 6, 5, 4, 3, 2}, 
    {5, "F_4"}, {0, "x"}}, {{3, 6, 5, 5, 4, 2}, {5, "F_4"}, {0, "x"}}, 
   {{3, 6, 6, 5, 4, 2}, {5, "F_4"}, {0, "x"}}, {{3, 6, 6, 5, 5, 2}, 
    {5, "F_4"}, {0, "x"}}, {{3, 6, 6, 6, 6, 3}, {6, "E_6"}, {0, "x"}}, 
   {{4, 7, 4, 2, -1, 0}, {5, "F_4"}, {0, "x"}}, {{4, 7, 5, 2, -1, 0}, 
    {5, "F_4"}, {0, "x"}}, {{4, 7, 5, 2, 0, 0}, {5, "F_4"}, {0, "x"}}, 
   {{4, 7, 5, 3, 0, 0}, {5, "F_4"}, {0, "x"}}, {{4, 7, 5, 3, 1, 0}, 
    {5, "F_4"}, {0, "x"}}, {{4, 7, 5, 3, 1, 1}, {5, "F_4"}, {0, "x"}}, 
   {{4, 7, 5, 4, 2, 1}, {5, "F_4"}, {0, "x"}}, {{4, 7, 6, 4, 2, 1}, 
    {5, "F_4"}, {0, "x"}}, {{4, 7, 6, 4, 3, 1}, {5, "F_4"}, {0, "x"}}, 
   {{4, 7, 6, 5, 3, 2}, {6, "E_6"}, {0, "x"}}, {{4, 7, 6, 5, 4, 2}, 
    {6, "E_6"}, {0, "x"}}, {{4, 7, 7, 6, 5, 3}, {7, "E_7"}, {0, "x"}}, 
   {{4, 7, 7, 7, 6, 3}, {7, "E_7"}, {0, "x"}}, {{4, 7, 7, 7, 7, 4}, 
    {7, "E_7"}, {0, "x"}}, {{4, 7, 8, 8, 8, 4}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 5, 2, -1, 0}, {5, "F_4"}, {0, "x"}}, 
   {{4, 8, 5, 3, 0, 0}, {5, "F_4"}, {0, "x"}}, {{4, 8, 6, 3, 0, 0}, 
    {5, "F_4"}, {0, "x"}}, {{4, 8, 6, 3, 1, 0}, {5, "F_4"}, {0, "x"}}, 
   {{4, 8, 6, 4, 1, 1}, {6, "E_6"}, {0, "x"}}, {{4, 8, 6, 4, 2, 1}, 
    {6, "E_6"}, {0, "x"}}, {{4, 8, 7, 5, 3, 2}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 7, 6, 4, 2}, {7, "E_7"}, {0, "x"}}, {{4, 8, 7, 6, 5, 3}, 
    {7, "E_7"}, {0, "x"}}, {{4, 8, 8, 7, 6, 3}, {7, "E_7"}, {0, "x"}}, 
   {{4, 8, 8, 8, 8, 4}, {7, "E_7"}, {0, "x"}}, {{5, 9, 6, 3, -1, 0}, 
    {6, "E_6"}, {0, "x"}}, {{5, 9, 6, 3, 0, 0}, {6, "E_6"}, {0, "x"}}, 
   {{5, 9, 7, 4, 1, 1}, {7, "E_7"}, {0, "x"}}, {{5, 9, 7, 5, 2, 1}, 
    {7, "E_7"}, {0, "x"}}, {{5, 9, 7, 5, 3, 2}, {7, "E_7"}, {0, "x"}}, 
   {{5, 9, 8, 6, 4, 2}, {7, "E_7"}, {0, "x"}}, {{5, 9, 8, 7, 5, 3}, 
    {7, "E_7"}, {0, "x"}}, {{5, 9, 8, 7, 6, 3}, {7, "E_7"}, {0, "x"}}, 
   {{5, 10, 7, 3, -1, 0}, {7, "E_7"}, {0, "x"}}, 
   {{5, 10, 7, 4, 0, 0}, {7, "E_7"}, {0, "x"}}, {{5, 10, 7, 4, 1, 1}, 
    {7, "E_7"}, {0, "x"}}, {{5, 10, 8, 5, 2, 1}, {7, "E_7"}, {0, "x"}}, 
   {{5, 10, 8, 6, 3, 2}, {7, "E_7"}, {0, "x"}}, {{5, 10, 8, 6, 4, 2}, 
    {7, "E_7"}, {0, "x"}}, {{6, 11, 7, 3, -1, 0}, {7, "E_7"}, {0, "x"}}, 
   {{6, 11, 8, 4, 0, 0}, {7, "E_7"}, {0, "x"}}, {{6, 11, 8, 5, 1, 1}, 
    {7, "E_7"}, {0, "x"}}, {{6, 11, 8, 5, 2, 1}, {7, "E_7"}, {0, "x"}}, 
   {{6, 12, 8, 4, -1, 0}, {7, "E_7"}, {0, "x"}}, 
   {{6, 12, 8, 4, 0, 0}, {7, "E_7"}, {0, "x"}}, {{6, 12, 12, 12, 12, 6}, 
    {8, "E_8"}, {0, "x"}}}}, {{{0, 1}, {1, 0}, {1, -1}, {1, -2}, {0, -1}, 
   {-1, 0}, {-1, 1}, {-1, 2}}, {{{-5, -9, -8, -6, -3, 1}, {0, "x"}, 
