LMFDB - Galois group: 44T42

Show commands: Magma

magma:G := TransitiveGroup(44, 42);

Group invariants

Abstract group:	$C_{11}^2:C_8$	magma:IdentifyGroup(G);
Order:	$968=2^{3} \cdot 11^{2}$	magma:Order(G);
Cyclic:	no	magma:IsCyclic(G);
Abelian:	no	magma:IsAbelian(G);
Solvable:	yes	magma:IsSolvable(G);
Nilpotency class:	not nilpotent	magma:NilpotencyClass(G);

Group action invariants

Degree $n$:	$44$	magma:t, n := TransitiveGroupIdentification(G); n;
Transitive number $t$:	$42$	magma:t, n := TransitiveGroupIdentification(G); t;
Parity:	$1$	magma:IsEven(G);
Primitive:	no	magma:IsPrimitive(G);
$\card{\Aut(F/K)}$:	$1$	magma:Order(Centralizer(SymmetricGroup(n), G));
Generators:	$(1,7)(2,6)(3,5)(8,11)(9,10)(12,16)(13,15)(17,22)(18,21)(19,20)(23,33)(24,32)(25,31)(26,30)(27,29)(34,40)(35,39)(36,38)(41,44)(42,43)$, $(1,14,29,39,9,16,25,38)(2,17,23,43,8,13,31,34)(3,20,28,36,7,21,26,41)(4,12,33,40,6,18,32,37)(5,15,27,44)(10,19,30,42,11,22,24,35)$	magma:Generators(G);

Low degree resolvents

$\card{(G/N)}$ Galois groups for stem field(s)
$2$: $C_2$
$4$: $C_4$
$8$: $C_8$

Resolvents shown for degrees $\leq 47$

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$
$4$:	$C_4$
$8$:	$C_8$

Subfields

Degree 2: $C_2$
Degree 4: $C_4$
Degree 11: None
Degree 22: None

Low degree siblings

44T42 x 2
Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

Label	Cycle Type	Size	Order	Index	Representative
1A	$1^{44}$	$1$	$1$	$0$	$()$
2A	$2^{20},1^{4}$	$121$	$2$	$20$	$( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)(13,22)(14,21)(15,20)(16,19)(17,18)(23,31)(24,30)(25,29)(26,28)(32,33)(34,35)(36,44)(37,43)(38,42)(39,41)$
4A1	$4^{10},2^{2}$	$121$	$4$	$32$	$( 1,25, 4,29)( 2,30, 3,24)( 5,23,11,31)( 6,28,10,26)( 7,33, 9,32)( 8,27)(12,40)(13,34,22,35)(14,39,21,41)(15,44,20,36)(16,38,19,42)(17,43,18,37)$
4A-1	$4^{10},2^{2}$	$121$	$4$	$32$	$( 1,29, 4,25)( 2,24, 3,30)( 5,31,11,23)( 6,26,10,28)( 7,32, 9,33)( 8,27)(12,40)(13,35,22,34)(14,41,21,39)(15,36,20,44)(16,42,19,38)(17,37,18,43)$
8A1	$8^{5},4$	$121$	$8$	$38$	$( 1,13,25,34, 4,22,29,35)( 2,16,30,38, 3,19,24,42)( 5,14,23,39,11,21,31,41)( 6,17,28,43,10,18,26,37)( 7,20,33,36, 9,15,32,44)( 8,12,27,40)$
8A-1	$8^{5},4$	$121$	$8$	$38$	$( 1,35,29,22, 4,34,25,13)( 2,42,24,19, 3,38,30,16)( 5,41,31,21,11,39,23,14)( 6,37,26,18,10,43,28,17)( 7,44,32,15, 9,36,33,20)( 8,40,27,12)$
8A3	$8^{5},4$	$121$	$8$	$38$	$( 1,34,29,13, 4,35,25,22)( 2,38,24,16, 3,42,30,19)( 5,39,31,14,11,41,23,21)( 6,43,26,17,10,37,28,18)( 7,36,32,20, 9,44,33,15)( 8,40,27,12)$
8A-3	$8^{5},4$	$121$	$8$	$38$	$( 1,22,25,35, 4,13,29,34)( 2,19,30,42, 3,16,24,38)( 5,21,23,41,11,14,31,39)( 6,18,28,37,10,17,26,43)( 7,15,33,44, 9,20,32,36)( 8,12,27,40)$
11A1	$11^{4}$	$8$	$11$	$40$	$( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,14,16,18,20,22,13,15,17,19,21)(23,32,30,28,26,24,33,31,29,27,25)(34,37,40,43,35,38,41,44,36,39,42)$
11A2	$11^{4}$	$8$	$11$	$40$	$( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,16,20,13,17,21,14,18,22,15,19)(23,30,26,33,29,25,32,28,24,31,27)(34,40,35,41,36,42,37,43,38,44,39)$
11A3	$11^{4}$	$8$	$11$	$40$	$( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,18,13,19,14,20,15,21,16,22,17)(23,28,33,27,32,26,31,25,30,24,29)(34,43,41,39,37,35,44,42,40,38,36)$
11A4	$11^{4}$	$8$	$11$	$40$	$( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,20,17,14,22,19,16,13,21,18,15)(23,26,29,32,24,27,30,33,25,28,31)(34,35,36,37,38,39,40,41,42,43,44)$
11A5	$11^{4}$	$8$	$11$	$40$	$( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,22,21,20,19,18,17,16,15,14,13)(23,24,25,26,27,28,29,30,31,32,33)(34,38,42,35,39,43,36,40,44,37,41)$
11B1	$11^{3},1^{11}$	$8$	$11$	$30$	$( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,19,15,22,18,14,21,17,13,20,16)(23,24,25,26,27,28,29,30,31,32,33)$
11B2	$11^{3},1^{11}$	$8$	$11$	$30$	$( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,15,18,21,13,16,19,22,14,17,20)(23,25,27,29,31,33,24,26,28,30,32)$
11B3	$11^{3},1^{11}$	$8$	$11$	$30$	$( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,22,21,20,19,18,17,16,15,14,13)(23,26,29,32,24,27,30,33,25,28,31)$
11B4	$11^{3},1^{11}$	$8$	$11$	$30$	$( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,18,13,19,14,20,15,21,16,22,17)(23,27,31,24,28,32,25,29,33,26,30)$
11B5	$11^{3},1^{11}$	$8$	$11$	$30$	$( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,14,16,18,20,22,13,15,17,19,21)(23,28,33,27,32,26,31,25,30,24,29)$
11C1	$11^{4}$	$8$	$11$	$40$	$( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,21,19,17,15,13,22,20,18,16,14)(23,33,32,31,30,29,28,27,26,25,24)(34,37,40,43,35,38,41,44,36,39,42)$
11C2	$11^{4}$	$8$	$11$	$40$	$( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,19,15,22,18,14,21,17,13,20,16)(23,32,30,28,26,24,33,31,29,27,25)(34,40,35,41,36,42,37,43,38,44,39)$
11C3	$11^{4}$	$8$	$11$	$40$	$( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,17,22,16,21,15,20,14,19,13,18)(23,31,28,25,33,30,27,24,32,29,26)(34,43,41,39,37,35,44,42,40,38,36)$
11C4	$11^{4}$	$8$	$11$	$40$	$( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,21,19,17,15,13,22,20,18,16,14)(23,30,26,33,29,25,32,28,24,31,27)(34,43,41,39,37,35,44,42,40,38,36)$
11C5	$11^{4}$	$8$	$11$	$40$	$( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,15,18,21,13,16,19,22,14,17,20)(23,33,32,31,30,29,28,27,26,25,24)(34,40,35,41,36,42,37,43,38,44,39)$

