LMFDB - Galois group: 39T42

Show commands: Magma

magma:G := TransitiveGroup(39, 42);

Group invariants

Abstract group:	$C_{13}^2:(C_4\times S_3)$	magma:IdentifyGroup(G);
Order:	$4056=2^{3} \cdot 3 \cdot 13^{2}$	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 $n$:	$39$	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:	$(1,31,21,4,29,22,2,39,17,12,28,16)(3,34,26,7,27,23,13,36,25,9,30,15)(5,37,18,10,38,24,11,33,20,6,32,14)(8,35,19)$, $(1,5,9,13,4,8,12,3,7,11,2,6,10)(14,35,24,39,21,30,18,34,15,38,25,29,22,33,19,37,16,28,26,32,23,36,20,27,17,31)$	magma:Generators(G);

Low degree resolvents

$\card{(G/N)}$ Galois groups for stem field(s)
$2$: $C_2$ x 3
$4$: $C_4$ x 2, $C_2^2$
$6$: $S_3$
$8$: $C_4\times C_2$
$12$: $D_{6}$
$24$: $S_3 \times C_4$

Resolvents shown for degrees $\leq 47$

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 3
$4$:	$C_4$ x 2, $C_2^2$
$6$:	$S_3$
$8$:	$C_4\times C_2$
$12$:	$D_{6}$
$24$:	$S_3 \times C_4$

