LMFDB - Galois group: 44T42

Show commands: Magma

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

Group action invariants

Degree $n$:	$44$	magma: t, n := TransitiveGroupIdentification(G); n;
Transitive number $t$:	$42$	magma: t, n := TransitiveGroupIdentification(G); t;
Group:	$C_{11}^2:C_8$
Parity:	$1$	magma: IsEven(G);
Primitive:	no	magma: IsPrimitive(G);
magma: NilpotencyClass(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

|G/N| Galois groups for stem field(s)
$2$: $C_2$
$4$: $C_4$
$8$: $C_8$

Resolvents shown for degrees $\leq 47$

\|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	Representative
	$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$1$	$1$	$()$
	$ 11, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$8$	$11$	$(12,20,17,14,22,19,16,13,21,18,15)(23,30,26,33,29,25,32,28,24,31,27) (34,38,42,35,39,43,36,40,44,37,41)$
	$ 11, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$8$	$11$	$(12,17,22,16,21,15,20,14,19,13,18)(23,26,29,32,24,27,30,33,25,28,31) (34,42,39,36,44,41,38,35,43,40,37)$
	$ 11, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$8$	$11$	$(12,22,21,20,19,18,17,16,15,14,13)(23,29,24,30,25,31,26,32,27,33,28) (34,39,44,38,43,37,42,36,41,35,40)$
	$ 11, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$8$	$11$	$(12,21,19,17,15,13,22,20,18,16,14)(23,24,25,26,27,28,29,30,31,32,33) (34,44,43,42,41,40,39,38,37,36,35)$
	$ 11, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$8$	$11$	$(12,19,15,22,18,14,21,17,13,20,16)(23,25,27,29,31,33,24,26,28,30,32) (34,43,41,39,37,35,44,42,40,38,36)$
	$ 11, 11, 11, 11 $	$8$	$11$	$( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,20,17,14,22,19,16,13,21,18,15) (23,25,27,29,31,33,24,26,28,30,32)(34,37,40,43,35,38,41,44,36,39,42)$
	$ 11, 11, 11, 11 $	$8$	$11$	$( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,17,22,16,21,15,20,14,19,13,18) (23,32,30,28,26,24,33,31,29,27,25)(34,41,37,44,40,36,43,39,35,42,38)$
	$ 11, 11, 11, 11 $	$8$	$11$	$( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,21,19,17,15,13,22,20,18,16,14) (23,30,26,33,29,25,32,28,24,31,27)(34,43,41,39,37,35,44,42,40,38,36)$
	$ 11, 11, 11, 11 $	$8$	$11$	$( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,19,15,22,18,14,21,17,13,20,16) (23,31,28,25,33,30,27,24,32,29,26)(34,42,39,36,44,41,38,35,43,40,37)$
	$ 11, 11, 11, 11 $	$8$	$11$	$( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,18,13,19,14,20,15,21,16,22,17) (23,26,29,32,24,27,30,33,25,28,31)(34,36,38,40,42,44,35,37,39,41,43)$
	$ 11, 11, 11, 11 $	$8$	$11$	$( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,16,20,13,17,21,14,18,22,15,19) (23,27,31,24,28,32,25,29,33,26,30)(34,35,36,37,38,39,40,41,42,43,44)$
	$ 11, 11, 11, 11 $	$8$	$11$	$( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,17,22,16,21,15,20,14,19,13,18) (23,27,31,24,28,32,25,29,33,26,30)(34,40,35,41,36,42,37,43,38,44,39)$
	$ 11, 11, 11, 11 $	$8$	$11$	$( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,22,21,20,19,18,17,16,15,14,13) (23,30,26,33,29,25,32,28,24,31,27)(34,37,40,43,35,38,41,44,36,39,42)$
	$ 11, 11, 11, 11 $	$8$	$11$	$( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,22,21,20,19,18,17,16,15,14,13) (23,31,28,25,33,30,27,24,32,29,26)(34,35,36,37,38,39,40,41,42,43,44)$
	$ 11, 11, 11, 11 $	$8$	$11$	$( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,21,19,17,15,13,22,20,18,16,14) (23,26,29,32,24,27,30,33,25,28,31)(34,40,35,41,36,42,37,43,38,44,39)$
	$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $	$121$	$2$	$( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)(23,27) (24,26)(28,33)(29,32)(30,31)(34,43)(35,42)(36,41)(37,40)(38,39)$
	$ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2 $	$121$	$4$	$( 1,29, 9,25)( 2,23, 8,31)( 3,28, 7,26)( 4,33, 6,32)( 5,27)(10,30,11,24) (12,40,18,37)(13,34,17,43)(14,39,16,38)(15,44)(19,42,22,35)(20,36,21,41)$
	$ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2 $	$121$	$4$	$( 1,32, 9,25)( 2,27, 8,30)( 3,33, 7,24)( 4,28, 6,29)( 5,23)(10,31,11,26) (12,37)(13,43,22,42)(14,38,21,36)(15,44,20,41)(16,39,19,35)(17,34,18,40)$
	$ 8, 8, 8, 8, 8, 4 $	$121$	$8$	$( 1,14,29,39, 9,16,25,38)( 2,17,23,43, 8,13,31,34)( 3,20,28,36, 7,21,26,41) ( 4,12,33,40, 6,18,32,37)( 5,15,27,44)(10,19,30,42,11,22,24,35)$
	$ 8, 8, 8, 8, 8, 4 $	$121$	$8$	$( 1,21,24,42, 2,18,29,38)( 3,15,23,34,11,13,30,35)( 4,12,28,41,10,16,25,39) ( 5,20,33,37, 9,19,31,43)( 6,17,27,44, 8,22,26,36)( 7,14,32,40)$
	$ 8, 8, 8, 8, 8, 4 $	$121$	$8$	$( 1,39,25,14, 9,38,29,16)( 2,43,31,17, 8,34,23,13)( 3,36,26,20, 7,41,28,21) ( 4,40,32,12, 6,37,33,18)( 5,44,27,15)(10,42,24,19,11,35,30,22)$
	$ 8, 8, 8, 8, 8, 4 $	$121$	$8$	$( 1,38,32,12, 7,36,24,16)( 2,34,27,20, 6,40,29,19)( 3,41,33,17, 5,44,23,22) ( 4,37,28,14)( 8,43,30,13,11,42,26,15)( 9,39,25,21,10,35,31,18)$

