# gps_st downloaded from the LMFDB on 26 May 2026.
# Search link: https://www.lmfdb.org/SatoTateGroup/?degree=6
# Query "{'degree': 6, 'rational': True}" returned 410 gps_sts, sorted by weight.

# Each entry in the following data list has the form:
#    [Label, Wt, Deg, $\mathrm{dim}_{\mathbb{R}}$, $\mathrm{G}^0$, Name, $\mathrm{G}/\mathrm{G}^0$, $\mathrm{Pr}[t\!=\!0]$, $\mathrm{E}[a_1^2]$, $\mathrm{E}[a_1^4]$, $\mathrm{E}[a_2]$]
# For more details, see the definitions at the bottom of the file.



"1.6.A.1.1a"	1	6	21	"USp(6)"	"\\mathrm{USp}(6)"	1	0	1	3	1
"1.6.B.1.1a"	1	6	9	"U(3)"	"\\mathrm{U}(3)"	1	0	2	12	1
"1.6.B.2.1a"	1	6	9	"U(3)"	"N(\\mathrm{U}(3))"	2	1/2	1	6	1
"1.6.C.1.1a"	1	6	13	"SU(2)xUSp(4)"	"\\mathrm{SU}(2)\\times \\mathrm{USp}(4)"	1	0	2	11	2
"1.6.D.1.1a"	1	6	11	"U(1)xUSp(4)"	"\\mathrm{U}(1)\\times \\mathrm{USp}(4)"	1	0	3	21	2
"1.6.D.2.1a"	1	6	11	"U(1)xUSp(4)"	"N(\\mathrm{U}(1)\\times \\mathrm{USp}(4))"	2	0	2	12	2
"1.6.E.1.1a"	1	6	9	"SU(2)^3"	"E"	1	0	3	24	3
"1.6.E.2.1a"	1	6	9	"SU(2)^3"	"E_{t}"	2	0	2	13	2
"1.6.E.3.1a"	1	6	9	"SU(2)^3"	"E_{s}"	3	2/3	1	8	1
"1.6.E.6.1a"	1	6	9	"SU(2)^3"	"E_{s,t}"	6	1/3	1	5	1
"1.6.F.1.1a"	1	6	7	"U(1)xSU(2)^2"	"F"	1	0	4	40	3
"1.6.F.2.1a"	1	6	7	"U(1)xSU(2)^2"	"F_{at}"	2	1/2	2	20	2
"1.6.F.2.1b"	1	6	7	"U(1)xSU(2)^2"	"F_{t}"	2	0	3	23	2
"1.6.F.2.1c"	1	6	7	"U(1)xSU(2)^2"	"F_{a}"	2	0	3	25	3
"1.6.F.4.2a"	1	6	7	"U(1)xSU(2)^2"	"F_{a,t}"	4	1/4	2	14	2
"1.6.G.1.1a"	1	6	5	"U(1)^2xSU(2)"	"F\\times \\mathrm{SU}(2)"	1	0	5	62	3
"1.6.G.2.1a"	1	6	5	"U(1)^2xSU(2)"	"F_{ab}\\times \\mathrm{SU}(2)"	2	0	3	32	3
"1.6.G.2.1b"	1	6	5	"U(1)^2xSU(2)"	"F_{a}\\times \\mathrm{SU}(2)"	2	0	4	41	3
"1.6.G.4.1a"	1	6	5	"U(1)^2xSU(2)"	"F_{ac}\\times \\mathrm{SU}(2)"	4	0	2	17	2
"1.6.G.4.2a"	1	6	5	"U(1)^2xSU(2)"	"F_{a,b}\\times \\mathrm{SU}(2)"	4	0	3	26	3
"1.6.H.1.1a"	1	6	3	"U(1)^3"	"H"	1	0	6	90	3
"1.6.H.2.1a"	1	6	3	"U(1)^3"	"H_{abc}"	2	1/2	3	45	3
"1.6.H.2.1b"	1	6	3	"U(1)^3"	"H_{ab}"	2	0	4	48	3
"1.6.H.2.1c"	1	6	3	"U(1)^3"	"H_{a}"	2	0	5	63	3
"1.6.H.3.1a"	1	6	3	"U(1)^3"	"H_{s}"	3	2/3	2	30	1
"1.6.H.4.1a"	1	6	3	"U(1)^3"	"H_{act}"	4	1/2	2	24	2
"1.6.H.4.1b"	1	6	3	"U(1)^3"	"H_{at}"	4	0	3	27	2
"1.6.H.4.2a"	1	6	3	"U(1)^3"	"H_{ab,bc}"	4	0	3	27	3
"1.6.H.4.2b"	1	6	3	"U(1)^3"	"H_{a,bc}"	4	1/4	3	33	3
"1.6.H.4.2c"	1	6	3	"U(1)^3"	"H_{a,b}"	4	0	4	42	3
"1.6.H.6.2a"	1	6	3	"U(1)^3"	"H_{abc,s}"	6	5/6	1	15	1
"1.6.H.8.2a"	1	6	3	"U(1)^3"	"H_{c,at}"	8	3/8	2	18	2
"1.6.H.8.5a"	1	6	3	"U(1)^3"	"H_{a,b,c}"	8	1/8	3	27	3
"1.6.I.1.1a"	1	6	6	"SU(2)xSU(2)_2"	"\\mathrm{SU}(2)\\times E_1"	1	0	5	58	4
"1.6.I.2.1a"	1	6	6	"SU(2)xSU(2)_2"	"\\mathrm{SU}(2)\\times E_2"	2	0	3	30	2
"1.6.I.2.1b"	1	6	6	"SU(2)xSU(2)_2"	"\\mathrm{SU}(2)\\times J(E_1)"	2	0	3	30	3
"1.6.I.3.1a"	1	6	6	"SU(2)xSU(2)_2"	"\\mathrm{SU}(2)\\times E_3"	3	0	3	26	2
"1.6.I.4.1a"	1	6	6	"SU(2)xSU(2)_2"	"\\mathrm{SU}(2)\\times E_4"	4	0	3	26	2
"1.6.I.4.2a"	1	6	6	"SU(2)xSU(2)_2"	"\\mathrm{SU}(2)\\times J(E_2)"	4	0	2	16	2
"1.6.I.6.1a"	1	6	6	"SU(2)xSU(2)_2"	"\\mathrm{SU}(2)\\times J(E_3)"	6	0	2	14	2
"1.6.I.6.2a"	1	6	6	"SU(2)xSU(2)_2"	"\\mathrm{SU}(2)\\times E_6"	6	0	3	26	2
"1.6.I.8.3a"	1	6	6	"SU(2)xSU(2)_2"	"\\mathrm{SU}(2)\\times J(E_4)"	8	0	2	14	2
"1.6.I.12.4a"	1	6	6	"SU(2)xSU(2)_2"	"\\mathrm{SU}(2)\\times J(E_6)"	12	0	2	14	2
"1.6.J.1.1a"	1	6	4	"U(1)xSU(2)_2"	"J_1(E_1)"	1	0	6	86	4
"1.6.J.2.1a"	1	6	4	"U(1)xSU(2)_2"	"J(E_2,E_1)"	2	1/2	3	43	2
"1.6.J.2.1b"	1	6	4	"U(1)xSU(2)_2"	"J_1(E_2)"	2	0	4	46	2
"1.6.J.2.1c"	1	6	4	"U(1)xSU(2)_2"	"J(J(E_1),E_1)"	2	1/2	3	43	3
"1.6.J.2.1d"	1	6	4	"U(1)xSU(2)_2"	"J_1(J(E_1))"	2	0	4	46	3
"1.6.J.2.1e"	1	6	4	"U(1)xSU(2)_2"	"J_2(E_1)"	2	0	5	59	4
"1.6.J.3.1a"	1	6	4	"U(1)xSU(2)_2"	"J_1(E_3)"	3	0	4	42	2
"1.6.J.4.1a"	1	6	4	"U(1)xSU(2)_2"	"J(E_4,E_2)"	4	0	3	27	2