Subfields

Degree 3: $S_3$
Degree 13: None

Low degree siblings

26T30, 39T42
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	$1^{39}$	$1$	$1$	$0$	$()$
2A	$2^{19},1$	$39$	$2$	$19$	$( 1,11)( 2,10)( 3, 9)( 4, 8)( 5, 7)(12,13)(14,35)(15,32)(16,29)(17,39)(18,36)(19,33)(20,30)(21,27)(22,37)(23,34)(24,31)(25,28)(26,38)$
2B	$2^{13},1^{13}$	$39$	$2$	$13$	$(14,33)(15,36)(16,39)(17,29)(18,32)(19,35)(20,38)(21,28)(22,31)(23,34)(24,37)(25,27)(26,30)$
2C	$2^{18},1^{3}$	$169$	$2$	$18$	$( 1, 3)( 4,13)( 5,12)( 6,11)( 7,10)( 8, 9)(14,16)(17,26)(18,25)(19,24)(20,23)(21,22)(27,29)(30,39)(31,38)(32,37)(33,36)(34,35)$
3A	$3^{13}$	$338$	$3$	$26$	$( 1,24,29)( 2,15,28)( 3,19,27)( 4,23,39)( 5,14,38)( 6,18,37)( 7,22,36)( 8,26,35)( 9,17,34)(10,21,33)(11,25,32)(12,16,31)(13,20,30)$
4A1	$4^{9},1^{3}$	$169$	$4$	$27$	$( 1,10, 3, 7)( 4,12,13, 5)( 6, 9,11, 8)(14,23,16,20)(17,25,26,18)(19,22,24,21)(27,36,29,33)(30,38,39,31)(32,35,37,34)$
4A-1	$4^{9},1^{3}$	$169$	$4$	$27$	$( 1, 7, 3,10)( 4, 5,13,12)( 6, 8,11, 9)(14,20,16,23)(17,18,26,25)(19,21,24,22)(27,33,29,36)(30,31,39,38)(32,34,37,35)$
4B1	$4^{9},2,1$	$507$	$4$	$28$	$( 1,23, 9,19)( 2,16, 8,26)( 3,22, 7,20)( 4,15, 6,14)( 5,21)(10,25,13,17)(11,18,12,24)(27,34,38,31)(28,29,37,36)(30,32,35,33)$
4B-1	$4^{9},2,1$	$507$	$4$	$28$	$( 1,19, 9,23)( 2,26, 8,16)( 3,20, 7,22)( 4,14, 6,15)( 5,21)(10,17,13,25)(11,24,12,18)(27,31,38,34)(28,36,37,29)(30,33,35,32)$
6A	$6^{6},3$	$338$	$6$	$32$	$( 1,27,24, 3,29,19)( 2,28,15)( 4,30,23,13,39,20)( 5,31,14,12,38,16)( 6,32,18,11,37,25)( 7,33,22,10,36,21)( 8,34,26, 9,35,17)$
12A1	$12^{3},3$	$338$	$12$	$35$	$( 1,22,27,10,24,36, 3,21,29, 7,19,33)( 2,15,28)( 4,14,30,12,23,38,13,16,39, 5,20,31)( 6,26,32, 9,18,35,11,17,37, 8,25,34)$
12A-1	$12^{3},3$	$338$	$12$	$35$	$( 1,33,19, 7,29,21, 3,36,24,10,27,22)( 2,28,15)( 4,31,20, 5,39,16,13,38,23,12,30,14)( 6,34,25, 8,37,17,11,35,18, 9,32,26)$
13A1	$13^{2},1^{13}$	$12$	$13$	$24$	$(14,20,26,19,25,18,24,17,23,16,22,15,21)(27,35,30,38,33,28,36,31,39,34,29,37,32)$
13A2	$13^{2},1^{13}$	$12$	$13$	$24$	$(14,26,25,24,23,22,21,20,19,18,17,16,15)(27,30,33,36,39,29,32,35,38,28,31,34,37)$