    {7, "E_7"}}, {{-5, -9, -7, -4, -2, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-5, -9, -6, -2, -1, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-5, -9, -5, 0, 0, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-5, -9, -4, 2, 1, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-5, -9, -3, 4, 2, 1}, {3, "G_2"}, {7, "E_7"}}, 
   {{-5, -9, -2, 6, 3, 1}, {5, "F_4"}, {7, "E_7"}}, 
   {{-4, -7, -7, -6, -3, 1}, {0, "x"}, {7, "E_7"}}, 
   {{-4, -7, -6, -4, -2, 1}, {0, "x"}, {6, "E_6"}}, 
   {{-4, -7, -5, -4, -1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -7, -5, -2, -1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -7, -4, -2, 0, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -7, -4, 0, 0, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -7, -3, 0, 1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -7, -3, 2, 1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -7, -2, 2, 2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-4, -7, -2, 4, 2, 1}, {3, "G_2"}, {5, "F_4"}}, 
   {{-4, -7, -1, 4, 3, 1}, {3, "G_2"}, {5, "F_4"}}, 
   {{-4, -7, -1, 6, 3, 1}, {5, "F_4"}, {5, "F_4"}}, 
   {{-3, -5, -5, -4, -2, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-3, -5, -5, -4, -1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-3, -5, -4, -4, -1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-3, -5, -4, -2, -1, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-3, -5, -4, -2, 0, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-3, -5, -3, -2, 0, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -5, -3, 0, 0, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -5, -3, 0, 1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -5, -2, 0, 1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -5, -2, 2, 1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -5, -2, 2, 2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -5, -1, 2, 2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-3, -5, -1, 4, 2, 1}, {3, "G_2"}, {3, "G_2"}}, 
   {{-3, -5, -1, 4, 3, 1}, {3, "G_2"}, {3, "G_2"}}, 
   {{-3, -5, 0, 4, 3, 1}, {3, "G_2"}, {3, "G_2"}}, 
   {{-3, -5, 0, 6, 3, 1}, {5, "F_4"}, {3, "G_2"}}, 
   {{-2, -5, -5, -4, -1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-2, -5, -4, -4, -1, 1}, {0, "x"}, {5, "F_4"}}, 
   {{-2, -5, -4, -2, 0, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-2, -5, -3, -2, -1, 1}, {0, "x"}, {4, "SO(8)"}}, 
   {{-2, -5, -3, -2, 0, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-2, -5, -3, 0, 1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-2, -5, -2, 0, 0, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-2, -5, -2, 0, 1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-2, -5, -2, 2, 2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-2, -5, -1, 2, 1, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-2, -5, -1, 2, 2, 1}, {0, "x"}, {3, "G_2"}}, 