"1.6.J.4.1b"	1	6	4	"U(1)xSU(2)_2"	"J_1(E_4)"	4	0	4	42	2
"1.6.J.4.2a"	1	6	4	"U(1)xSU(2)_2"	"J(J(E_2),E_2)"	4	1/2	2	23	2
"1.6.J.4.2b"	1	6	4	"U(1)xSU(2)_2"	"J(J(E_2),J(E_1))"	4	1/2	2	23	2
"1.6.J.4.2c"	1	6	4	"U(1)xSU(2)_2"	"J_1(J(E_2))"	4	0	3	26	2
"1.6.J.4.2d"	1	6	4	"U(1)xSU(2)_2"	"J_2(E_2)"	4	1/4	3	31	2
"1.6.J.4.2e"	1	6	4	"U(1)xSU(2)_2"	"J_2(J(E_1))"	4	1/4	3	31	3
"1.6.J.6.1a"	1	6	4	"U(1)xSU(2)_2"	"J(J(E_3),E_3)"	6	1/2	2	21	2
"1.6.J.6.1b"	1	6	4	"U(1)xSU(2)_2"	"J_1(J(E_3))"	6	0	3	24	2
"1.6.J.6.2a"	1	6	4	"U(1)xSU(2)_2"	"J(E_6,E_3)"	6	1/6	3	27	2
"1.6.J.6.2b"	1	6	4	"U(1)xSU(2)_2"	"J_2(E_3)"	6	0	3	27	2
"1.6.J.6.2c"	1	6	4	"U(1)xSU(2)_2"	"J_1(E_6)"	6	0	4	42	2
"1.6.J.8.2a"	1	6	4	"U(1)xSU(2)_2"	"J_2(E_4)"	8	1/8	3	27	2
"1.6.J.8.3a"	1	6	4	"U(1)xSU(2)_2"	"J(J(E_4),J(E_2))"	8	1/4	2	15	2
"1.6.J.8.3b"	1	6	4	"U(1)xSU(2)_2"	"J(J(E_4),E_4)"	8	1/2	2	21	2
"1.6.J.8.3c"	1	6	4	"U(1)xSU(2)_2"	"J_1(J(E_4))"	8	0	3	24	2
"1.6.J.8.5a"	1	6	4	"U(1)xSU(2)_2"	"J_2(J(E_2))"	8	3/8	2	17	2
"1.6.J.12.4a"	1	6	4	"U(1)xSU(2)_2"	"J(J(E_6),J(E_3))"	12	1/3	2	15	2
"1.6.J.12.4b"	1	6	4	"U(1)xSU(2)_2"	"J_2(J(E_3))"	12	1/4	2	15	2
"1.6.J.12.4c"	1	6	4	"U(1)xSU(2)_2"	"J(J(E_6),E_6)"	12	1/2	2	21	2
"1.6.J.12.4d"	1	6	4	"U(1)xSU(2)_2"	"J_1(J(E_6))"	12	0	3	24	2
"1.6.J.12.5a"	1	6	4	"U(1)xSU(2)_2"	"J_2(E_6)"	12	1/12	3	27	2
"1.6.J.16.11a"	1	6	4	"U(1)xSU(2)_2"	"J_2(J(E_4))"	16	5/16	2	15	2
"1.6.J.24.14a"	1	6	4	"U(1)xSU(2)_2"	"J_2(J(E_6))"	24	7/24	2	15	2
"1.6.K.1.1a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times C_1"	1	0	9	146	5
"1.6.K.2.1a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times J(C_1)"	2	0	5	74	2
"1.6.K.2.1b"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times C_2"	2	0	5	74	3
"1.6.K.2.1c"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times C_{2,1}"	2	0	5	74	4
"1.6.K.3.1a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times C_3"	3	0	5	62	3
"1.6.K.4.1a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times C_{4,1}"	4	0	3	38	2
"1.6.K.4.1b"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times C_4"	4	0	5	62	3
"1.6.K.4.2a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times D_2"	4	0	3	38	2
"1.6.K.4.2b"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times J(C_2)"	4	0	3	38	2
"1.6.K.4.2c"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times D_{2,1}"	4	0	3	38	3
"1.6.K.6.1a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times D_3"	6	0	3	32	2
"1.6.K.6.1b"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times D_{3,2}"	6	0	3	32	3
"1.6.K.6.2a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times J(C_3)"	6	0	3	32	2
"1.6.K.6.2b"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times C_{6,1}"	6	0	3	32	2
"1.6.K.6.2c"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times C_6"	6	0	5	62	3
"1.6.K.8.2a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times J(C_4)"	8	0	3	32	2
"1.6.K.8.3a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times D_{4,1}"	8	0	2	20	2
"1.6.K.8.3b"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times D_4"	8	0	3	32	2
"1.6.K.8.3c"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times D_{4,2}"	8	0	3	32	3
"1.6.K.8.5a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times J(D_2)"	8	0	2	20	2
"1.6.K.12.3a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times T"	12	0	3	26	2
"1.6.K.12.4a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times J(D_3)"	12	0	2	17	2
"1.6.K.12.4b"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times D_{6,1}"	12	0	2	17	2
"1.6.K.12.4c"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times D_6"	12	0	3	32	2
"1.6.K.12.4d"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times D_{6,2}"	12	0	3	32	3
