orbit: H:[ 0, 0, 0, 0, 0, 0, 0, 0 ] diagram:[0,0,0,0,0,0,0,0] dim:0
Centralizer: E8
Center is trivial
simply connected adjoint root datum of Lie type 'E8'

orbit: H:[ 2, 3, 4, 6, 5, 4, 3, 2 ] diagram:[0,0,0,0,0,0,0,1] dim:58
Centralizer: E7
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'E7'

orbit: H:[  4,  5,  7, 10,  8,  6,  4,  2 ] diagram:[1,0,0,0,0,0,0,0] dim:92
Centralizer: B6
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'B6'

orbit: H:[  4,  6,  8, 12, 10,  8,  6,  3 ] diagram:[0,0,0,0,0,0,1,0] dim:112
Centralizer: A1+F4
Group is semisimple
center=Z/2Z
simply connected adjoint root datum of Lie type 'F4'
simply connected root datum of Lie type 'A1'

orbit: H:[  4,  6,  8, 12, 10,  8,  6,  4 ] diagram:[0,0,0,0,0,0,0,2] dim:114
Centralizer: E6
Group is semisimple
center=Z/3Z
simply connected root datum of Lie type 'E6'

orbit: H:[  5,  8, 10, 15, 12,  9,  6,  3 ] diagram:[0,1,0,0,0,0,0,0] dim:128
Centralizer: C4
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'C4'

orbit: H:[  6,  8, 11, 16, 13, 10,  7,  4 ] diagram:[1,0,0,0,0,0,0,1] dim:136
Centralizer: A5
Group is semisimple
center=Z/6Z
simply connected root datum of Lie type 'A5'

orbit: H:[  6,  9, 12, 18, 15, 12,  8,  4 ] diagram:[0,0,0,0,0,1,0,0] dim:146
Centralizer: A1+B3
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'B3'
simply connected root datum of Lie type 'A1'

orbit: H:[  8, 11, 15, 22, 18, 14, 10,  6 ] diagram:[1,0,0,0,0,0,0,2] dim:148
Centralizer: B5
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'B5'

orbit: H:[  7, 10, 14, 20, 16, 12,  8,  4 ] diagram:[0,0,1,0,0,0,0,0] dim:154
Centralizer: A1+G2
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'
simply connected adjoint root datum of Lie type 'G2'

orbit: H:[  8, 10, 14, 20, 16, 12,  8,  4 ] diagram:[2,0,0,0,0,0,0,0] dim:156
Centralizer: 2G2
Center is trivial
simply connected adjoint root datum of Lie type 'G2'
simply connected adjoint root datum of Lie type 'G2'

orbit: H:[  8, 11, 15, 22, 18, 14, 10,  5 ] diagram:[1,0,0,0,0,0,1,0] dim:162
Centralizer: A1+G2
Group is semisimple
center=Z/2Z
simply connected adjoint root datum of Lie type 'G2'
simply connected root datum of Lie type 'A1'

orbit: H:[  8, 12, 16, 24, 20, 16, 11,  6 ] diagram:[0,0,0,0,0,1,0,1] dim:164
Centralizer: A1+B3
Group is semisimple
center=Z/2Z x Z/2Z
simply connected root datum of Lie type 'B3'
simply connected root datum of Lie type 'A1'

orbit: H:[  8, 12, 16, 24, 20, 16, 12,  6 ] diagram:[0,0,0,0,0,0,2,0] dim:166
Centralizer: D4
Group is semisimple
center=Z/2Z x Z/2Z
simply connected root datum of Lie type 'D4'

orbit: H:[ 12, 18, 24, 36, 30, 24, 18, 10 ] diagram:[0,0,0,0,0,0,2,2] dim:168
Centralizer: F4
Center is trivial
simply connected adjoint root datum of Lie type 'F4'

orbit: H:[  8, 12, 16, 24, 20, 15, 10,  5 ] diagram:[0,0,0,0,1,0,0,0] dim:168
Centralizer: B2
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'B2'