   {{-2, -5, -1, 4, 3, 1}, {3, "G_2"}, {3, "G_2"}}, 
   {{-2, -3, -3, -2, -1, 1}, {0, "x"}, {2, "SU(3)"}}, 
   {{-2, -3, -3, -2, 0, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -3, -2, -2, 0, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-2, -3, -2, 0, 0, 1}, {0, "x"}, {0, "x"}}, {{-2, -3, -2, 0, 1, 1}, 
    {0, "x"}, {0, "x"}}, {{-2, -3, -1, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -3, -1, 2, 1, 1}, {0, "x"}, {0, "x"}}, {{-2, -3, -1, 2, 2, 1}, 
    {0, "x"}, {0, "x"}}, {{-2, -3, 0, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-2, -3, 0, 4, 2, 1}, {3, "G_2"}, {0, "x"}}, 
   {{-2, -3, 1, 6, 3, 1}, {5, "F_4"}, {0, "x"}}, 
   {{-1, -3, -3, -2, 0, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-1, -3, -2, -2, 0, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-1, -3, -2, 0, 1, 1}, {0, "x"}, {0, "x"}}, {{-1, -3, -1, 0, 0, 1}, 
    {0, "x"}, {0, "x"}}, {{-1, -3, -1, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -3, -1, 2, 2, 1}, {0, "x"}, {0, "x"}}, {{-1, -1, -1, 0, 0, 1}, 
    {0, "x"}, {0, "x"}}, {{-1, -1, -1, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -1, 0, 0, 1, 1}, {0, "x"}, {0, "x"}}, {{-1, -1, 0, 2, 1, 1}, 
    {0, "x"}, {0, "x"}}, {{-1, -1, 1, 4, 2, 1}, {3, "G_2"}, {0, "x"}}, 
   {{-1, -1, 2, 6, 3, 1}, {5, "F_4"}, {0, "x"}}, 
   {{0, -1, -1, 0, 1, 1}, {0, "x"}, {0, "x"}}, {{0, 0, 0, 0, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 0, 0, 1, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 0, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{0, 0, 1, 1, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 0, 1, 2, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 1, 3, 1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{0, 0, 1, 3, 2, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{0, 0, 2, 3, 2, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{0, 0, 2, 4, 2, 0}, {3, "G_2"}, {0, "x"}}, {{0, 0, 2, 5, 2, 0}, 
    {5, "F_4"}, {0, "x"}}, {{0, 0, 2, 5, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{0, 0, 3, 5, 3, 0}, {5, "F_4"}, {0, "x"}}, {{0, 0, 3, 6, 3, 0}, 
    {5, "F_4"}, {0, "x"}}, {{0, 0, 4, 7, 4, 0}, {7, "E_7"}, {0, "x"}}, 
   {{0, 0, 4, 8, 4, 0}, {7, "E_7"}, {0, "x"}}, {{0, 1, -4, -8, -4, 0}, 
    {0, "x"}, {7, "E_7"}}, {{0, 1, -3, -7, -4, 0}, {0, "x"}, {7, "E_7"}}, 
   {{0, 1, -3, -6, -3, 0}, {0, "x"}, {5, "F_4"}}, 
   {{0, 1, -2, -5, -3, 0}, {0, "x"}, {5, "F_4"}}, 