13A4	$13^{2},1^{13}$	$12$	$13$	$24$	$(14,25,23,21,19,17,15,26,24,22,20,18,16)(27,33,39,32,38,31,37,30,36,29,35,28,34)$
13B1	$13^{3}$	$12$	$13$	$36$	$( 1, 4, 7,10,13, 3, 6, 9,12, 2, 5, 8,11)(14,21,15,22,16,23,17,24,18,25,19,26,20)(27,35,30,38,33,28,36,31,39,34,29,37,32)$
13B2	$13^{3}$	$12$	$13$	$36$	$( 1, 7,13, 6,12, 5,11, 4,10, 3, 9, 2, 8)(14,15,16,17,18,19,20,21,22,23,24,25,26)(27,30,33,36,39,29,32,35,38,28,31,34,37)$
13B4	$13^{3}$	$12$	$13$	$36$	$( 1,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(14,16,18,20,22,24,26,15,17,19,21,23,25)(27,33,39,32,38,31,37,30,36,29,35,28,34)$
13C	$13^{3}$	$24$	$13$	$36$	$( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13)(14,26,25,24,23,22,21,20,19,18,17,16,15)(27,31,35,39,30,34,38,29,33,37,28,32,36)$
13D1	$13^{3}$	$24$	$13$	$36$	$( 1, 7,13, 6,12, 5,11, 4,10, 3, 9, 2, 8)(14,19,24,16,21,26,18,23,15,20,25,17,22)(27,31,35,39,30,34,38,29,33,37,28,32,36)$
13D2	$13^{3}$	$24$	$13$	$36$	$( 1, 8, 2, 9, 3,10, 4,11, 5,12, 6,13, 7)(14,18,22,26,17,21,25,16,20,24,15,19,23)(27,35,30,38,33,28,36,31,39,34,29,37,32)$
13D4	$13^{3}$	$24$	$13$	$36$	$( 1, 9, 4,12, 7, 2,10, 5,13, 8, 3,11, 6)(14,22,17,25,20,15,23,18,26,21,16,24,19)(27,37,34,31,28,38,35,32,29,39,36,33,30)$
26A1	$26,2^{6},1$	$156$	$26$	$31$	$( 1,11)( 2,10)( 3, 9)( 4, 8)( 5, 7)(12,13)(14,39,20,34,26,29,19,37,25,32,18,27,24,35,17,30,23,38,16,33,22,28,15,36,21,31)$
26A3	$26,2^{6},1$	$156$	$26$	$31$	$( 1,11)( 2,10)( 3, 9)( 4, 8)( 5, 7)(12,13)(14,34,19,32,24,30,16,28,21,39,26,37,18,35,23,33,15,31,20,29,25,27,17,38,22,36)$
26A7	$26,2^{6},1$	$156$	$26$	$31$	$( 1,11)( 2,10)( 3, 9)( 4, 8)( 5, 7)(12,13)(14,37,17,28,20,32,23,36,26,27,16,31,19,35,22,39,25,30,15,34,18,38,21,29,24,33)$
26B1	$26,13$	$156$	$26$	$37$	$( 1, 9, 4,12, 7, 2,10, 5,13, 8, 3,11, 6)(14,37,21,32,15,27,22,35,16,30,23,38,17,33,24,28,18,36,25,31,19,39,26,34,20,29)$
26B3	$26,13$	$156$	$26$	$37$	$( 1,12,10, 8, 6, 4, 2,13,11, 9, 7, 5, 3)(14,32,22,30,17,28,25,39,20,37,15,35,23,33,18,31,26,29,21,27,16,38,24,36,19,34)$
26B7	$26,13$	$156$	$26$	$37$	$( 1, 5, 9,13, 4, 8,12, 3, 7,11, 2, 6,10)(14,35,24,39,21,30,18,34,15,38,25,29,22,33,19,37,16,28,26,32,23,36,20,27,17,31)$