orbit: H:[  9, 13, 18, 26, 21, 16, 11,  6 ] diagram:[0,0,1,0,0,0,0,1] dim:172
Centralizer: A1+B2
Group is semisimple
center=Z/2Z x Z/2Z
simply connected root datum of Lie type 'B2'
simply connected root datum of Lie type 'A1'

orbit: H:[  9, 14, 18, 27, 22, 17, 12,  6 ] diagram:[0,1,0,0,0,0,1,0] dim:176
Centralizer: 3A1
Group is semisimple
center=Z/2Z x Z/2Z x Z/2Z
simply connected root datum of Lie type 'A1'
simply connected root datum of Lie type 'A1'
simply connected root datum of Lie type 'A1'

orbit: H:[ 10, 14, 19, 28, 23, 18, 12,  6 ] diagram:[1,0,0,0,0,1,0,0] dim:178
Centralizer: B2+T1
Center is a connected complex torus of rank 1
simply connected root datum of Lie type 'B2'

orbit: H:[ 12, 16, 22, 32, 26, 20, 14,  8 ] diagram:[2,0,0,0,0,0,0,2] dim:180
Centralizer: A4
Group is semisimple
center=Z/5Z
simply connected root datum of Lie type 'A4'

orbit: H:[ 10, 15, 20, 30, 24, 18, 12,  6 ] diagram:[0,0,0,1,0,0,0,0] dim:182
Centralizer: 2A1
Group is semisimple
center=Z/2Z
adjoint root datum of Lie type 'A1'
simply connected root datum of Lie type 'A1'

orbit: H:[ 13, 20, 26, 39, 32, 25, 18, 10 ] diagram:[0,1,0,0,0,0,1,2] dim:184
Centralizer: C3
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'C3'

orbit: H:[ 10, 16, 20, 30, 24, 18, 12,  6 ] diagram:[0,2,0,0,0,0,0,0] dim:184
Centralizer: A2
Center is trivial
adjoint root datum of Lie type 'A2'

orbit: H:[ 12, 17, 23, 34, 28, 22, 15,  8 ] diagram:[1,0,0,0,0,1,0,1] dim:188
Centralizer: A2+T1
Center is a connected complex torus of rank 1
simply connected root datum of Lie type 'A2'

orbit: H:[ 12, 17, 23, 34, 28, 21, 14,  7 ] diagram:[1,0,0,0,1,0,0,0] dim:188
Centralizer: C2
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'C2'

orbit: H:[ 14, 20, 27, 40, 33, 26, 18, 10 ] diagram:[1,0,0,0,0,1,0,2] dim:190
Centralizer: A3
Group is semisimple
center=Z/4Z
simply connected root datum of Lie type 'A3'

orbit: H:[ 12, 18, 24, 36, 29, 22, 15,  8 ] diagram:[0,0,0,1,0,0,0,1] dim:192
Centralizer: A1+T1
Center is a connected complex torus of rank 1
simply connected root datum of Lie type 'A1'

orbit: H:[ 12, 18, 24, 36, 30, 24, 16,  8 ] diagram:[0,0,0,0,0,2,0,0] dim:194
Centralizer: 2A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'
simply connected root datum of Lie type 'A1'

orbit: H:[ 16, 22, 30, 44, 36, 28, 19, 10 ] diagram:[2,0,0,0,0,1,0,1] dim:196
Centralizer: A1+G2
Group is semisimple
center=Z/2Z
simply connected adjoint root datum of Lie type 'G2'
simply connected root datum of Lie type 'A1'

orbit: H:[ 14, 21, 28, 42, 34, 26, 18, 10 ] diagram:[0,0,0,1,0,0,0,2] dim:196
Centralizer: 2A1
Group is semisimple
center=Z/2Z
adjoint root datum of Lie type 'A1'
simply connected root datum of Lie type 'A1'

