Galois group: 39T9

• Label: 39T9
• Degree: $39$
• Order: $156$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• pp-group: no
• Group: $C_{39}:C_4$

Group action invariants

Degree $n$:		$39$
Transitive number $t$:		$9$
Group:		$C_{39}:C_4$
Parity:		$1$
Primitive:		no
$\card{\Aut(F/K)}$:		$1$
Generators:		(1,14,26,37,12,22,36,9,19,31,6,16,29,2,15,27,38,10,23,34,7,20,32,4,17,30,3,13,25,39,11,24,35,8,21,33,5,18,28), (1,20,31,13)(2,19,32,15)(3,21,33,14)(4,34,28,38)(5,36,29,37)(6,35,30,39)(7,12,26,24)(8,11,27,23)(9,10,25,22)(16,18)

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$
$4$:	$C_4$
$6$:	$S_3$
$12$:	$C_3 : C_4$
$52$:	$C_{13}:C_4$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 13: $C_{13}:C_4$

Low degree siblings

There are no siblings 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	$2^{18},1^{3}$	$13$	$2$	$18$	$( 1,31)( 2,32)( 3,33)( 4,28)( 5,29)( 6,30)( 7,26)( 8,27)( 9,25)(10,22)(11,23)(12,24)(13,20)(14,21)(15,19)(34,38)(35,39)(36,37)$
3A	$3^{13}$	$2$	$3$	$26$	$( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,17,18)(19,20,21)(22,23,24)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)$
4A1	$4^{9},2,1$	$39$	$4$	$28$	$( 1,13,31,20)( 2,15,32,19)( 3,14,33,21)( 4,38,28,34)( 5,37,29,36)( 6,39,30,35)( 7,24,26,12)( 8,23,27,11)( 9,22,25,10)(16,18)$
4A-1	$4^{9},2,1$	$39$	$4$	$28$	$( 1,20,31,13)( 2,19,32,15)( 3,21,33,14)( 4,34,28,38)( 5,36,29,37)( 6,35,30,39)( 7,12,26,24)( 8,11,27,23)( 9,10,25,22)(16,18)$
6A	$6^{6},3$	$26$	$6$	$32$	$( 1, 2, 3)( 4,37, 6,39, 5,38)( 7,36, 9,35, 8,34)(10,31,12,33,11,32)(13,30,15,29,14,28)(16,27,18,26,17,25)(19,23,21,22,20,24)$
13A1	$13^{3}$	$4$	$13$	$36$	$( 1,13,27,37,11,23,36, 8,20,31, 5,17,29)( 2,14,25,38,12,24,34, 9,21,32, 6,18,30)( 3,15,26,39,10,22,35, 7,19,33, 4,16,28)$
13A2	$13^{3}$	$4$	$13$	$36$	$( 1,27,11,36,20, 5,29,13,37,23, 8,31,17)( 2,25,12,34,21, 6,30,14,38,24, 9,32,18)( 3,26,10,35,19, 4,28,15,39,22, 7,33,16)$
13A4	$13^{3}$	$4$	$13$	$36$	$( 1,11,20,29,37, 8,17,27,36, 5,13,23,31)( 2,12,21,30,38, 9,18,25,34, 6,14,24,32)( 3,10,19,28,39, 7,16,26,35, 4,15,22,33)$