Malle's constant $a(G)$: $1/13$

magma:ConjugacyClasses(G);

Character table

		1A	2A	2B	2C	3A	4A1	4A-1	4B1	4B-1	6A	12A1	12A-1	13A1	13A2	13A4	13B1	13B2	13B4	13C	13D1	13D2	13D4	26A1	26A3	26A7	26B1	26B3	26B7
	Size	1	39	39	169	338	169	169	507	507	338	338	338	12	12	12	12	12	12	24	24	24	24	156	156	156	156	156	156
	2 P	1A	1A	1A	1A	3A	2C	2C	2C	2C	3A	6A	6A	13A2	13A4	13A1	13B2	13B4	13B1	13C	13D2	13D4	13D1	13A1	13A2	13A4	13B1	13B2	13B4
	3 P	1A	2A	2B	2C	1A	4A-1	4A1	4B-1	4B1	2C	4A1	4A-1	13A2	13A4	13A1	13B2	13B4	13B1	13C	13D2	13D4	13D1	26A3	26A7	26A1	26B3	26B7	26B1
	13 P	1A	2A	2B	2C	3A	4A1	4A-1	4B1	4B-1	6A	12A1	12A-1	1A	1A	1A	1A	1A	1A	1A	1A	1A	1A	2A	2A	2A	2B	2B	2B
	Type
4056.bb.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
4056.bb.1b	R	$1$	$- 1$	$- 1$	$1$	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$
4056.bb.1c	R	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$
4056.bb.1d	R	$1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
4056.bb.1e1	C	$1$	$- 1$	$1$	$- 1$	$1$	$- i$	$i$	$i$	$- i$	$- 1$	$i$	$- i$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$1$	$- 1$	$1$	$- 1$	$1$
4056.bb.1e2	C	$1$	$- 1$	$1$	$- 1$	$1$	$i$	$- i$	$- i$	$i$	$- 1$	$- i$	$i$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$1$	$- 1$	$1$	$- 1$	$1$
4056.bb.1f1	C	$1$	$1$	$- 1$	$- 1$	$1$	$- i$	$i$	$- i$	$i$	$- 1$	$i$	$- i$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$1$	$- 1$	$1$	$- 1$
4056.bb.1f2	C	$1$	$1$	$- 1$	$- 1$	$1$	$i$	$- i$	$i$	$- i$	$- 1$	$- i$	$i$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$1$	$- 1$	$1$	$- 1$
4056.bb.2a	R	$2$	$0$	$0$	$2$	$- 1$	$2$	$2$	$0$	$0$	$- 1$	$- 1$	$- 1$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$0$	$0$	$0$
4056.bb.2b	R	$2$	$0$	$0$	$2$	$- 1$	$- 2$	$- 2$	$0$	$0$	$- 1$	$1$	$1$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$0$	$0$	$0$
4056.bb.2c1	C	$2$	$0$	$0$	$- 2$	$- 1$	$- 2 i$	$2 i$	$0$	$0$	$1$	$- i$	$i$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$0$	$0$	$0$
4056.bb.2c2	C	$2$	$0$	$0$	$- 2$	$- 1$	$2 i$	$- 2 i$	$0$	$0$	$1$	$i$	$- i$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$0$	$0$	$0$	$0$	$0$	$0$
4056.bb.12a1	R	$12$	$0$	$4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + 4 + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 4 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 2 - ζ_{13}^{2} - ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$2 ζ_{13}^{- 5} + 2 ζ_{13}^{- 1} + 4 + 2 ζ_{13} + 2 ζ_{13}^{5}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 1 - ζ_{13}^{2} - ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$- 1$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3} + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - 2 ζ_{13}^{- 3} - 2 ζ_{13}^{- 2} - 2 - 2 ζ_{13}^{2} - 2 ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} - 1 + ζ_{13}^{2} + ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$0$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + ζ_{13}^{4} + ζ_{13}^{6}$	$0$	$ζ_{13}^{- 5} + ζ_{13}^{- 1} + ζ_{13} + ζ_{13}^{5}$	$0$	$ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3}$
4056.bb.12a2	R	$12$	$0$	$4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2 ζ_{13}^{- 5} + 2 ζ_{13}^{- 1} + 4 + 2 ζ_{13} + 2 ζ_{13}^{5}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + 4 + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 4 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 1 - ζ_{13}^{2} - ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 2 - ζ_{13}^{2} - ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$- 1$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - 2 ζ_{13}^{- 3} - 2 ζ_{13}^{- 2} - 2 - 2 ζ_{13}^{2} - 2 ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} - 1 + ζ_{13}^{2} + ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3} + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$0$	$ζ_{13}^{- 5} + ζ_{13}^{- 1} + ζ_{13} + ζ_{13}^{5}$	$0$	$ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3}$	$0$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + ζ_{13}^{4} + ζ_{13}^{6}$