orbit: H:[ 13, 19, 26, 38, 31, 24, 16,  8 ] diagram:[0,0,1,0,0,1,0,0] dim:196
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[ 16, 22, 30, 44, 36, 28, 20, 10 ] diagram:[2,0,0,0,0,0,2,0] dim:198
Centralizer: G2
Center is trivial
simply connected adjoint root datum of Lie type 'G2'

orbit: H:[ 14, 22, 28, 42, 34, 26, 18, 10 ] diagram:[0,2,0,0,0,0,0,2] dim:198
Centralizer: A2
Group is semisimple
center=Z/3Z
simply connected root datum of Lie type 'A2'

orbit: H:[ 20, 28, 38, 56, 46, 36, 26, 14 ] diagram:[2,0,0,0,0,0,2,2] dim:200
Centralizer: B3
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'B3'

orbit: H:[ 14, 21, 28, 42, 34, 26, 18,  9 ] diagram:[0,0,0,1,0,0,1,0] dim:200
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[ 16, 23, 31, 46, 37, 28, 19, 10 ] diagram:[1,0,0,1,0,0,0,1] dim:202
Centralizer: 2A1
Group is semisimple
center=Z/2Z x Z/2Z
simply connected root datum of Lie type 'A1'
simply connected root datum of Lie type 'A1'

orbit: H:[ 15, 22, 30, 44, 36, 28, 19, 10 ] diagram:[0,0,1,0,0,1,0,1] dim:202
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[ 16, 24, 32, 47, 38, 29, 20, 10 ] diagram:[0,1,1,0,0,0,1,0] dim:204
Centralizer: 2A1
Group is semisimple
center=Z/2Z x Z/2Z
simply connected root datum of Lie type 'A1'
simply connected root datum of Lie type 'A1'

orbit: H:[ 16, 23, 31, 46, 38, 29, 20, 10 ] diagram:[1,0,0,0,1,0,1,0] dim:204
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[ 16, 24, 32, 48, 39, 30, 20, 10 ] diagram:[0,0,0,1,0,1,0,0] dim:206
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[ 20, 29, 39, 58, 48, 37, 26, 14 ] diagram:[1,0,0,0,1,0,1,2] dim:208
Centralizer: 2A1
Group is semisimple
center=Z/2Z x Z/2Z
simply connected root datum of Lie type 'A1'
simply connected root datum of Lie type 'A1'

orbit: H:[ 16, 24, 32, 48, 40, 30, 20, 10 ] diagram:[0,0,0,0,2,0,0,0] dim:208
Centralizer: e
Center is trivial

orbit: H:[ 20, 28, 38, 56, 46, 36, 24, 12 ] diagram:[2,0,0,0,0,2,0,0] dim:210
Centralizer: 2A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'
simply connected root datum of Lie type 'A1'

orbit: H:[ 20, 30, 40, 59, 48, 37, 26, 14 ] diagram:[0,1,1,0,0,0,1,2] dim:210
Centralizer: 2A1
Group is semisimple
center=Z/2Z x Z/2Z
simply connected root datum of Lie type 'A1'
simply connected root datum of Lie type 'A1'

orbit: H:[ 20, 30, 40, 60, 49, 38, 26, 14 ] diagram:[0,0,0,1,0,1,0,2] dim:212
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[ 20, 29, 39, 58, 47, 36, 24, 12 ] diagram:[1,0,0,1,0,1,0,0] dim:212
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[ 24, 34, 46, 68, 56, 44, 30, 16 ] diagram:[2,0,0,0,0,2,0,2] dim:214
Centralizer: A2
Group is semisimple
center=Z/3Z
simply connected root datum of Lie type 'A2'

orbit: H:[ 20, 30, 40, 60, 50, 38, 26, 14 ] diagram:[0,0,0,0,2,0,0,2] dim:214
Centralizer: T1
Center is a connected complex torus of rank 1