"1.6.K.12.5a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times J(C_6)"	12	0	3	32	2
"1.6.K.16.11a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times J(D_4)"	16	0	2	17	2
"1.6.K.24.12a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times O_1"	24	0	2	14	2
"1.6.K.24.12b"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times O"	24	0	3	26	2
"1.6.K.24.13a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times J(T)"	24	0	2	14	2
"1.6.K.24.14a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times J(D_6)"	24	0	2	17	2
"1.6.K.48.48a"	1	6	4	"SU(2)xU(1)_2"	"\\mathrm{SU}(2)\\times J(O)"	48	0	2	14	2
"1.6.L.1.1a"	1	6	6	"U(1)xU(1)_2"	"L_1(C_1)"	1	0	10	198	5
"1.6.L.2.1a"	1	6	6	"U(1)xU(1)_2"	"L(J(C_1),C_1)"	2	1/2	5	99	2
"1.6.L.2.1b"	1	6	6	"U(1)xU(1)_2"	"L_1(J(C_1))"	2	0	6	102	2
"1.6.L.2.1c"	1	6	6	"U(1)xU(1)_2"	"L(C_2,C_1)"	2	1/2	5	99	3
"1.6.L.2.1d"	1	6	6	"U(1)xU(1)_2"	"L_1(C_2)"	2	0	6	102	3
"1.6.L.2.1e"	1	6	6	"U(1)xU(1)_2"	"L(C_{2,1},C_1)"	2	1/2	5	99	4
"1.6.L.2.1f"	1	6	6	"U(1)xU(1)_2"	"L_1(C_{2,1})"	2	0	6	102	4
"1.6.L.2.1g"	1	6	6	"U(1)xU(1)_2"	"L_2(C_1)"	2	0	9	147	5
"1.6.L.3.1a"	1	6	6	"U(1)xU(1)_2"	"L_1(C_3)"	3	0	6	90	3
"1.6.L.4.1a"	1	6	6	"U(1)xU(1)_2"	"L(C_{4,1},C_2)"	4	1/2	3	51	2
"1.6.L.4.1b"	1	6	6	"U(1)xU(1)_2"	"L_1(C_{4,1})"	4	0	4	54	2
"1.6.L.4.1c"	1	6	6	"U(1)xU(1)_2"	"L(C_4,C_2)"	4	0	5	63	3
"1.6.L.4.1d"	1	6	6	"U(1)xU(1)_2"	"L_1(C_4)"	4	0	6	90	3
"1.6.L.4.2a"	1	6	6	"U(1)xU(1)_2"	"L(D_2,C_2)"	4	1/2	3	51	2
"1.6.L.4.2b"	1	6	6	"U(1)xU(1)_2"	"L(J(C_2),J(C_1))"	4	1/2	3	51	2
"1.6.L.4.2c"	1	6	6	"U(1)xU(1)_2"	"L(J(C_2),C_2)"	4	1/2	3	51	2
"1.6.L.4.2d"	1	6	6	"U(1)xU(1)_2"	"L(J(C_2),C_{2,1})"	4	1/2	3	51	2
"1.6.L.4.2e"	1	6	6	"U(1)xU(1)_2"	"L_1(D_2)"	4	0	4	54	2
"1.6.L.4.2f"	1	6	6	"U(1)xU(1)_2"	"L_1(J(C_2))"	4	0	4	54	2
"1.6.L.4.2g"	1	6	6	"U(1)xU(1)_2"	"L_2(J(C_1))"	4	1/4	5	75	2
"1.6.L.4.2h"	1	6	6	"U(1)xU(1)_2"	"L(D_{2,1},C_2)"	4	1/2	3	51	3
"1.6.L.4.2i"	1	6	6	"U(1)xU(1)_2"	"L(D_{2,1},C_{2,1})"	4	1/2	3	51	3
"1.6.L.4.2j"	1	6	6	"U(1)xU(1)_2"	"L_1(D_{2,1})"	4	0	4	54	3
"1.6.L.4.2k"	1	6	6	"U(1)xU(1)_2"	"L_2(C_2)"	4	1/4	5	75	3
"1.6.L.4.2l"	1	6	6	"U(1)xU(1)_2"	"L_2(C_{2,1})"	4	1/4	5	75	4
"1.6.L.6.1a"	1	6	6	"U(1)xU(1)_2"	"L(D_3,C_3)"	6	1/2	3	45	2
"1.6.L.6.1b"	1	6	6	"U(1)xU(1)_2"	"L_1(D_3)"	6	0	4	48	2
"1.6.L.6.1c"	1	6	6	"U(1)xU(1)_2"	"L(D_{3,2},C_3)"	6	1/2	3	45	3
"1.6.L.6.1d"	1	6	6	"U(1)xU(1)_2"	"L_1(D_{3,2})"	6	0	4	48	3
"1.6.L.6.2a"	1	6	6	"U(1)xU(1)_2"	"L(J(C_3),C_3)"	6	1/2	3	45	2
"1.6.L.6.2b"	1	6	6	"U(1)xU(1)_2"	"L(C_{6,1},C_3)"	6	1/2	3	45	2
"1.6.L.6.2c"	1	6	6	"U(1)xU(1)_2"	"L_1(J(C_3))"	6	0	4	48	2
"1.6.L.6.2d"	1	6	6	"U(1)xU(1)_2"	"L_1(C_{6,1})"	6	0	4	48	2
"1.6.L.6.2e"	1	6	6	"U(1)xU(1)_2"	"L(C_6,C_3)"	6	1/6	5	63	3
"1.6.L.6.2f"	1	6	6	"U(1)xU(1)_2"	"L_2(C_3)"	6	0	5	63	3
"1.6.L.6.2g"	1	6	6	"U(1)xU(1)_2"	"L_1(C_6)"	6	0	6	90	3
"1.6.L.8.2a"	1	6	6	"U(1)xU(1)_2"	"L(J(C_4),C_{4,1})"	8	1/4	3	33	2
"1.6.L.8.2b"	1	6	6	"U(1)xU(1)_2"	"L(J(C_4),J(C_2))"	8	1/4	3	33	2
"1.6.L.8.2c"	1	6	6	"U(1)xU(1)_2"	"L_2(C_{4,1})"	8	3/8	3	39	2
"1.6.L.8.2d"	1	6	6	"U(1)xU(1)_2"	"L(J(C_4),C_4)"	8	1/2	3	45	2
"1.6.L.8.2e"	1	6	6	"U(1)xU(1)_2"	"L_1(J(C_4))"	8	0	4	48	2
"1.6.L.8.2f"	1	6	6	"U(1)xU(1)_2"	"L_2(C_4)"	8	1/8	5	63	3
"1.6.L.8.3a"	1	6	6	"U(1)xU(1)_2"	"L(D_{4,1},C_{4,1})"	8	1/2	2	27	2
"1.6.L.8.3b"	1	6	6	"U(1)xU(1)_2"	"L(D_{4,1},D_2)"	8	1/2	2	27	2
"1.6.L.8.3c"	1	6	6	"U(1)xU(1)_2"	"L(D_{4,1},D_{2,1})"	8	1/2	2	27	2
"1.6.L.8.3d"	1	6	6	"U(1)xU(1)_2"	"L_1(D_{4,1})"	8	0	3	30	2
"1.6.L.8.3e"	1	6	6	"U(1)xU(1)_2"	"L(D_4,D_2)"	8	1/4	3	33	2
"1.6.L.8.3f"	1	6	6	"U(1)xU(1)_2"	"L(D_4,C_4)"	8	1/2	3	45	2
"1.6.L.8.3g"	1	6	6	"U(1)xU(1)_2"	"L_1(D_4)"	8	0	4	48	2
"1.6.L.8.3h"	1	6	6	"U(1)xU(1)_2"	"L(D_{4,2},D_{2,1})"	8	1/4	3	33	3
"1.6.L.8.3i"	1	6	6	"U(1)xU(1)_2"	"L(D_{4,2},C_4)"	8	1/2	3	45	3