4056.bb.12a3	R	$12$	$0$	$4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 4 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3}$	$2 ζ_{13}^{- 5} + 2 ζ_{13}^{- 1} + 4 + 2 ζ_{13} + 2 ζ_{13}^{5}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 1 - ζ_{13}^{2} - ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + 4 + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 2 - ζ_{13}^{2} - ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$- 1$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} - 1 + ζ_{13}^{2} + ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3} + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - 2 ζ_{13}^{- 3} - 2 ζ_{13}^{- 2} - 2 - 2 ζ_{13}^{2} - 2 ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$0$	$ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3}$	$0$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + ζ_{13}^{4} + ζ_{13}^{6}$	$0$	$ζ_{13}^{- 5} + ζ_{13}^{- 1} + ζ_{13} + ζ_{13}^{5}$
4056.bb.12b1	R	$12$	$4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 1 - ζ_{13}^{2} - ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 4 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 2 - ζ_{13}^{2} - ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + 4 + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$2 ζ_{13}^{- 5} + 2 ζ_{13}^{- 1} + 4 + 2 ζ_{13} + 2 ζ_{13}^{5}$	$- 1$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} - 1 + ζ_{13}^{2} + ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3} + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - 2 ζ_{13}^{- 3} - 2 ζ_{13}^{- 2} - 2 - 2 ζ_{13}^{2} - 2 ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + ζ_{13}^{4} + ζ_{13}^{6}$	$0$	$ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3}$	$0$	$ζ_{13}^{- 5} + ζ_{13}^{- 1} + ζ_{13} + ζ_{13}^{5}$	$0$
4056.bb.12b2	R	$12$	$4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 2 - ζ_{13}^{2} - ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$2 ζ_{13}^{- 5} + 2 ζ_{13}^{- 1} + 4 + 2 ζ_{13} + 2 ζ_{13}^{5}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 1 - ζ_{13}^{2} - ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 4 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + 4 + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$- 1$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - 2 ζ_{13}^{- 3} - 2 ζ_{13}^{- 2} - 2 - 2 ζ_{13}^{2} - 2 ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} - 1 + ζ_{13}^{2} + ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3} + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3}$	$0$	$ζ_{13}^{- 5} + ζ_{13}^{- 1} + ζ_{13} + ζ_{13}^{5}$	$0$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + ζ_{13}^{4} + ζ_{13}^{6}$	$0$
4056.bb.12b3	R	$12$	$4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 2 - ζ_{13}^{2} - ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 1 - ζ_{13}^{2} - ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + 4 + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$2 ζ_{13}^{- 5} + 2 ζ_{13}^{- 1} + 4 + 2 ζ_{13} + 2 ζ_{13}^{5}$	$2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 4 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3}$	$- 1$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3} + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - 2 ζ_{13}^{- 3} - 2 ζ_{13}^{- 2} - 2 - 2 ζ_{13}^{2} - 2 ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} - 1 + ζ_{13}^{2} + ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$ζ_{13}^{- 5} + ζ_{13}^{- 1} + ζ_{13} + ζ_{13}^{5}$	$0$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + ζ_{13}^{4} + ζ_{13}^{6}$	$0$	$ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3}$	$0$
4056.bb.12c1	R	$12$	$- 4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 1 - ζ_{13}^{2} - ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 4 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 2 - ζ_{13}^{2} - ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + 4 + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$2 ζ_{13}^{- 5} + 2 ζ_{13}^{- 1} + 4 + 2 ζ_{13} + 2 ζ_{13}^{5}$	$- 1$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} - 1 + ζ_{13}^{2} + ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3} + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - 2 ζ_{13}^{- 3} - 2 ζ_{13}^{- 2} - 2 - 2 ζ_{13}^{2} - 2 ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - ζ_{13}^{4} - ζ_{13}^{6}$	$0$	$- ζ_{13}^{- 3} - ζ_{13}^{- 2} - ζ_{13}^{2} - ζ_{13}^{3}$	$0$	$- ζ_{13}^{- 5} - ζ_{13}^{- 1} - ζ_{13} - ζ_{13}^{5}$	$0$