   {{0, 1, -2, -5, -2, 0}, {0, "x"}, {5, "F_4"}}, 
   {{0, 1, -2, -4, -2, 0}, {0, "x"}, {3, "G_2"}}, 
   {{0, 1, -1, -4, -2, 0}, {0, "x"}, {3, "G_2"}}, 
   {{0, 1, -1, -3, -2, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{0, 1, -1, -3, -1, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{0, 1, -1, -2, -1, 0}, {0, "x"}, {0, "x"}}, {{0, 1, 0, -2, -1, 0}, 
    {0, "x"}, {0, "x"}}, {{0, 1, 0, -1, -1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 0, -1, 0, 0}, {0, "x"}, {0, "x"}}, {{0, 1, 1, 1, 0, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 1, 1, 1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 1, 2, 1, 0}, {0, "x"}, {0, "x"}}, {{0, 1, 1, 2, 1, 1}, {0, "x"}, 
    {0, "x"}}, {{0, 1, 2, 2, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 2, 3, 1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{0, 1, 2, 3, 2, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{0, 1, 2, 4, 2, 0}, {3, "G_2"}, {0, "x"}}, {{0, 1, 2, 4, 2, 1}, 
    {3, "G_2"}, {0, "x"}}, {{0, 1, 3, 4, 2, 0}, {3, "G_2"}, {0, "x"}}, 
   {{0, 1, 3, 5, 2, 0}, {5, "F_4"}, {0, "x"}}, {{0, 1, 3, 5, 3, 0}, 
    {5, "F_4"}, {0, "x"}}, {{0, 1, 3, 6, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{0, 1, 3, 6, 3, 1}, {5, "F_4"}, {0, "x"}}, {{1, 1, -2, -6, -3, 0}, 
    {0, "x"}, {5, "F_4"}}, {{1, 1, -2, -5, -2, 0}, {0, "x"}, {5, "F_4"}}, 
   {{1, 1, -1, -4, -2, 0}, {0, "x"}, {3, "G_2"}}, 
   {{1, 1, -1, -3, -1, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, 1, 0, -2, -1, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 1, 1, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 1, 2, 2, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 2, 3, 2, 0}, {2, "SU(3)"}, {0, "x"}}, 
   {{1, 1, 3, 4, 2, 0}, {3, "G_2"}, {0, "x"}}, {{1, 1, 3, 5, 3, 0}, 
    {5, "F_4"}, {0, "x"}}, {{1, 1, 4, 6, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{1, 1, 4, 7, 4, 0}, {7, "E_7"}, {0, "x"}}, {{1, 1, 5, 8, 4, 0}, 
    {7, "E_7"}, {0, "x"}}, {{1, 2, -3, -8, -4, 0}, {0, "x"}, {7, "E_7"}}, 
   {{1, 2, -3, -7, -4, 0}, {0, "x"}, {7, "E_7"}}, 
   {{1, 2, -2, -6, -3, 0}, {0, "x"}, {5, "F_4"}}, 
   {{1, 2, -2, -5, -3, 0}, {0, "x"}, {5, "F_4"}}, 
   {{1, 2, -2, -5, -2, 0}, {0, "x"}, {5, "F_4"}}, 
   {{1, 2, -1, -5, -2, 0}, {0, "x"}, {5, "F_4"}}, 
   {{1, 2, -1, -4, -2, 0}, {0, "x"}, {3, "G_2"}}, 
   {{1, 2, -1, -3, -2, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, 2, -1, -3, -1, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, 2, 0, -3, -1, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, 2, 0, -2, -1, 0}, {0, "x"}, {0, "x"}}, {{1, 2, 2, 2, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{1, 2, 2, 3, 1, 0}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 2, 2, 3, 2, 0}, {2, "SU(3)"}, {0, "x"}}, 