39A1	$39$	$4$	$39$	$38$	$( 1,24, 4,27, 9,28,11,32,15,36,18,39,20, 2,22, 5,25, 7,29,12,33,13,34,16,37,21, 3,23, 6,26, 8,30,10,31,14,35,17,38,19)$
39A-1	$39$	$4$	$39$	$38$	$( 1,34,28,23,18,10, 5,38,33,27,21,15, 8, 2,35,29,24,16,11, 6,39,31,25,19,13, 9, 3,36,30,22,17,12, 4,37,32,26,20,14, 7)$
39A2	$39$	$4$	$39$	$38$	$( 1,30,16, 5,32,19, 8,34,22,11,38,26,13, 2,28,17, 6,33,20, 9,35,23,12,39,27,14, 3,29,18, 4,31,21, 7,36,24,10,37,25,15)$
39A-2	$39$	$4$	$39$	$38$	$( 1,32,22,13, 6,35,27,18, 7,37,30,19,11, 2,33,23,14, 4,36,25,16, 8,38,28,20,12, 3,31,24,15, 5,34,26,17, 9,39,29,21,10)$
39A4	$39$	$4$	$39$	$38$	$( 1,18,33, 8,24,39,13,30, 4,20,34,10,27, 2,16,31, 9,22,37,14,28, 5,21,35,11,25, 3,17,32, 7,23,38,15,29, 6,19,36,12,26)$
39A-4	$39$	$4$	$39$	$38$	$( 1, 6, 7,11,14,16,20,24,26,29,32,35,37, 2, 4, 8,12,15,17,21,22,27,30,33,36,38, 3, 5, 9,10,13,18,19,23,25,28,31,34,39)$

Malle's constant $a(G)$:     $1/18$

Group invariants

Order:		$156=2^{2} \cdot 3 \cdot 13$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent
Label:		156.10
Character table:

		1A	2A	3A	4A1	4A-1	6A	13A1	13A2	13A4	39A1	39A-1	39A2	39A-2	39A4	39A-4
	Size	1	13	2	39	39	26	4	4	4	4	4	4	4	4	4
	2 P	1A	1A	3A	2A	2A	3A	13A2	13A4	13A1	39A-4	39A-2	39A4	39A2	39A-1	39A1
	3 P	1A	2A	1A	4A-1	4A1	2A	13A2	13A4	13A1	13A2	13A1	13A2	13A1	13A4	13A4
	13 P	1A	2A	3A	4A1	4A-1	6A	1A	1A	1A	3A	3A	3A	3A	3A	3A
	Type
156.10.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
156.10.1b	R	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
156.10.1c1	C	$1$	$-1$	$1$	$-i$	$i$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
156.10.1c2	C	$1$	$-1$	$1$	$i$	$-i$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
156.10.2a	R	$2$	$2$	$-1$	$0$	$0$	$-1$	$2$	$2$	$2$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$
156.10.2b	S	$2$	$-2$	$-1$	$0$	$0$	$1$	$2$	$2$	$2$	$-1$	$-1$	$-1$	$-1$	$-1$	$-1$