"1.6.L.8.3j"	1	6	6	"U(1)xU(1)_2"	"L_1(D_{4,2})"	8	0	4	48	3
"1.6.L.8.5a"	1	6	6	"U(1)xU(1)_2"	"L(J(D_2),D_2)"	8	1/2	2	27	2
"1.6.L.8.5b"	1	6	6	"U(1)xU(1)_2"	"L(J(D_2),J(C_2))"	8	1/2	2	27	2
"1.6.L.8.5c"	1	6	6	"U(1)xU(1)_2"	"L(J(D_2),D_{2,1})"	8	1/2	2	27	2
"1.6.L.8.5d"	1	6	6	"U(1)xU(1)_2"	"L_1(J(D_2))"	8	0	3	30	2
"1.6.L.8.5e"	1	6	6	"U(1)xU(1)_2"	"L_2(D_2)"	8	3/8	3	39	2
"1.6.L.8.5f"	1	6	6	"U(1)xU(1)_2"	"L_2(J(C_2))"	8	3/8	3	39	2
"1.6.L.8.5g"	1	6	6	"U(1)xU(1)_2"	"L_2(D_{2,1})"	8	3/8	3	39	3
"1.6.L.12.3a"	1	6	6	"U(1)xU(1)_2"	"L_1(T)"	12	0	4	42	2
"1.6.L.12.4a"	1	6	6	"U(1)xU(1)_2"	"L(J(D_3),J(C_3))"	12	1/2	2	24	2
"1.6.L.12.4b"	1	6	6	"U(1)xU(1)_2"	"L(J(D_3),D_3)"	12	1/2	2	24	2
"1.6.L.12.4c"	1	6	6	"U(1)xU(1)_2"	"L(D_{6,1},D_3)"	12	1/2	2	24	2
"1.6.L.12.4d"	1	6	6	"U(1)xU(1)_2"	"L(D_{6,1},C_{6,1})"	12	1/2	2	24	2
"1.6.L.12.4e"	1	6	6	"U(1)xU(1)_2"	"L(J(D_3),D_{3,2})"	12	1/2	2	24	2
"1.6.L.12.4f"	1	6	6	"U(1)xU(1)_2"	"L(D_{6,1},D_{3,2})"	12	1/2	2	24	2
"1.6.L.12.4g"	1	6	6	"U(1)xU(1)_2"	"L_1(J(D_3))"	12	0	3	27	2
"1.6.L.12.4h"	1	6	6	"U(1)xU(1)_2"	"L_1(D_{6,1})"	12	0	3	27	2
"1.6.L.12.4i"	1	6	6	"U(1)xU(1)_2"	"L(D_6,D_3)"	12	1/3	3	33	2
"1.6.L.12.4j"	1	6	6	"U(1)xU(1)_2"	"L_2(D_3)"	12	1/4	3	33	2
"1.6.L.12.4k"	1	6	6	"U(1)xU(1)_2"	"L(D_6,C_6)"	12	1/2	3	45	2
"1.6.L.12.4l"	1	6	6	"U(1)xU(1)_2"	"L_1(D_6)"	12	0	4	48	2
"1.6.L.12.4m"	1	6	6	"U(1)xU(1)_2"	"L(D_{6,2},D_{3,2})"	12	1/3	3	33	3
"1.6.L.12.4n"	1	6	6	"U(1)xU(1)_2"	"L_2(D_{3,2})"	12	1/4	3	33	3
"1.6.L.12.4o"	1	6	6	"U(1)xU(1)_2"	"L(D_{6,2},C_6)"	12	1/2	3	45	3
"1.6.L.12.4p"	1	6	6	"U(1)xU(1)_2"	"L_1(D_{6,2})"	12	0	4	48	3
"1.6.L.12.5a"	1	6	6	"U(1)xU(1)_2"	"L(J(C_6),J(C_3))"	12	1/3	3	33	2
"1.6.L.12.5b"	1	6	6	"U(1)xU(1)_2"	"L(J(C_6),C_{6,1})"	12	1/3	3	33	2
"1.6.L.12.5c"	1	6	6	"U(1)xU(1)_2"	"L_2(J(C_3))"	12	1/4	3	33	2
"1.6.L.12.5d"	1	6	6	"U(1)xU(1)_2"	"L_2(C_{6,1})"	12	1/4	3	33	2
"1.6.L.12.5e"	1	6	6	"U(1)xU(1)_2"	"L(J(C_6),C_6)"	12	1/2	3	45	2
"1.6.L.12.5f"	1	6	6	"U(1)xU(1)_2"	"L_1(J(C_6))"	12	0	4	48	2
"1.6.L.12.5g"	1	6	6	"U(1)xU(1)_2"	"L_2(C_6)"	12	1/12	5	63	3
"1.6.L.16.10a"	1	6	6	"U(1)xU(1)_2"	"L_2(J(C_4))"	16	5/16	3	33	2
"1.6.L.16.11a"	1	6	6	"U(1)xU(1)_2"	"L(J(D_4),D_{4,1})"	16	3/8	2	18	2
"1.6.L.16.11b"	1	6	6	"U(1)xU(1)_2"	"L(J(D_4),J(D_2))"	16	3/8	2	18	2
"1.6.L.16.11c"	1	6	6	"U(1)xU(1)_2"	"L_2(D_{4,1})"	16	7/16	2	21	2
"1.6.L.16.11d"	1	6	6	"U(1)xU(1)_2"	"L(J(D_4),D_4)"	16	1/2	2	24	2
"1.6.L.16.11e"	1	6	6	"U(1)xU(1)_2"	"L(J(D_4),J(C_4))"	16	1/2	2	24	2
"1.6.L.16.11f"	1	6	6	"U(1)xU(1)_2"	"L(J(D_4),D_{4,2})"	16	1/2	2	24	2
"1.6.L.16.11g"	1	6	6	"U(1)xU(1)_2"	"L_1(J(D_4))"	16	0	3	27	2
"1.6.L.16.11h"	1	6	6	"U(1)xU(1)_2"	"L_2(D_4)"	16	5/16	3	33	2
"1.6.L.16.11i"	1	6	6	"U(1)xU(1)_2"	"L_2(D_{4,2})"	16	5/16	3	33	3
"1.6.L.16.14a"	1	6	6	"U(1)xU(1)_2"	"L_2(J(D_2))"	16	7/16	2	21	2
"1.6.L.24.12a"	1	6	6	"U(1)xU(1)_2"	"L(O_1,T)"	24	1/2	2	21	2
"1.6.L.24.12b"	1	6	6	"U(1)xU(1)_2"	"L_1(O_1)"	24	0	3	24	2
"1.6.L.24.12c"	1	6	6	"U(1)xU(1)_2"	"L(O,T)"	24	1/4	3	27	2
"1.6.L.24.12d"	1	6	6	"U(1)xU(1)_2"	"L_1(O)"	24	0	4	42	2
"1.6.L.24.13a"	1	6	6	"U(1)xU(1)_2"	"L(J(T),T)"	24	1/2	2	21	2
"1.6.L.24.13b"	1	6	6	"U(1)xU(1)_2"	"L_1(J(T))"	24	0	3	24	2
"1.6.L.24.13c"	1	6	6	"U(1)xU(1)_2"	"L_2(T)"	24	1/8	3	27	2
"1.6.L.24.14a"	1	6	6	"U(1)xU(1)_2"	"L(J(D_6),J(D_3))"	24	5/12	2	18	2
"1.6.L.24.14b"	1	6	6	"U(1)xU(1)_2"	"L(J(D_6),D_{6,1})"	24	5/12	2	18	2
"1.6.L.24.14c"	1	6	6	"U(1)xU(1)_2"	"L_2(J(D_3))"	24	3/8	2	18	2
"1.6.L.24.14d"	1	6	6	"U(1)xU(1)_2"	"L_2(D_{6,1})"	24	3/8	2	18	2
"1.6.L.24.14e"	1	6	6	"U(1)xU(1)_2"	"L(J(D_6),J(C_6))"	24	1/2	2	24	2
"1.6.L.24.14f"	1	6	6	"U(1)xU(1)_2"	"L(J(D_6),D_6)"	24	1/2	2	24	2
"1.6.L.24.14g"	1	6	6	"U(1)xU(1)_2"	"L(J(D_6),D_{6,2})"	24	1/2	2	24	2