   {{1, 2, 3, 3, 2, 0}, {3, "G_2"}, {0, "x"}}, {{1, 2, 3, 4, 2, 0}, 
    {3, "G_2"}, {0, "x"}}, {{1, 2, 3, 5, 2, 0}, {5, "F_4"}, {0, "x"}}, 
   {{1, 2, 3, 5, 3, 0}, {5, "F_4"}, {0, "x"}}, {{1, 2, 4, 5, 3, 0}, 
    {5, "F_4"}, {0, "x"}}, {{1, 2, 4, 6, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{1, 2, 5, 7, 4, 0}, {7, "E_7"}, {0, "x"}}, {{1, 2, 5, 8, 4, 0}, 
    {7, "E_7"}, {0, "x"}}, {{1, 3, -3, -8, -4, 0}, {1, "SU(2)"}, {7, "E_7"}}, 
   {{1, 3, -2, -7, -4, 0}, {1, "SU(2)"}, {7, "E_7"}}, 
   {{1, 3, -2, -6, -3, 0}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{1, 3, -1, -5, -3, 0}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{1, 3, -1, -5, -2, 0}, {1, "SU(2)"}, {5, "F_4"}}, 
   {{1, 3, -1, -4, -2, 0}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{1, 3, 0, -4, -2, 0}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{1, 3, 0, -3, -2, 0}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{1, 3, 0, -3, -1, 0}, {1, "SU(2)"}, {1, "SU(2)"}}, 
   {{1, 3, 3, 3, 1, 0}, {2, "SU(3)"}, {0, "x"}}, 
   {{1, 3, 3, 3, 2, 0}, {3, "G_2"}, {0, "x"}}, {{1, 3, 3, 4, 2, 0}, 
    {3, "G_2"}, {0, "x"}}, {{1, 3, 3, 4, 2, 1}, {5, "F_4"}, {0, "x"}}, 
   {{1, 3, 4, 4, 2, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{1, 3, 4, 5, 2, 0}, {5, "F_4"}, {0, "x"}}, {{1, 3, 4, 5, 3, 0}, 
    {5, "F_4"}, {0, "x"}}, {{1, 3, 4, 6, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{1, 3, 4, 6, 3, 1}, {5, "F_4"}, {0, "x"}}, {{2, 3, -1, -6, -3, 0}, 
    {1, "SU(2)"}, {5, "F_4"}}, {{2, 3, -1, -5, -2, 0}, {1, "SU(2)"}, 
    {5, "F_4"}}, {{2, 3, 0, -4, -2, 0}, {1, "SU(2)"}, {3, "G_2"}}, 
   {{2, 3, 3, 3, 2, 0}, {3, "G_2"}, {0, "x"}}, {{2, 3, 4, 4, 2, 0}, 
    {4, "SO(8)"}, {0, "x"}}, {{2, 3, 4, 5, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{2, 3, 5, 6, 3, 0}, {5, "F_4"}, {0, "x"}}, {{2, 3, 5, 7, 4, 0}, 
    {7, "E_7"}, {0, "x"}}, {{2, 3, 6, 8, 4, 0}, {7, "E_7"}, {0, "x"}}, 
   {{2, 4, -2, -8, -4, 0}, {3, "G_2"}, {7, "E_7"}}, 
   {{2, 4, -2, -7, -4, 0}, {3, "G_2"}, {7, "E_7"}}, 
   {{2, 4, -1, -6, -3, 0}, {3, "G_2"}, {5, "F_4"}}, 
   {{2, 4, -1, -5, -3, 0}, {3, "G_2"}, {5, "F_4"}}, 
   {{2, 4, -1, -5, -2, 0}, {3, "G_2"}, {5, "F_4"}}, 
   {{2, 4, 0, -5, -2, 0}, {3, "G_2"}, {5, "F_4"}}, 
   {{2, 4, 0, -4, -2, 0}, {3, "G_2"}, {3, "G_2"}}, 
   {{2, 4, 4, 4, 2, 0}, {4, "SO(8)"}, {0, "x"}}, 
   {{2, 4, 4, 5, 2, 0}, {5, "F_4"}, {0, "x"}}, {{2, 4, 4, 5, 3, 0}, 
    {5, "F_4"}, {0, "x"}}, {{2, 4, 5, 5, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{2, 4, 5, 6, 3, 0}, {5, "F_4"}, {0, "x"}}, {{2, 4, 6, 7, 4, 0}, 