156.10.4a1	R	$4$	$0$	$4$	$0$	$0$	$0$	${\zeta }_{13}^{-6}+{\zeta }_{13}^{-4}+{\zeta }_{13}^4+{\zeta }_{13}^6$	${\zeta }_{13}^{-5}+{\zeta }_{13}^{-1}+{\zeta }_{13}+{\zeta }_{13}^5$	${\zeta }_{13}^{-3}+{\zeta }_{13}^{-2}+{\zeta }_{13}^2+{\zeta }_{13}^3$	${\zeta }_{13}^{-3}+{\zeta }_{13}^{-2}+{\zeta }_{13}^2+{\zeta }_{13}^3$	${\zeta }_{13}^{-3}+{\zeta }_{13}^{-2}+{\zeta }_{13}^2+{\zeta }_{13}^3$	${\zeta }_{13}^{-6}+{\zeta }_{13}^{-4}+{\zeta }_{13}^4+{\zeta }_{13}^6$	${\zeta }_{13}^{-6}+{\zeta }_{13}^{-4}+{\zeta }_{13}^4+{\zeta }_{13}^6$	${\zeta }_{13}^{-5}+{\zeta }_{13}^{-1}+{\zeta }_{13}+{\zeta }_{13}^5$	${\zeta }_{13}^{-5}+{\zeta }_{13}^{-1}+{\zeta }_{13}+{\zeta }_{13}^5$
156.10.4a2	R	$4$	$0$	$4$	$0$	$0$	$0$	${\zeta }_{13}^{-5}+{\zeta }_{13}^{-1}+{\zeta }_{13}+{\zeta }_{13}^5$	${\zeta }_{13}^{-3}+{\zeta }_{13}^{-2}+{\zeta }_{13}^2+{\zeta }_{13}^3$	${\zeta }_{13}^{-6}+{\zeta }_{13}^{-4}+{\zeta }_{13}^4+{\zeta }_{13}^6$	${\zeta }_{13}^{-6}+{\zeta }_{13}^{-4}+{\zeta }_{13}^4+{\zeta }_{13}^6$	${\zeta }_{13}^{-6}+{\zeta }_{13}^{-4}+{\zeta }_{13}^4+{\zeta }_{13}^6$	${\zeta }_{13}^{-5}+{\zeta }_{13}^{-1}+{\zeta }_{13}+{\zeta }_{13}^5$	${\zeta }_{13}^{-5}+{\zeta }_{13}^{-1}+{\zeta }_{13}+{\zeta }_{13}^5$	${\zeta }_{13}^{-3}+{\zeta }_{13}^{-2}+{\zeta }_{13}^2+{\zeta }_{13}^3$	${\zeta }_{13}^{-3}+{\zeta }_{13}^{-2}+{\zeta }_{13}^2+{\zeta }_{13}^3$
156.10.4a3	R	$4$	$0$	$4$	$0$	$0$	$0$	${\zeta }_{13}^{-3}+{\zeta }_{13}^{-2}+{\zeta }_{13}^2+{\zeta }_{13}^3$	${\zeta }_{13}^{-6}+{\zeta }_{13}^{-4}+{\zeta }_{13}^4+{\zeta }_{13}^6$	${\zeta }_{13}^{-5}+{\zeta }_{13}^{-1}+{\zeta }_{13}+{\zeta }_{13}^5$	${\zeta }_{13}^{-5}+{\zeta }_{13}^{-1}+{\zeta }_{13}+{\zeta }_{13}^5$	${\zeta }_{13}^{-5}+{\zeta }_{13}^{-1}+{\zeta }_{13}+{\zeta }_{13}^5$	${\zeta }_{13}^{-3}+{\zeta }_{13}^{-2}+{\zeta }_{13}^2+{\zeta }_{13}^3$	${\zeta }_{13}^{-3}+{\zeta }_{13}^{-2}+{\zeta }_{13}^2+{\zeta }_{13}^3$	${\zeta }_{13}^{-6}+{\zeta }_{13}^{-4}+{\zeta }_{13}^4+{\zeta }_{13}^6$	${\zeta }_{13}^{-6}+{\zeta }_{13}^{-4}+{\zeta }_{13}^4+{\zeta }_{13}^6$
156.10.4b1	C	$4$	$0$	$-2$	$0$	$0$	$0$	${\zeta }_{39}^{-18}-{\zeta }_{39}+{\zeta }_{39}^{12}-{\zeta }_{39}^{14}+{\zeta }_{39}^{18}$	${\zeta }_{39}^{-19}-{\zeta }_{39}^{-18}-1+{\zeta }_{39}+{\zeta }_{39}^4-{\zeta }_{39}^6+{\zeta }_{39}^7-{\zeta }_{39}^9-{\zeta }_{39}^{12}+{\zeta }_{39}^{14}+{\zeta }_{39}^{17}-{\zeta }_{39}^{18}$	$-{\zeta }_{39}^{-19}-{\zeta }_{39}^4+{\zeta }_{39}^6-{\zeta }_{39}^7+{\zeta }_{39}^9-{\zeta }_{39}^{17}$	${\zeta }_{39}^{-19}+{\zeta }_{39}^{-17}+{\zeta }_{39}^4-{\zeta }_{39}^6-{\zeta }_{39}^{19}$	$-{\zeta }_{39}^{-17}+{\zeta }_{39}^7-{\zeta }_{39}^9+{\zeta }_{39}^{17}+{\zeta }_{39}^{19}$	${\zeta }_{39}^{-19}-{\zeta }_{39}^{-17}+{\zeta }_{39}^{-16}-1+{\zeta }_{39}+{\zeta }_{39}^2-{\zeta }_{39}^3+2{\zeta }_{39}^5-{\zeta }_{39}^6+2{\zeta }_{39}^8-{\zeta }_{39}^9+{\zeta }_{39}^{11}-{\zeta }_{39}^{12}-{\zeta }_{39}^{13}+{\zeta }_{39}^{14}-{\zeta }_{39}^{16}+{\zeta }_{39}^{17}-{\zeta }_{39}^{19}$	$-{\zeta }_{39}^{-19}-{\zeta }_{39}^{-18}+{\zeta }_{39}^{-17}-{\zeta }_{39}^{-16}+1-{\zeta }_{39}^2+{\zeta }_{39}^3-2{\zeta }_{39}^5+{\zeta }_{39}^6-2{\zeta }_{39}^8+{\zeta }_{39}^9-{\zeta }_{39}^{11}+{\zeta }_{39}^{13}+{\zeta }_{39}^{16}-{\zeta }_{39}^{17}-{\zeta }_{39}^{18}+{\zeta }_{39}^{19}$	${\zeta }_{39}^2+{\zeta }_{39}^{10}+{\zeta }_{39}^{11}+{\zeta }_{39}^{16}$	$-{\zeta }_{39}^{-19}+{\zeta }_{39}^{-18}+1-{\zeta }_{39}-{\zeta }_{39}^2-{\zeta }_{39}^4+{\zeta }_{39}^6-{\zeta }_{39}^7+{\zeta }_{39}^9-{\zeta }_{39}^{10}-{\zeta }_{39}^{11}+{\zeta }_{39}^{12}-{\zeta }_{39}^{14}-{\zeta }_{39}^{16}-{\zeta }_{39}^{17}+{\zeta }_{39}^{18}$
156.10.4b2	C	$4$	$0$	$-2$	$0$	$0$	$0$	${\zeta }_{39}^{-18}-{\zeta }_{39}+{\zeta }_{39}^{12}-{\zeta }_{39}^{14}+{\zeta }_{39}^{18}$	${\zeta }_{39}^{-19}-{\zeta }_{39}^{-18}-1+{\zeta }_{39}+{\zeta }_{39}^4-{\zeta }_{39}^6+{\zeta }_{39}^7-{\zeta }_{39}^9-{\zeta }_{39}^{12}+{\zeta }_{39}^{14}+{\zeta }_{39}^{17}-{\zeta }_{39}^{18}$	$-{\zeta }_{39}^{-19}-{\zeta }_{39}^4+{\zeta }_{39}^6-{\zeta }_{39}^7+{\zeta }_{39}^9-{\zeta }_{39}^{17}$	$-{\zeta }_{39}^{-17}+{\zeta }_{39}^7-{\zeta }_{39}^9+{\zeta }_{39}^{17}+{\zeta }_{39}^{19}$	${\zeta }_{39}^{-19}+{\zeta }_{39}^{-17}+{\zeta }_{39}^4-{\zeta }_{39}^6-{\zeta }_{39}^{19}$	$-{\zeta }_{39}^{-19}-{\zeta }_{39}^{-18}+{\zeta }_{39}^{-17}-{\zeta }_{39}^{-16}+1-{\zeta }_{39}^2+{\zeta }_{39}^3-2{\zeta }_{39}^5+{\zeta }_{39}^6-2{\zeta }_{39}^8+{\zeta }_{39}^9-{\zeta }_{39}^{11}+{\zeta }_{39}^{13}+{\zeta }_{39}^{16}-{\zeta }_{39}^{17}-{\zeta }_{39}^{18}+{\zeta }_{39}^{19}$	${\zeta }_{39}^{-19}-{\zeta }_{39}^{-17}+{\zeta }_{39}^{-16}-1+{\zeta }_{39}+{\zeta }_{39}^2-{\zeta }_{39}^3+2{\zeta }_{39}^5-{\zeta }_{39}^6+2{\zeta }_{39}^8-{\zeta }_{39}^9+{\zeta }_{39}^{11}-{\zeta }_{39}^{12}-{\zeta }_{39}^{13}+{\zeta }_{39}^{14}-{\zeta }_{39}^{16}+{\zeta }_{39}^{17}-{\zeta }_{39}^{19}$	$-{\zeta }_{39}^{-19}+{\zeta }_{39}^{-18}+1-{\zeta }_{39}-{\zeta }_{39}^2-{\zeta }_{39}^4+{\zeta }_{39}^6-{\zeta }_{39}^7+{\zeta }_{39}^9-{\zeta }_{39}^{10}-{\zeta }_{39}^{11}+{\zeta }_{39}^{12}-{\zeta }_{39}^{14}-{\zeta }_{39}^{16}-{\zeta }_{39}^{17}+{\zeta }_{39}^{18}$	${\zeta }_{39}^2+{\zeta }_{39}^{10}+{\zeta }_{39}^{11}+{\zeta }_{39}^{16}$
156.10.4b3	C	$4$	$0$	$-2$	$0$	$0$	$0$	${\zeta }_{39}^{-19}-{\zeta }_{39}^{-18}-1+{\zeta }_{39}+{\zeta }_{39}^4-{\zeta }_{39}^6+{\zeta }_{39}^7-{\zeta }_{39}^9-{\zeta }_{39}^{12}+{\zeta }_{39}^{14}+{\zeta }_{39}^{17}-{\zeta }_{39}^{18}$	$-{\zeta }_{39}^{-19}-{\zeta }_{39}^4+{\zeta }_{39}^6-{\zeta }_{39}^7+{\zeta }_{39}^9-{\zeta }_{39}^{17}$	${\zeta }_{39}^{-18}-{\zeta }_{39}+{\zeta }_{39}^{12}-{\zeta }_{39}^{14}+{\zeta }_{39}^{18}$	$-{\zeta }_{39}^{-19}-{\zeta }_{39}^{-18}+{\zeta }_{39}^{-17}-{\zeta }_{39}^{-16}+1-{\zeta }_{39}^2+{\zeta }_{39}^3-2{\zeta }_{39}^5+{\zeta }_{39}^6-2{\zeta }_{39}^8+{\zeta }_{39}^9-{\zeta }_{39}^{11}+{\zeta }_{39}^{13}+{\zeta }_{39}^{16}-{\zeta }_{39}^{17}-{\zeta }_{39}^{18}+{\zeta }_{39}^{19}$	${\zeta }_{39}^{-19}-{\zeta }_{39}^{-17}+{\zeta }_{39}^{-16}-1+{\zeta }_{39}+{\zeta }_{39}^2-{\zeta }_{39}^3+2{\zeta }_{39}^5-{\zeta }_{39}^6+2{\zeta }_{39}^8-{\zeta }_{39}^9+{\zeta }_{39}^{11}-{\zeta }_{39}^{12}-{\zeta }_{39}^{13}+{\zeta }_{39}^{14}-{\zeta }_{39}^{16}+{\zeta }_{39}^{17}-{\zeta }_{39}^{19}$	$-{\zeta }_{39}^{-19}+{\zeta }_{39}^{-18}+1-{\zeta }_{39}-{\zeta }_{39}^2-{\zeta }_{39}^4+{\zeta }_{39}^6-{\zeta }_{39}^7+{\zeta }_{39}^9-{\zeta }_{39}^{10}-{\zeta }_{39}^{11}+{\zeta }_{39}^{12}-{\zeta }_{39}^{14}-{\zeta }_{39}^{16}-{\zeta }_{39}^{17}+{\zeta }_{39}^{18}$	${\zeta }_{39}^2+{\zeta }_{39}^{10}+{\zeta }_{39}^{11}+{\zeta }_{39}^{16}$	$-{\zeta }_{39}^{-17}+{\zeta }_{39}^7-{\zeta }_{39}^9+{\zeta }_{39}^{17}+{\zeta }_{39}^{19}$	${\zeta }_{39}^{-19}+{\zeta }_{39}^{-17}+{\zeta }_{39}^4-{\zeta }_{39}^6-{\zeta }_{39}^{19}$