"1.6.L.24.14h"	1	6	6	"U(1)xU(1)_2"	"L_1(J(D_6))"	24	0	3	27	2
"1.6.L.24.14i"	1	6	6	"U(1)xU(1)_2"	"L_2(D_6)"	24	7/24	3	33	2
"1.6.L.24.14j"	1	6	6	"U(1)xU(1)_2"	"L_2(D_{6,2})"	24	7/24	3	33	3
"1.6.L.24.15a"	1	6	6	"U(1)xU(1)_2"	"L_2(J(C_6))"	24	7/24	3	33	2
"1.6.L.32.46a"	1	6	6	"U(1)xU(1)_2"	"L_2(J(D_4))"	32	13/32	2	18	2
"1.6.L.48.48a"	1	6	6	"U(1)xU(1)_2"	"L(J(O),J(T))"	48	3/8	2	15	2
"1.6.L.48.48b"	1	6	6	"U(1)xU(1)_2"	"L(J(O),O_1)"	48	3/8	2	15	2
"1.6.L.48.48c"	1	6	6	"U(1)xU(1)_2"	"L_2(O_1)"	48	5/16	2	15	2
"1.6.L.48.48d"	1	6	6	"U(1)xU(1)_2"	"L(J(O),O)"	48	1/2	2	21	2
"1.6.L.48.48e"	1	6	6	"U(1)xU(1)_2"	"L_1(J(O))"	48	0	3	24	2
"1.6.L.48.48f"	1	6	6	"U(1)xU(1)_2"	"L_2(O)"	48	3/16	3	27	2
"1.6.L.48.49a"	1	6	6	"U(1)xU(1)_2"	"L_2(J(T))"	48	5/16	2	15	2
"1.6.L.48.51a"	1	6	6	"U(1)xU(1)_2"	"L_2(J(D_6))"	48	19/48	2	18	2
"1.6.L.96.226a"	1	6	6	"U(1)xU(1)_2"	"L_2(J(O))"	96	11/32	2	15	2
"1.6.M.1.1a"	1	6	3	"SU(2)_3"	"M(C_1)"	1	0	9	162	6
"1.6.M.2.1a"	1	6	3	"SU(2)_3"	"M(C_2)"	2	0	5	82	4
"1.6.M.3.1a"	1	6	3	"SU(2)_3"	"M(C_3)"	3	2/3	3	54	2
"1.6.M.4.1a"	1	6	3	"SU(2)_3"	"M(C_4)"	4	0	3	42	2
"1.6.M.4.2a"	1	6	3	"SU(2)_3"	"M(D_2)"	4	0	3	42	3
"1.6.M.6.1a"	1	6	3	"SU(2)_3"	"M(D_3)"	6	1/3	2	28	2
"1.6.M.6.2a"	1	6	3	"SU(2)_3"	"M(C_6)"	6	1/3	3	38	2
"1.6.M.8.3a"	1	6	3	"SU(2)_3"	"M(D_4)"	8	0	2	22	2
"1.6.M.12.3a"	1	6	3	"SU(2)_3"	"M(A_4)"	12	2/3	1	14	1
"1.6.M.12.4a"	1	6	3	"SU(2)_3"	"M(D_6)"	12	1/6	2	20	2
"1.6.M.24.12a"	1	6	3	"SU(2)_3"	"M(S_4)"	24	1/3	1	8	1
"1.6.N.1.1a"	1	6	1	"U(1)_3"	"A(1,1)"	1	0	18	486	9
"1.6.N.2.1a"	1	6	1	"U(1)_3"	"A(1,2)"	2	0	10	246	5
"1.6.N.2.1b"	1	6	1	"U(1)_3"	"J(A(1,1))"	2	1/2	9	243	6
"1.6.N.3.1a"	1	6	1	"U(1)_3"	"A(3,1)"	3	2/3	6	162	3
"1.6.N.3.1b"	1	6	1	"U(1)_3"	"A(1,3)"	3	0	10	198	5
"1.6.N.4.1a"	1	6	1	"U(1)_3"	"J_n(A(1,2))"	4	1/2	5	123	2
"1.6.N.4.1b"	1	6	1	"U(1)_3"	"A(1,4)_2"	4	0	6	126	3
"1.6.N.4.1c"	1	6	1	"U(1)_3"	"A(1,4)_1"	4	0	10	198	5
"1.6.N.4.2a"	1	6	1	"U(1)_3"	"A(2,2)"	4	0	6	126	3
"1.6.N.4.2b"	1	6	1	"U(1)_3"	"J(A(1,2))"	4	1/2	5	123	4
"1.6.N.6.1a"	1	6	1	"U(1)_3"	"B(3,1)"	6	1/3	4	84	2
"1.6.N.6.1b"	1	6	1	"U(1)_3"	"J(A(3,1))"	6	5/6	3	81	3
"1.6.N.6.1c"	1	6	1	"U(1)_3"	"J(A(1,3))"	6	1/2	5	99	4
"1.6.N.6.2a"	1	6	1	"U(1)_3"	"J_s(A(3,1))"	6	5/6	3	81	2
"1.6.N.6.2b"	1	6	1	"U(1)_3"	"A(1,6)_2"	6	0	6	102	3
"1.6.N.6.2c"	1	6	1	"U(1)_3"	"A(3,2)"	6	1/3	6	114	3
"1.6.N.6.2d"	1	6	1	"U(1)_3"	"A(1,6)_1"	6	0	10	198	5
"1.6.N.7.1a"	1	6	1	"U(1)_3"	"A(1,7)"	7	0	6	90	3
"1.6.N.8.1a"	1	6	1	"U(1)_3"	"J_n(A(1,4)_2)"	8	1/2	3	63	2
"1.6.N.8.1b"	1	6	1	"U(1)_3"	"A(1,8)_1"	8	0	6	90	3
"1.6.N.8.1c"	1	6	1	"U(1)_3"	"A(1,8)_2"	8	0	6	102	3
"1.6.N.8.2a"	1	6	1	"U(1)_3"	"J_s(A(1,4)_2)"	8	1/2	3	63	2
"1.6.N.8.2b"	1	6	1	"U(1)_3"	"A(2,4)"	8	0	6	102	3
"1.6.N.8.3a"	1	6	1	"U(1)_3"	"J_s(A(2,2))"	8	1/2	3	63	2
"1.6.N.8.3b"	1	6	1	"U(1)_3"	"B(1,4)_2"	8	0	4	66	2
"1.6.N.8.3c"	1	6	1	"U(1)_3"	"J(A(1,4)_2)"	8	1/2	3	63	3
"1.6.N.8.3d"	1	6	1	"U(1)_3"	"J(A(1,4)_1)"	8	1/2	5	99	4
"1.6.N.8.4a"	1	6	1	"U(1)_3"	"B(1,4;2)_2"	8	0	4	66	2
"1.6.N.8.4b"	1	6	1	"U(1)_3"	"J_n(A(1,4)_1)"	8	1/2	5	99	2
"1.6.N.8.5a"	1	6	1	"U(1)_3"	"J(A(2,2))"	8	1/2	3	63	3
"1.6.N.9.2a"	1	6	1	"U(1)_3"	"C(3,1)"	9	8/9	2	54	1
"1.6.N.9.2b"	1	6	1	"U(1)_3"	"A(3,3)"	9	2/9	6	90	3
"1.6.N.12.1a"	1	6	1	"U(1)_3"	"B(3,2;2)"	12	1/6	4	60	2
"1.6.N.12.1b"	1	6	1	"U(1)_3"	"J_n(A(1,6)_1)"	12	1/2	5	99	2
"1.6.N.12.2a"	1	6	1	"U(1)_3"	"J_n(A(3,2))"	12	2/3	3	57	2
"1.6.N.12.2b"	1	6	1	"U(1)_3"	"A(3,4)"	12	1/6	6	90	3
"1.6.N.12.2c"	1	6	1	"U(1)_3"	"A(1,12)"	12	0	6	102	3
"1.6.N.12.3a"	1	6	1	"U(1)_3"	"C(2,2)"	12	2/3	2	42	1
"1.6.N.12.4a"	1	6	1	"U(1)_3"	"J(B(3,1))"	12	2/3	2	42	2
"1.6.N.12.4b"	1	6	1	"U(1)_3"	"B(3,2)"	12	1/6	4	60	2
"1.6.N.12.4c"	1	6	1	"U(1)_3"	"J(A(1,6)_2)"	12	1/2	3	51	3
"1.6.N.12.4d"	1	6	1	"U(1)_3"	"J(A(3,2))"	12	2/3	3	57	3