    {7, "E_7"}, {0, "x"}}, {{2, 4, 6, 8, 4, 0}, {7, "E_7"}, {0, "x"}}, 
   {{2, 5, -2, -8, -4, 0}, {5, "F_4"}, {7, "E_7"}}, 
   {{2, 5, -1, -7, -4, 0}, {5, "F_4"}, {7, "E_7"}}, 
   {{2, 5, -1, -6, -3, 0}, {5, "F_4"}, {5, "F_4"}}, 
   {{2, 5, 0, -5, -3, 0}, {5, "F_4"}, {5, "F_4"}}, 
   {{2, 5, 0, -5, -2, 0}, {5, "F_4"}, {5, "F_4"}}, 
   {{2, 5, 5, 5, 2, 0}, {5, "F_4"}, {0, "x"}}, {{2, 5, 5, 5, 3, 0}, 
    {5, "F_4"}, {0, "x"}}, {{2, 5, 5, 6, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{2, 5, 5, 6, 3, 1}, {6, "E_6"}, {0, "x"}}, {{3, 5, 0, -6, -3, 0}, 
    {5, "F_4"}, {5, "F_4"}}, {{3, 5, 5, 5, 3, 0}, {5, "F_4"}, {0, "x"}}, 
   {{3, 5, 6, 6, 3, 0}, {6, "E_6"}, {0, "x"}}, {{3, 5, 6, 7, 4, 0}, 
    {7, "E_7"}, {0, "x"}}, {{3, 5, 7, 8, 4, 0}, {7, "E_7"}, {0, "x"}}, 
   {{3, 6, -1, -8, -4, 0}, {5, "F_4"}, {7, "E_7"}}, 
   {{3, 6, -1, -7, -4, 0}, {5, "F_4"}, {7, "E_7"}}, 
   {{3, 6, 0, -6, -3, 0}, {5, "F_4"}, {5, "F_4"}}, 
   {{3, 6, 6, 6, 3, 0}, {6, "E_6"}, {0, "x"}}, {{3, 6, 7, 7, 4, 0}, 
    {7, "E_7"}, {0, "x"}}, {{3, 6, 7, 8, 4, 0}, {7, "E_7"}, {0, "x"}}, 
   {{4, 7, 7, 7, 4, 0}, {7, "E_7"}, {0, "x"}}, {{4, 7, 8, 8, 4, 0}, 
    {7, "E_7"}, {0, "x"}}, {{4, 8, 0, -8, -4, 0}, {7, "E_7"}, {7, "E_7"}}, 
   {{4, 8, 8, 8, 4, 0}, {7, "E_7"}, {0, "x"}}, {{6, 12, 12, 12, 6, 0}, 
    {8, "E_8"}, {0, "x"}}}}, {{{0, 1}, {1, 0}, {2, -1}, {1, -1}, {0, -1}, 
   {-1, -1}, {-2, -1}, {-1, 0}}, {{{-1, -1, 0, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, -1, 0, 1, 1, 1}, {0, "x"}, {0, "x"}}, {{-1, -1, 0, 1, 2, 1}, 
    {0, "x"}, {0, "x"}}, {{-1, 0, 0, 1, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, 0, 0, 1, 2, 1}, {0, "x"}, {0, "x"}}, {{-1, 0, 1, 1, 2, 1}, {0, "x"}, 
    {0, "x"}}, {{-1, 0, 1, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{-1, 0, 1, 2, 3, 1}, {0, "x"}, {0, "x"}}, {{-1, 0, 1, 2, 3, 2}, {0, "x"}, 
    {0, "x"}}, {{-1, 0, 1, 2, 4, 2}, {0, "x"}, {0, "x"}}, 
   {{-1, 0, 1, 3, 4, 2}, {0, "x"}, {0, "x"}}, {{-1, 0, 2, 3, 4, 2}, {0, "x"}, 
    {0, "x"}}, {{-1, 0, 2, 3, 5, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-1, 0, 2, 3, 5, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-1, 0, 2, 4, 5, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-1, 0, 2, 4, 5, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-1, 1, 2, 3, 4, 2}, {0, "x"}, {0, "x"}}, {{-1, 1, 2, 3, 5, 2}, 
    {1, "SU(2)"}, {0, "x"}}, {{-1, 1, 2, 4, 5, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{-1, 1, 2, 4, 5, 3}, {1, "SU(2)"}, {0, "x"}}, 
   {{-1, 1, 2, 4, 6, 3}, {2, "SU(3)"}, {0, "x"}}, 
   {{-1, 1, 3, 4, 6, 3}, {2, "SU(3)"}, {0, "x"}}, 