4056.bb.12c2	R	$12$	$- 4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 2 - ζ_{13}^{2} - ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$2 ζ_{13}^{- 5} + 2 ζ_{13}^{- 1} + 4 + 2 ζ_{13} + 2 ζ_{13}^{5}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 1 - ζ_{13}^{2} - ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 4 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + 4 + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$- 1$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - 2 ζ_{13}^{- 3} - 2 ζ_{13}^{- 2} - 2 - 2 ζ_{13}^{2} - 2 ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} - 1 + ζ_{13}^{2} + ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3} + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$- ζ_{13}^{- 3} - ζ_{13}^{- 2} - ζ_{13}^{2} - ζ_{13}^{3}$	$0$	$- ζ_{13}^{- 5} - ζ_{13}^{- 1} - ζ_{13} - ζ_{13}^{5}$	$0$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - ζ_{13}^{4} - ζ_{13}^{6}$	$0$
4056.bb.12c3	R	$12$	$- 4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 2 - ζ_{13}^{2} - ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 1 - ζ_{13}^{2} - ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + 4 + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$2 ζ_{13}^{- 5} + 2 ζ_{13}^{- 1} + 4 + 2 ζ_{13} + 2 ζ_{13}^{5}$	$2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 4 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3}$	$- 1$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3} + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - 2 ζ_{13}^{- 3} - 2 ζ_{13}^{- 2} - 2 - 2 ζ_{13}^{2} - 2 ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} - 1 + ζ_{13}^{2} + ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$- ζ_{13}^{- 5} - ζ_{13}^{- 1} - ζ_{13} - ζ_{13}^{5}$	$0$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - ζ_{13}^{4} - ζ_{13}^{6}$	$0$	$- ζ_{13}^{- 3} - ζ_{13}^{- 2} - ζ_{13}^{2} - ζ_{13}^{3}$	$0$
4056.bb.12d1	R	$12$	$0$	$- 4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + 4 + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 4 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 2 - ζ_{13}^{2} - ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$2 ζ_{13}^{- 5} + 2 ζ_{13}^{- 1} + 4 + 2 ζ_{13} + 2 ζ_{13}^{5}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 1 - ζ_{13}^{2} - ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$- 1$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3} + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - 2 ζ_{13}^{- 3} - 2 ζ_{13}^{- 2} - 2 - 2 ζ_{13}^{2} - 2 ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} - 1 + ζ_{13}^{2} + ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$0$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - ζ_{13}^{4} - ζ_{13}^{6}$	$0$	$- ζ_{13}^{- 5} - ζ_{13}^{- 1} - ζ_{13} - ζ_{13}^{5}$	$0$	$- ζ_{13}^{- 3} - ζ_{13}^{- 2} - ζ_{13}^{2} - ζ_{13}^{3}$
4056.bb.12d2	R	$12$	$0$	$- 4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2 ζ_{13}^{- 5} + 2 ζ_{13}^{- 1} + 4 + 2 ζ_{13} + 2 ζ_{13}^{5}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + 4 + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 4 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 1 - ζ_{13}^{2} - ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 2 - ζ_{13}^{2} - ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$- 1$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - 2 ζ_{13}^{- 3} - 2 ζ_{13}^{- 2} - 2 - 2 ζ_{13}^{2} - 2 ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} - 1 + ζ_{13}^{2} + ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3} + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$0$	$- ζ_{13}^{- 5} - ζ_{13}^{- 1} - ζ_{13} - ζ_{13}^{5}$	$0$	$- ζ_{13}^{- 3} - ζ_{13}^{- 2} - ζ_{13}^{2} - ζ_{13}^{3}$	$0$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - ζ_{13}^{4} - ζ_{13}^{6}$