156.10.4b4	C	$4$	$0$	$-2$	$0$	$0$	$0$	${\zeta }_{39}^{-19}-{\zeta }_{39}^{-18}-1+{\zeta }_{39}+{\zeta }_{39}^4-{\zeta }_{39}^6+{\zeta }_{39}^7-{\zeta }_{39}^9-{\zeta }_{39}^{12}+{\zeta }_{39}^{14}+{\zeta }_{39}^{17}-{\zeta }_{39}^{18}$	$-{\zeta }_{39}^{-19}-{\zeta }_{39}^4+{\zeta }_{39}^6-{\zeta }_{39}^7+{\zeta }_{39}^9-{\zeta }_{39}^{17}$	${\zeta }_{39}^{-18}-{\zeta }_{39}+{\zeta }_{39}^{12}-{\zeta }_{39}^{14}+{\zeta }_{39}^{18}$	${\zeta }_{39}^{-19}-{\zeta }_{39}^{-17}+{\zeta }_{39}^{-16}-1+{\zeta }_{39}+{\zeta }_{39}^2-{\zeta }_{39}^3+2{\zeta }_{39}^5-{\zeta }_{39}^6+2{\zeta }_{39}^8-{\zeta }_{39}^9+{\zeta }_{39}^{11}-{\zeta }_{39}^{12}-{\zeta }_{39}^{13}+{\zeta }_{39}^{14}-{\zeta }_{39}^{16}+{\zeta }_{39}^{17}-{\zeta }_{39}^{19}$	$-{\zeta }_{39}^{-19}-{\zeta }_{39}^{-18}+{\zeta }_{39}^{-17}-{\zeta }_{39}^{-16}+1-{\zeta }_{39}^2+{\zeta }_{39}^3-2{\zeta }_{39}^5+{\zeta }_{39}^6-2{\zeta }_{39}^8+{\zeta }_{39}^9-{\zeta }_{39}^{11}+{\zeta }_{39}^{13}+{\zeta }_{39}^{16}-{\zeta }_{39}^{17}-{\zeta }_{39}^{18}+{\zeta }_{39}^{19}$	${\zeta }_{39}^2+{\zeta }_{39}^{10}+{\zeta }_{39}^{11}+{\zeta }_{39}^{16}$	$-{\zeta }_{39}^{-19}+{\zeta }_{39}^{-18}+1-{\zeta }_{39}-{\zeta }_{39}^2-{\zeta }_{39}^4+{\zeta }_{39}^6-{\zeta }_{39}^7+{\zeta }_{39}^9-{\zeta }_{39}^{10}-{\zeta }_{39}^{11}+{\zeta }_{39}^{12}-{\zeta }_{39}^{14}-{\zeta }_{39}^{16}-{\zeta }_{39}^{17}+{\zeta }_{39}^{18}$	${\zeta }_{39}^{-19}+{\zeta }_{39}^{-17}+{\zeta }_{39}^4-{\zeta }_{39}^6-{\zeta }_{39}^{19}$	$-{\zeta }_{39}^{-17}+{\zeta }_{39}^7-{\zeta }_{39}^9+{\zeta }_{39}^{17}+{\zeta }_{39}^{19}$