   {{-1, 1, 3, 5, 6, 3}, {3, "G_2"}, {0, "x"}}, {{-1, 1, 3, 5, 7, 3}, 
    {3, "G_2"}, {0, "x"}}, {{-1, 1, 3, 5, 7, 4}, {3, "G_2"}, {0, "x"}}, 
   {{-1, 1, 4, 6, 8, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{-1, 1, 4, 6, 9, 4}, {5, "F_4"}, {0, "x"}}, {{-1, 1, 4, 6, 9, 5}, 
    {5, "F_4"}, {0, "x"}}, {{-1, 2, 4, 6, 8, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{-1, 2, 4, 7, 9, 4}, {5, "F_4"}, {0, "x"}}, {{-1, 2, 4, 7, 9, 5}, 
    {5, "F_4"}, {0, "x"}}, {{-1, 2, 5, 7, 10, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-1, 2, 5, 8, 10, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-1, 2, 5, 8, 11, 5}, {5, "F_4"}, {0, "x"}}, 
   {{-1, 2, 5, 8, 11, 6}, {5, "F_4"}, {0, "x"}}, 
   {{-1, 3, 6, 9, 12, 6}, {6, "E_6"}, {0, "x"}}, 
   {{-1, 3, 7, 11, 14, 7}, {7, "E_7"}, {0, "x"}}, 
   {{-1, 3, 7, 11, 15, 8}, {7, "E_7"}, {0, "x"}}, 
   {{-1, 4, 8, 12, 16, 8}, {7, "E_7"}, {0, "x"}}, 
   {{0, 0, 0, 0, 0, 0}, {0, "x"}, {0, "x"}}, {{0, 0, 0, 0, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 0, 0, 1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 1, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{0, 0, 1, 1, 2, 1}, {0, "x"}, 
    {0, "x"}}, {{0, 0, 1, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 1, 2, 3, 1}, {0, "x"}, {0, "x"}}, {{0, 1, 1, 1, 1, 0}, {0, "x"}, 
    {0, "x"}}, {{0, 1, 1, 2, 2, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 1, 2, 3, 1}, {0, "x"}, {0, "x"}}, {{0, 1, 2, 2, 3, 1}, {0, "x"}, 
    {0, "x"}}, {{0, 1, 2, 3, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 2, 3, 4, 2}, {0, "x"}, {0, "x"}}, {{0, 1, 2, 3, 5, 2}, 
    {1, "SU(2)"}, {0, "x"}}, {{0, 1, 2, 4, 5, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{0, 1, 3, 4, 5, 2}, {1, "SU(2)"}, {0, "x"}}, 
   {{0, 1, 3, 4, 6, 3}, {2, "SU(3)"}, {0, "x"}}, 
   {{0, 1, 3, 5, 6, 3}, {3, "G_2"}, {0, "x"}}, {{0, 2, 3, 4, 5, 2}, 
    {2, "SU(3)"}, {0, "x"}}, {{0, 2, 3, 5, 6, 3}, {3, "G_2"}, {0, "x"}}, 
   {{0, 2, 3, 5, 7, 3}, {3, "G_2"}, {0, "x"}}, {{0, 2, 4, 5, 7, 3}, 
    {3, "G_2"}, {0, "x"}}, {{0, 2, 4, 6, 7, 3}, {4, "SO(8)"}, {0, "x"}}, 
   {{0, 2, 4, 6, 8, 4}, {4, "SO(8)"}, {0, "x"}}, 
   {{0, 2, 5, 7, 9, 4}, {5, "F_4"}, {0, "x"}}, {{0, 2, 5, 7, 10, 5}, 
    {5, "F_4"}, {0, "x"}}, {{0, 3, 5, 7, 9, 4}, {5, "F_4"}, {0, "x"}}, 
   {{0, 3, 5, 8, 10, 5}, {5, "F_4"}, {0, "x"}}, {{0, 3, 6, 8, 11, 5}, 
    {5, "F_4"}, {0, "x"}}, {{0, 3, 6, 9, 12, 6}, {6, "E_6"}, {0, "x"}}, 
   {{0, 4, 8, 12, 16, 8}, {7, "E_7"}, {0, "x"}}, 
   {{0, 6, 12, 18, 24, 12}, {8, "E_8"}, {0, "x"}}, 
   {{1, 0, 0, -1, -1, 0}, {0, "x"}, {0, "x"}}, {{1, 0, 0, 0, -1, 0}, 