"1.6.N.12.4e"	1	6	1	"U(1)_3"	"J(A(1,6)_1)"	12	1/2	5	99	4
"1.6.N.12.5a"	1	6	1	"U(1)_3"	"J_s(A(3,2))"	12	2/3	3	57	2
"1.6.N.12.5b"	1	6	1	"U(1)_3"	"A(6,2)"	12	1/6	6	90	3
"1.6.N.12.5c"	1	6	1	"U(1)_3"	"A(2,6)"	12	0	6	102	3
"1.6.N.14.1a"	1	6	1	"U(1)_3"	"J(A(1,7))"	14	1/2	3	45	3
"1.6.N.16.2a"	1	6	1	"U(1)_3"	"A(4,4)"	16	0	6	90	3
"1.6.N.16.6a"	1	6	1	"U(1)_3"	"J_s(A(1,8)_1)"	16	1/2	3	45	2
"1.6.N.16.6b"	1	6	1	"U(1)_3"	"J_n(A(2,4))"	16	1/2	3	51	2
"1.6.N.16.6c"	1	6	1	"U(1)_3"	"B(2,4;4)"	16	0	4	54	2
"1.6.N.16.7a"	1	6	1	"U(1)_3"	"J_s(B(1,4)_2)"	16	1/2	2	33	2
"1.6.N.16.7b"	1	6	1	"U(1)_3"	"J(A(1,8)_1)"	16	1/2	3	45	3
"1.6.N.16.7c"	1	6	1	"U(1)_3"	"J(A(1,8)_2)"	16	1/2	3	51	3
"1.6.N.16.8a"	1	6	1	"U(1)_3"	"J_s(B(1,4;2)_2)"	16	1/2	2	33	2
"1.6.N.16.8b"	1	6	1	"U(1)_3"	"J_s(A(1,8)_2)"	16	1/2	3	51	2
"1.6.N.16.8c"	1	6	1	"U(1)_3"	"B(1,8)_1"	16	0	4	48	2
"1.6.N.16.11a"	1	6	1	"U(1)_3"	"J(B(1,4)_2)"	16	1/2	2	33	2
"1.6.N.16.11b"	1	6	1	"U(1)_3"	"J(A(2,4))"	16	1/2	3	51	3
"1.6.N.16.13a"	1	6	1	"U(1)_3"	"J(B(1,4;2)_2)"	16	1/2	2	33	2
"1.6.N.16.13b"	1	6	1	"U(1)_3"	"J_s(A(2,4))"	16	1/2	3	51	2
"1.6.N.16.13c"	1	6	1	"U(1)_3"	"B(2,4)"	16	0	4	54	2
"1.6.N.18.3a"	1	6	1	"U(1)_3"	"J(C(3,1))"	18	17/18	1	27	1
"1.6.N.18.3b"	1	6	1	"U(1)_3"	"J_s(A(3,3))"	18	11/18	3	45	2
"1.6.N.18.3c"	1	6	1	"U(1)_3"	"B(3,3)"	18	1/9	4	48	2
"1.6.N.18.4a"	1	6	1	"U(1)_3"	"D(3,1)"	18	4/9	2	30	1
"1.6.N.18.4b"	1	6	1	"U(1)_3"	"J(A(3,3))"	18	11/18	3	45	3
"1.6.N.18.5a"	1	6	1	"U(1)_3"	"A(3,6)"	18	1/9	6	90	3
"1.6.N.21.1a"	1	6	1	"U(1)_3"	"C(1,7)"	21	2/3	2	30	1
"1.6.N.24.1a"	1	6	1	"U(1)_3"	"J_n(A(1,12))"	24	1/2	3	51	2
"1.6.N.24.1b"	1	6	1	"U(1)_3"	"B(3,4;4)"	24	1/12	4	48	2
"1.6.N.24.3a"	1	6	1	"U(1)_3"	"B(T,1;1)"	24	0	4	42	2
"1.6.N.24.3b"	1	6	1	"U(1)_3"	"B(T,1)"	24	1/3	4	54	2
"1.6.N.24.5a"	1	6	1	"U(1)_3"	"J_s(B(3,2;2))"	24	7/12	2	30	2
"1.6.N.24.5b"	1	6	1	"U(1)_3"	"J_s(A(1,12))"	24	1/2	3	51	2
"1.6.N.24.5c"	1	6	1	"U(1)_3"	"B(3,4)"	24	1/12	4	48	2
"1.6.N.24.6a"	1	6	1	"U(1)_3"	"J_s(B(3,2))"	24	7/12	2	30	2
"1.6.N.24.6b"	1	6	1	"U(1)_3"	"J(A(3,4))"	24	7/12	3	45	3
"1.6.N.24.6c"	1	6	1	"U(1)_3"	"J(A(1,12))"	24	1/2	3	51	3
"1.6.N.24.8a"	1	6	1	"U(1)_3"	"J(B(3,2;2))"	24	7/12	2	30	2
"1.6.N.24.8b"	1	6	1	"U(1)_3"	"J_s(A(2,6))"	24	1/2	3	51	2
"1.6.N.24.8c"	1	6	1	"U(1)_3"	"B(6,2)"	24	1/12	4	48	2
"1.6.N.24.10a"	1	6	1	"U(1)_3"	"J_s(A(6,2))"	24	7/12	3	45	2
"1.6.N.24.10b"	1	6	1	"U(1)_3"	"J_s(A(3,4))"	24	7/12	3	45	2
"1.6.N.24.10c"	1	6	1	"U(1)_3"	"B(1,12)"	24	0	4	54	2
"1.6.N.24.11a"	1	6	1	"U(1)_3"	"J_n(A(3,4))"	24	7/12	3	45	2
"1.6.N.24.11b"	1	6	1	"U(1)_3"	"B(1,12;2)"	24	0	4	54	2
"1.6.N.24.12a"	1	6	1	"U(1)_3"	"J_s(C(2,2))"	24	5/6	1	21	1
"1.6.N.24.12b"	1	6	1	"U(1)_3"	"D(2,2)"	24	1/3	2	24	1
"1.6.N.24.13a"	1	6	1	"U(1)_3"	"J(C(2,2))"	24	5/6	1	21	1
"1.6.N.24.14a"	1	6	1	"U(1)_3"	"J(B(3,2))"	24	7/12	2	30	2
"1.6.N.24.14b"	1	6	1	"U(1)_3"	"J(A(6,2))"	24	7/12	3	45	3
"1.6.N.24.14c"	1	6	1	"U(1)_3"	"J(A(2,6))"	24	1/2	3	51	3
"1.6.N.27.3a"	1	6	1	"U(1)_3"	"C(3,3)"	27	20/27	2	30	1
"1.6.N.32.7a"	1	6	1	"U(1)_3"	"J_s(B(2,4;4))"	32	1/2	2	27	2
"1.6.N.32.11a"	1	6	1	"U(1)_3"	"J_s(A(4,4))"	32	1/2	3	45	2
"1.6.N.32.11b"	1	6	1	"U(1)_3"	"B(4,4)"	32	0	4	48	2
"1.6.N.32.34a"	1	6	1	"U(1)_3"	"J(A(4,4))"	32	1/2	3	45	3
"1.6.N.32.43a"	1	6	1	"U(1)_3"	"J(B(1,8)_1)"	32	1/2	2	24	2
"1.6.N.32.43b"	1	6	1	"U(1)_3"	"J_s(B(2,4))"	32	1/2	2	27	2
"1.6.N.32.43c"	1	6	1	"U(1)_3"	"J(B(2,4;4))"	32	1/2	2	27	2
"1.6.N.32.49a"	1	6	1	"U(1)_3"	"J(B(2,4))"	32	1/2	2	27	2
"1.6.N.36.6a"	1	6	1	"U(1)_3"	"J_n(A(3,6))"	36	5/9	3	45	2
"1.6.N.36.6b"	1	6	1	"U(1)_3"	"B(3,6;2)"	36	1/18	4	48	2
"1.6.N.36.9a"	1	6	1	"U(1)_3"	"E(36)"	36	2/9	2	18	1
"1.6.N.36.10a"	1	6	1	"U(1)_3"	"J(D(3,1))"	36	13/18	1	15	1
"1.6.N.36.10b"	1	6	1	"U(1)_3"	"J(B(3,3))"	36	5/9	2	24	2
"1.6.N.36.11a"	1	6	1	"U(1)_3"	"C(6,2)"	36	13/18	2	30	1