4056.bb.12d3	R	$12$	$0$	$- 4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 4 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3}$	$2 ζ_{13}^{- 5} + 2 ζ_{13}^{- 1} + 4 + 2 ζ_{13} + 2 ζ_{13}^{5}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 1 - ζ_{13}^{2} - ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + 4 + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - ζ_{13}^{- 3} - ζ_{13}^{- 2} - 2 - ζ_{13}^{2} - ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$ζ_{13}^{- 6} + ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + ζ_{13}^{4} + ζ_{13}^{6}$	$- 1$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} - 1 + ζ_{13}^{2} + ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$2 ζ_{13}^{- 6} + 2 ζ_{13}^{- 4} + ζ_{13}^{- 3} + ζ_{13}^{- 2} + ζ_{13}^{2} + ζ_{13}^{3} + 2 ζ_{13}^{4} + 2 ζ_{13}^{6}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - 2 ζ_{13}^{- 3} - 2 ζ_{13}^{- 2} - 2 - 2 ζ_{13}^{2} - 2 ζ_{13}^{3} - ζ_{13}^{4} - ζ_{13}^{6}$	$0$	$- ζ_{13}^{- 3} - ζ_{13}^{- 2} - ζ_{13}^{2} - ζ_{13}^{3}$	$0$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} - ζ_{13}^{4} - ζ_{13}^{6}$	$0$	$- ζ_{13}^{- 5} - ζ_{13}^{- 1} - ζ_{13} - ζ_{13}^{5}$
4056.bb.24a	R	$24$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- 2$	$- 2$	$- 2$	$- 2$	$- 2$	$- 2$	$11$	$- 2$	$- 2$	$- 2$	$0$	$0$	$0$	$0$	$0$	$0$
4056.bb.24b1	R	$24$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$4 ζ_{13}^{- 6} + 4 ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + 4 ζ_{13}^{4} + 4 ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} - 2 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$4 ζ_{13}^{- 6} + 4 ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + 4 ζ_{13}^{4} + 4 ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - 4 ζ_{13}^{- 3} - 4 ζ_{13}^{- 2} - 4 - 4 ζ_{13}^{2} - 4 ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - 4 ζ_{13}^{- 3} - 4 ζ_{13}^{- 2} - 4 - 4 ζ_{13}^{2} - 4 ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} - 2 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$- 2$	$- ζ_{13}^{- 3} - ζ_{13}^{- 2} + 2 - ζ_{13}^{2} - ζ_{13}^{3}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + 2 - ζ_{13}^{4} - ζ_{13}^{6}$	$- ζ_{13}^{- 5} - ζ_{13}^{- 1} + 2 - ζ_{13} - ζ_{13}^{5}$	$0$	$0$	$0$	$0$	$0$	$0$
4056.bb.24b2	R	$24$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - 4 ζ_{13}^{- 3} - 4 ζ_{13}^{- 2} - 4 - 4 ζ_{13}^{2} - 4 ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$4 ζ_{13}^{- 6} + 4 ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + 4 ζ_{13}^{4} + 4 ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - 4 ζ_{13}^{- 3} - 4 ζ_{13}^{- 2} - 4 - 4 ζ_{13}^{2} - 4 ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} - 2 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} - 2 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$4 ζ_{13}^{- 6} + 4 ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + 4 ζ_{13}^{4} + 4 ζ_{13}^{6}$	$- 2$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + 2 - ζ_{13}^{4} - ζ_{13}^{6}$	$- ζ_{13}^{- 5} - ζ_{13}^{- 1} + 2 - ζ_{13} - ζ_{13}^{5}$	$- ζ_{13}^{- 3} - ζ_{13}^{- 2} + 2 - ζ_{13}^{2} - ζ_{13}^{3}$	$0$	$0$	$0$	$0$	$0$	$0$
4056.bb.24b3	R	$24$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} - 2 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - 4 ζ_{13}^{- 3} - 4 ζ_{13}^{- 2} - 4 - 4 ζ_{13}^{2} - 4 ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} - 2 + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$4 ζ_{13}^{- 6} + 4 ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + 4 ζ_{13}^{4} + 4 ζ_{13}^{6}$	$4 ζ_{13}^{- 6} + 4 ζ_{13}^{- 4} + 2 ζ_{13}^{- 3} + 2 ζ_{13}^{- 2} + 2 ζ_{13}^{2} + 2 ζ_{13}^{3} + 4 ζ_{13}^{4} + 4 ζ_{13}^{6}$	$- 2 ζ_{13}^{- 6} - 2 ζ_{13}^{- 4} - 4 ζ_{13}^{- 3} - 4 ζ_{13}^{- 2} - 4 - 4 ζ_{13}^{2} - 4 ζ_{13}^{3} - 2 ζ_{13}^{4} - 2 ζ_{13}^{6}$	$- 2$	$- ζ_{13}^{- 5} - ζ_{13}^{- 1} + 2 - ζ_{13} - ζ_{13}^{5}$	$- ζ_{13}^{- 3} - ζ_{13}^{- 2} + 2 - ζ_{13}^{2} - ζ_{13}^{3}$	$- ζ_{13}^{- 6} - ζ_{13}^{- 4} + 2 - ζ_{13}^{4} - ζ_{13}^{6}$	$0$	$0$	$0$	$0$	$0$	$0$

magma:CharacterTable(G);

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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	39T42

Degree	$39$
Order	$4056$
Cyclic	no
Abelian	no
Solvable	yes
Primitive	no
$p$-group	no
Group:	$C_{13}^2:(C_4\times S_3)$