    {0, "x"}, {0, "x"}}, {{1, 1, 0, -1, -1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 1, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 2, 2, 3, 1}, {0, "x"}, 
    {0, "x"}}, {{1, 1, 2, 3, 3, 1}, {0, "x"}, {0, "x"}}, 
   {{1, 2, 2, 3, 3, 1}, {1, "SU(2)"}, {0, "x"}}, 
   {{1, 2, 3, 4, 5, 2}, {2, "SU(3)"}, {0, "x"}}, 
   {{1, 2, 4, 5, 7, 3}, {5, "F_4"}, {0, "x"}}, {{1, 3, 4, 6, 7, 3}, 
    {5, "F_4"}, {0, "x"}}, {{1, 3, 5, 7, 9, 4}, {5, "F_4"}, {0, "x"}}, 
   {{1, 3, 6, 8, 11, 5}, {6, "E_6"}, {0, "x"}}}}, 
 {{{0, 1}, {1, 0}, {2, -1}, {1, -1}, {0, -1}, {-1, -1}, {-1, 0}, {-1, 1}, 
   {-1, 2}}, {{{-1, -2, -2, -3, -2, 0, 1}, {0, "x"}, {1, "SU(2)"}}, 
   {{-1, -1, 0, 0, 0, 1, 1}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 0, 0, 0, 0, 0}, {0, "x"}, {0, "x"}}, {{0, 0, 0, 1, 0, 0, 0}, 
    {0, "x"}, {0, "x"}}, {{0, 0, 0, 1, 1, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 0, 1, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{0, 0, 1, 1, 1, 0, 0}, 
    {0, "x"}, {0, "x"}}, {{0, 0, 1, 1, 1, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 0, 1, 2, 1, 0, 0}, {0, "x"}, {0, "x"}}, {{0, 0, 1, 2, 1, 1, 0}, 
    {0, "x"}, {0, "x"}}, {{0, 0, 1, 2, 2, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 1, 1, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{0, 1, 1, 2, 1, 1, 0}, 
    {0, "x"}, {0, "x"}}, {{0, 1, 1, 2, 2, 1, 0}, {0, "x"}, {0, "x"}}, 
   {{0, 1, 2, 3, 2, 1, 0}, {0, "x"}, {0, "x"}}, {{0, 1, 2, 4, 2, 1, 0}, 
    {1, "SU(2)"}, {0, "x"}}, {{0, 1, 2, 4, 3, 1, 0}, {2, "SU(3)"}, {0, "x"}}, 
   {{0, 1, 2, 4, 3, 2, 0}, {3, "G_2"}, {0, "x"}}, 
   {{0, 1, 3, 5, 3, 1, 0}, {3, "G_2"}, {0, "x"}}, 
   {{0, 1, 3, 5, 3, 2, 0}, {3, "G_2"}, {0, "x"}}, 
   {{0, 2, 3, 5, 3, 2, 0}, {3, "G_2"}, {0, "x"}}, 
   {{1, -1, -3, -4, -2, -1, 0}, {0, "x"}, {2, "SU(3)"}}, 
   {{1, -1, -2, -4, -3, -1, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, -1, -2, -4, -2, -1, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, 0, -2, -4, -3, -1, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, 0, -2, -4, -2, -1, 0}, {0, "x"}, {1, "SU(2)"}}, 
   {{1, 0, -1, -1, -1, -1, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 0, -1, -1, -1, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 0, -1, -1, 0, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 0, 0, -1, -1, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 0, 0, -1, 0, 0, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 0, -1, -1, 0, 0}, 
    {0, "x"}, {0, "x"}}, {{1, 1, 1, 2, 1, 0, 0}, {0, "x"}, {0, "x"}}, 
   {{1, 1, 1, 2, 1, 1, 0}, {0, "x"}, {0, "x"}}, {{1, 1, 2, 2, 1, 1, 0}, 
    {1, "SU(2)"}, {0, "x"}}, {{1, 2, 3, 5, 3, 1, 0}, {4, "SO(8)"}, 
    {0, "x"}}}}};