"1.6.N.36.12a"	1	6	1	"U(1)_3"	"J_s(A(3,6))"	36	5/9	3	45	2
"1.6.N.36.12b"	1	6	1	"U(1)_3"	"B(3,6)"	36	1/18	4	48	2
"1.6.N.36.13a"	1	6	1	"U(1)_3"	"J(A(3,6))"	36	5/9	3	45	3
"1.6.N.36.14a"	1	6	1	"U(1)_3"	"A(6,6)"	36	1/18	6	90	3
"1.6.N.42.1a"	1	6	1	"U(1)_3"	"J(C(1,7))"	42	5/6	1	15	1
"1.6.N.48.3a"	1	6	1	"U(1)_3"	"C(4,4)"	48	2/3	2	30	1
"1.6.N.48.15a"	1	6	1	"U(1)_3"	"J(B(3,4;4))"	48	13/24	2	24	2
"1.6.N.48.15b"	1	6	1	"U(1)_3"	"J_s(B(1,12))"	48	1/2	2	27	2
"1.6.N.48.17a"	1	6	1	"U(1)_3"	"J_s(B(3,4;4))"	48	13/24	2	24	2
"1.6.N.48.17b"	1	6	1	"U(1)_3"	"J_s(B(1,12;2))"	48	1/2	2	27	2
"1.6.N.48.29a"	1	6	1	"U(1)_3"	"J_s(B(T,1;1))"	48	1/2	2	21	2
"1.6.N.48.29b"	1	6	1	"U(1)_3"	"J_s(B(T,1))"	48	2/3	2	27	2
"1.6.N.48.29c"	1	6	1	"U(1)_3"	"B(O,1)"	48	1/6	4	42	2
"1.6.N.48.33a"	1	6	1	"U(1)_3"	"J(B(T,1))"	48	2/3	2	27	2
"1.6.N.48.33b"	1	6	1	"U(1)_3"	"B(T,2)"	48	1/6	4	42	2
"1.6.N.48.38a"	1	6	1	"U(1)_3"	"J(B(6,2))"	48	13/24	2	24	2
"1.6.N.48.38b"	1	6	1	"U(1)_3"	"J(B(3,4))"	48	13/24	2	24	2
"1.6.N.48.38c"	1	6	1	"U(1)_3"	"J(B(1,12))"	48	1/2	2	27	2
"1.6.N.48.41a"	1	6	1	"U(1)_3"	"J_s(B(3,4))"	48	13/24	2	24	2
"1.6.N.48.41b"	1	6	1	"U(1)_3"	"J(B(1,12;2))"	48	1/2	2	27	2
"1.6.N.48.48a"	1	6	1	"U(1)_3"	"J(D(2,2))"	48	2/3	1	12	1
"1.6.N.54.5a"	1	6	1	"U(1)_3"	"J(C(3,3))"	54	47/54	1	15	1
"1.6.N.54.5b"	1	6	1	"U(1)_3"	"D(3,3)"	54	10/27	2	18	1
"1.6.N.54.8a"	1	6	1	"U(1)_3"	"J_s(C(3,3))"	54	47/54	1	15	1
"1.6.N.64.134a"	1	6	1	"U(1)_3"	"J(B(4,4))"	64	1/2	2	24	2
"1.6.N.72.21a"	1	6	1	"U(1)_3"	"J_s(B(3,6;2))"	72	19/36	2	24	2
"1.6.N.72.23a"	1	6	1	"U(1)_3"	"J_s(B(3,6))"	72	19/36	2	24	2
"1.6.N.72.23b"	1	6	1	"U(1)_3"	"J(B(3,6;2))"	72	19/36	2	24	2
"1.6.N.72.25a"	1	6	1	"U(1)_3"	"B(T,3)"	72	1/9	4	42	2
"1.6.N.72.30a"	1	6	1	"U(1)_3"	"J_s(A(6,6))"	72	19/36	3	45	2
"1.6.N.72.30b"	1	6	1	"U(1)_3"	"B(6,6)"	72	1/36	4	48	2
"1.6.N.72.39a"	1	6	1	"U(1)_3"	"J_n(E(36))"	72	11/18	1	9	1
"1.6.N.72.40a"	1	6	1	"U(1)_3"	"J(E(36))"	72	11/18	1	9	1
"1.6.N.72.41a"	1	6	1	"U(1)_3"	"E(72)"	72	1/9	2	12	1
"1.6.N.72.42a"	1	6	1	"U(1)_3"	"J_s(C(6,2))"	72	31/36	1	15	1
"1.6.N.72.43a"	1	6	1	"U(1)_3"	"D(6,2)"	72	13/36	2	18	1
"1.6.N.72.44a"	1	6	1	"U(1)_3"	"J(C(6,2))"	72	31/36	1	15	1
"1.6.N.72.46a"	1	6	1	"U(1)_3"	"J(B(3,6))"	72	19/36	2	24	2
"1.6.N.72.49a"	1	6	1	"U(1)_3"	"J(A(6,6))"	72	19/36	3	45	3
"1.6.N.96.64a"	1	6	1	"U(1)_3"	"J_s(C(4,4))"	96	5/6	1	15	1
"1.6.N.96.64b"	1	6	1	"U(1)_3"	"D(4,4)"	96	1/3	2	18	1
"1.6.N.96.67a"	1	6	1	"U(1)_3"	"B(O,2)"	96	1/12	4	42	2
"1.6.N.96.72a"	1	6	1	"U(1)_3"	"J(C(4,4))"	96	5/6	1	15	1
"1.6.N.96.193a"	1	6	1	"U(1)_3"	"J(B(O,1))"	96	7/12	2	21	2
"1.6.N.96.193b"	1	6	1	"U(1)_3"	"J_s(B(T,2))"	96	7/12	2	21	2
"1.6.N.96.201a"	1	6	1	"U(1)_3"	"J(B(T,2))"	96	7/12	2	21	2
"1.6.N.108.17a"	1	6	1	"U(1)_3"	"J(D(3,3))"	108	37/54	1	9	1
"1.6.N.108.22a"	1	6	1	"U(1)_3"	"C(6,6)"	108	37/54	2	30	1
"1.6.N.144.125a"	1	6	1	"U(1)_3"	"J_s(B(T,3))"	144	5/9	2	21	2
"1.6.N.144.127a"	1	6	1	"U(1)_3"	"J(B(T,3))"	144	5/9	2	21	2
"1.6.N.144.154a"	1	6	1	"U(1)_3"	"J(B(6,6))"	144	37/72	2	24	2
"1.6.N.144.182a"	1	6	1	"U(1)_3"	"J(E(72))"	144	5/9	1	6	1
"1.6.N.144.183a"	1	6	1	"U(1)_3"	"J(D(6,2))"	144	49/72	1	9	1
"1.6.N.168.42a"	1	6	1	"U(1)_3"	"E(168)"	168	1/3	2	12	1
"1.6.N.192.956a"	1	6	1	"U(1)_3"	"J(D(4,4))"	192	2/3	1	9	1
"1.6.N.192.988a"	1	6	1	"U(1)_3"	"J(B(O,2))"	192	13/24	2	21	2
"1.6.N.216.92a"	1	6	1	"U(1)_3"	"D(6,6)"	216	37/108	2	18	1
"1.6.N.216.95a"	1	6	1	"U(1)_3"	"J_s(C(6,6))"	216	91/108	1	15	1
"1.6.N.216.99a"	1	6	1	"U(1)_3"	"J(C(6,6))"	216	91/108	1	15	1
"1.6.N.216.153a"	1	6	1	"U(1)_3"	"E(216)"	216	7/27	2	12	1
"1.6.N.336.208a"	1	6	1	"U(1)_3"	"J(E(168))"	336	2/3	1	6	1
"1.6.N.432.523a"	1	6	1	"U(1)_3"	"J(D(6,6))"	432	145/216	1	9	1
"1.6.N.432.734a"	1	6	1	"U(1)_3"	"J(E(216))"	432	17/27	1	6	1