orbit: H:[ 32, 46, 62, 92, 76, 60, 42, 22 ] diagram:[2,0,0,0,0,2,2,2] dim:216
Centralizer: G2
Center is trivial
simply connected adjoint root datum of Lie type 'G2'

orbit: H:[ 28, 40, 54, 79, 64, 49, 34, 18 ] diagram:[2,1,1,0,0,0,1,2] dim:216
Centralizer: B2
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'B2'

orbit: H:[ 22, 32, 43, 64, 52, 40, 27, 14 ] diagram:[1,0,0,1,0,1,0,1] dim:216
Centralizer: T1
Center is a connected complex torus of rank 1

orbit: H:[ 24, 35, 47, 70, 57, 44, 30, 16 ] diagram:[1,0,0,1,0,1,0,2] dim:218
Centralizer: T1
Center is a connected complex torus of rank 1

orbit: H:[ 24, 35, 47, 70, 57, 44, 30, 15 ] diagram:[1,0,0,1,0,1,1,0] dim:218
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[ 28, 40, 54, 80, 65, 50, 34, 18 ] diagram:[2,0,0,1,0,1,0,2] dim:220
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[ 24, 36, 48, 72, 58, 44, 30, 16 ] diagram:[0,0,0,2,0,0,0,2] dim:220
Centralizer: e
Center is trivial

orbit: H:[ 32, 47, 63, 94, 77, 60, 42, 22 ] diagram:[1,0,0,1,0,1,2,2] dim:222
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[ 28, 40, 54, 80, 66, 50, 34, 18 ] diagram:[2,0,0,0,2,0,0,2] dim:222
Centralizer: T1
Center is a connected complex torus of rank 1

orbit: H:[ 32, 48, 64, 95, 78, 60, 42, 22 ] diagram:[0,1,1,0,1,0,2,2] dim:224
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[ 28, 42, 56, 84, 68, 52, 36, 18 ] diagram:[0,0,0,2,0,0,2,0] dim:224
Centralizer: e
Center is trivial

orbit: H:[  36,  52,  70, 103,  84,  64,  43,  22 ] diagram:[2,1,1,0,1,1,0,1] dim:226
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[ 32, 48, 64, 96, 78, 60, 42, 22 ] diagram:[0,0,0,2,0,0,2,2] dim:226
Centralizer: e
Center is trivial

orbit: H:[  40,  58,  78, 115,  94,  72,  50,  26 ] diagram:[2,1,1,0,1,0,2,2] dim:228
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[  36,  52,  70, 104,  84,  64,  44,  22 ] diagram:[2,0,0,2,0,0,2,0] dim:228
Centralizer: e
Center is trivial

orbit: H:[  40,  58,  78, 116,  94,  72,  50,  26 ] diagram:[2,0,0,2,0,0,2,2] dim:230
Centralizer: e
Center is trivial

orbit: H:[  52,  76, 102, 151, 124,  96,  66,  34 ] diagram:[2,1,1,0,1,2,2,2] dim:232
Centralizer: A1
Group is semisimple
center=Z/2Z
simply connected root datum of Lie type 'A1'

orbit: H:[  44,  64,  86, 128, 104,  80,  54,  28 ] diagram:[2,0,0,2,0,2,0,2] dim:232
Centralizer: e
Center is trivial

orbit: H:[  52,  76, 102, 152, 124,  96,  66,  34 ] diagram:[2,0,0,2,0,2,2,2] dim:234
Centralizer: e
Center is trivial

orbit: H:[  60,  88, 118, 174, 142, 108,  74,  38 ] diagram:[2,2,2,0,2,0,2,2] dim:236
Centralizer: e
Center is trivial

orbit: H:[  72, 106, 142, 210, 172, 132,  90,  46 ] diagram:[2,2,2,0,2,2,2,2] dim:238
Centralizer: e
Center is trivial

orbit: H:[  92, 136, 182, 270, 220, 168, 114,  58 ] diagram:[2,2,2,2,2,2,2,2] dim:240
Centralizer: e
Center is trivial