magma: ConjugacyClasses(G);

Group invariants

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
Label:	968.35	magma: IdentifyGroup(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	4A1	4A-1	4A-1	11B3	11A3	11C2	11C1	11C4	11A2	11B5	11C3	11B2	11A5	11B1	11C5	11A1	11B4	11A4
	11 P	1A	2A	4A1	4A-1	8A1	8A-3	8A-1	8A3	11B2	11A2	11C5	11C3	11C1	11A5	11B4	11C2	11B5	11A4	11B3	11C4	11A3	11B1	11A1
	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	$1$	$- 1$	$- ζ_{8}^{2}$	$ζ_{8}^{2}$	$ζ_{8}^{3}$	$- ζ_{8}$	$ζ_{8}$	$- ζ_{8}^{3}$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
968.35.1d2	C	$1$	$- 1$	$ζ_{8}^{2}$	$- ζ_{8}^{2}$	$- ζ_{8}$	$ζ_{8}^{3}$	$- ζ_{8}^{3}$	$ζ_{8}$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
968.35.1d3	C	$1$	$- 1$	$- ζ_{8}^{2}$	$ζ_{8}^{2}$	$- ζ_{8}^{3}$	$ζ_{8}$	$- ζ_{8}$	$ζ_{8}^{3}$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
968.35.1d4	C	$1$	$- 1$	$ζ_{8}^{2}$	$- ζ_{8}^{2}$	$ζ_{8}$	$- ζ_{8}^{3}$	$ζ_{8}^{3}$	$- ζ_{8}$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
968.35.8a1	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$
968.35.8a2	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$
968.35.8a3	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$
968.35.8a4	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$
968.35.8a5	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$
968.35.8b1	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$
968.35.8b2	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$
968.35.8b3	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$
968.35.8b4	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$
968.35.8b5	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$
968.35.8c1	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$
968.35.8c2	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$
968.35.8c3	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$
968.35.8c4	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$
968.35.8c5	R	$8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{11}^{- 3} + 2 ζ_{11}^{- 1} + 2 + 2 ζ_{11} + ζ_{11}^{3}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 2} + 2 + 2 ζ_{11}^{2} + ζ_{11}^{5}$	$2 ζ_{11}^{- 3} + ζ_{11}^{- 2} + 2 + ζ_{11}^{2} + 2 ζ_{11}^{3}$	$2 ζ_{11}^{- 4} + ζ_{11}^{- 1} + 2 + ζ_{11} + 2 ζ_{11}^{4}$	$2 ζ_{11}^{- 5} + ζ_{11}^{- 4} + 2 + ζ_{11}^{4} + 2 ζ_{11}^{5}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 5} + 2 ζ_{11}^{- 4} + ζ_{11}^{- 3} + ζ_{11}^{3} + 2 ζ_{11}^{4} + ζ_{11}^{5}$	$- ζ_{11}^{- 4} + ζ_{11}^{- 3} - ζ_{11}^{- 2} - 1 - ζ_{11}^{2} + ζ_{11}^{3} - ζ_{11}^{4}$	$- 2 ζ_{11}^{- 5} - ζ_{11}^{- 4} - 2 ζ_{11}^{- 3} - ζ_{11}^{- 2} - 2 - ζ_{11}^{2} - 2 ζ_{11}^{3} - ζ_{11}^{4} - 2 ζ_{11}^{5}$	$ζ_{11}^{- 5} - ζ_{11}^{- 4} - ζ_{11}^{- 3} - 1 - ζ_{11}^{3} - ζ_{11}^{4} + ζ_{11}^{5}$	$ζ_{11}^{- 4} + ζ_{11}^{- 3} + 2 ζ_{11}^{- 2} + 2 ζ_{11}^{2} + ζ_{11}^{3} + ζ_{11}^{4}$

magma: CharacterTable(G);

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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:	$C_{11}^2:C_8$