# Label --
#    In general Sato-Tate group labels have the form $w.d.A.c.ns$, where

#    * $w$ is the weight (nonnegative integer);
#    * $d$ is the degree (positive integer, even if $w$ is odd);
#    * $A$ is an uppercase letter that identifies the identity component among those of weight $w$ and degree $d$ (ordered by moment simplex);
#    * $c$ is the number of components (positive integer);
#    * $n$ is the second digit of the GAP id $[c,n]$ of the component group (positive integer);
#    * $s$ is a lowercase letter used to distinguish groups for which all the preceding invariants coincide (ordered by moment simplex).

#    When $w=0$ we the identity component is necessarily trivial and the $A$ is omitted.  When $w=0$ and $d=1$ there is exactly one Sato-Tate group for each value of $c$ and we may omit $n$ and $s$.


#Wt (weight) --
#    The **weight** $w$ of the Sato-Tate group $G$ of a motive $X$ is determined by the cohomology group $H^w(X,\mathbb{Q}_\ell)$ used to define $G$. For a prime of norm $q$, the characteristic polynomial of Frobenius is a Weil $q^w$-polynomial.




#Deg (degree) --
#    The **degree** $d$ of a Sato-Tate group is the degree of the characteristic polynomials of its elements, equivalently, the dimension of the $d\times d$ matrices it contains.

#    For an abelian variety $A$ over a number field, the degree $d$ of its Sato-Tate group is twice its dimension $g$ as an abelian variety (if $A=\mathrm{Jac}(C)$ is the Jacobian of a curve $C$, then $g$ is also the genus of $C$).  The degree $d=2g$ is then also the degree of the characteristic polynomials of the Frobenius endomorphism of the reductions of $A$ modulo good primes.



#$\mathrm{dim}_{\mathbb{R}}$ (real_dimension) --
#    The **real dimension** of a Sato-Tate group is its dimension as a real Lie group.


#$\mathrm{G}^0$ (identity_component) --
#    The **identity component** of a Sato-Tate group $G$ is the connected component $G^0$ of the identity element.  As a compact Lie group, the identity component $G^0$ is a normal subgroup of finite index.  The quotient $G/G^0$ is the component group of $G$.


#Name (pretty) --
#    The names of the Sato-Tate groups of weight 1 and degree 4 are taken from \cite{arXiv:1110.6638,doi:10.1112/S0010437X12000279}.


#$\mathrm{G}/\mathrm{G}^0$ (components) --
#    The **component group** of a Sato-Tate group $G$ is the quotient $G/G^0$ of $G$ by its identity component $G^0$, which is a normal subgroup of finite index.

#    If $G$ is the Sato-Tate group of a motive defined over a number field $K$, then the component group $G/G^0$ is canonically isomorphic to the Galois group of a finite extension $L/K$. For the motive attached to an abelian variety $A$ of dimension at most 3, $L$ is the smallest field over which all endomorphisms of $A_{\overline{K}}$ (the base change of $A$ to an algebraic closure of $K$) are defined.

#    Component groups are named according to their isomorphism type.  This does not determine them uniquely; one can obtain a more explicit description by examining the list of generators.  Common notations used in component group names include:

#    * $C_n$, the cyclic group of order $n$;
#    * $D_n$, the dihedral group of order $2n$;
#    * $A_n$, the alternating group on $n$ letters;
#    * $S_n$, the symmetric group on $n$ letters.


#$\mathrm{Pr}[t\!=\!0]$ (trace_zero_density) --
#    The **trace zero density** of a Sato-Tate group is the probability that a randomly sampled element (chosen according to the Haar measure) has trace zero.

#    On each component of a Sato-Tate group, the trace is either constant and equal to zero, or varies continuously taking each particular value with probability zero; so this probability is simply the ratio of the number of components on which the trace is identically zero to the total number of components.



#$\mathrm{E}[a_1^2]$ (second_trace_moment) --
#    The **second trace moment** of a Sato-Tate group $G$ is the expected value of the square of the trace of a random element of $G$ (under its Haar measure).

#    When $G$ is the Sato-Tate group of an abelian variety, this is equal to the dimension of its endomorphism algebra \cite{arxiv:1910.00518,mr:4038255}.


#$\mathrm{E}[a_1^4]$ (fourth_trace_moment) --
#    The **fourth trace moment** of a Sato-Tate group $G$ is the expected value of the fourth power of the trace of a random element of $G$ (under the Haar measure).

#    By a result known as "Larsen's alternative" \cite{mr:2058618}, if the fourth trace moment is less than or equal to 5 then $G$ is irreducible, and for $G$ of odd weight, the fourth trace moment is 3 when $G=\mathrm{USp}(2g)$ and greater than 3 otherwise.


#$\mathrm{E}[a_2]$ (first_a2_moment) --
#    The **first $a_2$ moment** of a Sato-Tate group $G$ is the expected value of the quadratic coefficient of the characteristic polynomial of a random element of $G$ (under its Haar measure).

#    When $G$ is the Sato-Tate group of an abelian variety, the first $a_2$ moment is equal to the rank of its Néron–Severi group \cite{arxiv:1910.00518,mr:4038255}.