Malle's constant $a(G)$: $1/20$

magma:ConjugacyClasses(G);

Character table

		1A	2A	4A1	4A-1	8A1	8A-1	8A3	8A-3	11A1	11A2	11A3	11A4	11A5	11B1	11B2	11B3	11B4	11B5	11C1	11C2	11C3	11C4	11C5
	Size	1	121	121	121	121	121	121	121	8	8	8	8	8	8	8	8	8	8	8	8	8	8	8
	2 P	1A	1A	2A	2A	4A1	4A-1	4A-1	4A1	11A2	11A4	11A5	11A3	11A1	11B2	11B4	11B5	11B3	11B1	11C2	11C4	11C5	11C3	11C1
	11 P	1A	2A	4A1	4A-1	8A-3	8A3	8A-1	8A1	11A5	11A1	11A4	11A2	11A3	11B5	11B1	11B4	11B2	11B3	11C5	11C1	11C4	11C2	11C3
	Type
968.35.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
968.35.1b	R	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
968.35.1c1	C	$1$	$1$	$- 1$	$- 1$	$- i$	$- i$	$i$	$i$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
968.35.1c2	C	$1$	$1$	$- 1$	$- 1$	$i$	$i$	$- i$	$- i$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
968.35.1d1	C	$1$	$- 1$	$- ζ_{8}^{2}$	$ζ_{8}^{2}$	$ζ_{8}^{3}$	$- ζ_{8}^{3}$	$- ζ_{8}$	$ζ_{8}$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
968.35.1d2	C	$1$	$- 1$	$ζ_{8}^{2}$	$- ζ_{8}^{2}$	$- ζ_{8}$	$ζ_{8}$	$ζ_{8}^{3}$	$- ζ_{8}^{3}$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
968.35.1d3	C	$1$	$- 1$	$- ζ_{8}^{2}$	$ζ_{8}^{2}$	$- ζ_{8}^{3}$	$ζ_{8}^{3}$	$ζ_{8}$	$- ζ_{8}$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
968.35.1d4	C	$1$	$- 1$	$ζ_{8}^{2}$	$- ζ_{8}^{2}$	$ζ_{8}$	$- ζ_{8}$	$- ζ_{8}^{3}$	$ζ_{8}^{3}$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
968.35.8a1	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$
968.35.8a2	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$
968.35.8a3	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$
968.35.8a4	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$
968.35.8a5	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$
968.35.8b1	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$
968.35.8b2	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$
968.35.8b3	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$
968.35.8b4	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$
968.35.8b5	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$
968.35.8c1	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$
968.35.8c2	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$
968.35.8c3	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$
968.35.8c4	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$
968.35.8c5	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$

magma:CharacterTable(G);

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	44T42

Degree	$44$
Order	$968$
Cyclic	no
Abelian	no
Solvable	yes
Primitive	no
$p$-group	no
Group:	$C_{11}^2:C_8$