orbit: H:[ 0, 0, 0, 0 ] diagram:[0,0,0,0] dim:0
Centralizer: F4
simply connected adjoint root datum of Lie type 'F4'

orbit: H:[ 2, 3, 2, 1 ] diagram:[1,0,0,0] dim:16
Centralizer: C3
simply connected root datum of Lie type 'C3'

orbit: H:[ 2, 4, 3, 2 ] diagram:[0,0,0,1] dim:22
Centralizer: A3
simply connected root datum of Lie type 'A3'

orbit: H:[ 3, 6, 4, 2 ] diagram:[0,1,0,0] dim:28
Centralizer: 2A1
simply connected root datum of Lie type 'A1'
adjoint root datum of Lie type 'A1'

orbit: H:[ 4, 6, 4, 2 ] diagram:[2,0,0,0] dim:30
Centralizer: A2
simply connected root datum of Lie type 'A2'

orbit: H:[ 4, 8, 6, 4 ] diagram:[0,0,0,2] dim:30
Centralizer: G2
simply connected adjoint root datum of Lie type 'G2'

orbit: H:[ 4, 8, 6, 3 ] diagram:[0,0,1,0] dim:34
Centralizer: A1
simply connected root datum of Lie type 'A1'

orbit: H:[  6, 10,  7,  4 ] diagram:[2,0,0,1] dim:36
Centralizer: 2A1
simply connected root datum of Lie type 'A1'
simply connected root datum of Lie type 'A1'

orbit: H:[  5, 10,  7,  4 ] diagram:[0,1,0,1] dim:36
Centralizer: A1
simply connected root datum of Lie type 'A1'

orbit: H:[  6, 11,  8,  4 ] diagram:[1,0,1,0] dim:38
Centralizer: A1
simply connected root datum of Lie type 'A1'

orbit: H:[  6, 12,  8,  4 ] diagram:[0,2,0,0] dim:40
Centralizer: e
simply connected adjoint root datum of empty Lie type

orbit: H:[ 10, 18, 12,  6 ] diagram:[2,2,0,0] dim:42
Centralizer: A1
adjoint root datum of Lie type 'A1'

orbit: H:[ 10, 19, 14,  8 ] diagram:[1,0,1,2] dim:42
Centralizer: A1
simply connected root datum of Lie type 'A1'

orbit: H:[ 10, 20, 14,  8 ] diagram:[0,2,0,2] dim:44
Centralizer: e
simply connected adjoint root datum of empty Lie type

orbit: H:[ 14, 26, 18, 10 ] diagram:[2,2,0,2] dim:46
Centralizer: e
simply connected adjoint root datum of empty Lie type

orbit: H:[ 22, 42, 30, 16 ] diagram:[2,2,2,2] dim:48
Centralizer: e
simply connected adjoint root datum of empty Lie type