156.10.4b5	C	$4$	$0$	$-2$	$0$	$0$	$0$	$-{\zeta }_{39}^{-19}-{\zeta }_{39}^4+{\zeta }_{39}^6-{\zeta }_{39}^7+{\zeta }_{39}^9-{\zeta }_{39}^{17}$	${\zeta }_{39}^{-18}-{\zeta }_{39}+{\zeta }_{39}^{12}-{\zeta }_{39}^{14}+{\zeta }_{39}^{18}$	${\zeta }_{39}^{-19}-{\zeta }_{39}^{-18}-1+{\zeta }_{39}+{\zeta }_{39}^4-{\zeta }_{39}^6+{\zeta }_{39}^7-{\zeta }_{39}^9-{\zeta }_{39}^{12}+{\zeta }_{39}^{14}+{\zeta }_{39}^{17}-{\zeta }_{39}^{18}$	$-{\zeta }_{39}^{-19}+{\zeta }_{39}^{-18}+1-{\zeta }_{39}-{\zeta }_{39}^2-{\zeta }_{39}^4+{\zeta }_{39}^6-{\zeta }_{39}^7+{\zeta }_{39}^9-{\zeta }_{39}^{10}-{\zeta }_{39}^{11}+{\zeta }_{39}^{12}-{\zeta }_{39}^{14}-{\zeta }_{39}^{16}-{\zeta }_{39}^{17}+{\zeta }_{39}^{18}$	${\zeta }_{39}^2+{\zeta }_{39}^{10}+{\zeta }_{39}^{11}+{\zeta }_{39}^{16}$	$-{\zeta }_{39}^{-17}+{\zeta }_{39}^7-{\zeta }_{39}^9+{\zeta }_{39}^{17}+{\zeta }_{39}^{19}$	${\zeta }_{39}^{-19}+{\zeta }_{39}^{-17}+{\zeta }_{39}^4-{\zeta }_{39}^6-{\zeta }_{39}^{19}$	$-{\zeta }_{39}^{-19}-{\zeta }_{39}^{-18}+{\zeta }_{39}^{-17}-{\zeta }_{39}^{-16}+1-{\zeta }_{39}^2+{\zeta }_{39}^3-2{\zeta }_{39}^5+{\zeta }_{39}^6-2{\zeta }_{39}^8+{\zeta }_{39}^9-{\zeta }_{39}^{11}+{\zeta }_{39}^{13}+{\zeta }_{39}^{16}-{\zeta }_{39}^{17}-{\zeta }_{39}^{18}+{\zeta }_{39}^{19}$	${\zeta }_{39}^{-19}-{\zeta }_{39}^{-17}+{\zeta }_{39}^{-16}-1+{\zeta }_{39}+{\zeta }_{39}^2-{\zeta }_{39}^3+2{\zeta }_{39}^5-{\zeta }_{39}^6+2{\zeta }_{39}^8-{\zeta }_{39}^9+{\zeta }_{39}^{11}-{\zeta }_{39}^{12}-{\zeta }_{39}^{13}+{\zeta }_{39}^{14}-{\zeta }_{39}^{16}+{\zeta }_{39}^{17}-{\zeta }_{39}^{19}$
156.10.4b6	C	$4$	$0$	$-2$	$0$	$0$	$0$	$-{\zeta }_{39}^{-19}-{\zeta }_{39}^4+{\zeta }_{39}^6-{\zeta }_{39}^7+{\zeta }_{39}^9-{\zeta }_{39}^{17}$	${\zeta }_{39}^{-18}-{\zeta }_{39}+{\zeta }_{39}^{12}-{\zeta }_{39}^{14}+{\zeta }_{39}^{18}$	${\zeta }_{39}^{-19}-{\zeta }_{39}^{-18}-1+{\zeta }_{39}+{\zeta }_{39}^4-{\zeta }_{39}^6+{\zeta }_{39}^7-{\zeta }_{39}^9-{\zeta }_{39}^{12}+{\zeta }_{39}^{14}+{\zeta }_{39}^{17}-{\zeta }_{39}^{18}$	${\zeta }_{39}^2+{\zeta }_{39}^{10}+{\zeta }_{39}^{11}+{\zeta }_{39}^{16}$	$-{\zeta }_{39}^{-19}+{\zeta }_{39}^{-18}+1-{\zeta }_{39}-{\zeta }_{39}^2-{\zeta }_{39}^4+{\zeta }_{39}^6-{\zeta }_{39}^7+{\zeta }_{39}^9-{\zeta }_{39}^{10}-{\zeta }_{39}^{11}+{\zeta }_{39}^{12}-{\zeta }_{39}^{14}-{\zeta }_{39}^{16}-{\zeta }_{39}^{17}+{\zeta }_{39}^{18}$	${\zeta }_{39}^{-19}+{\zeta }_{39}^{-17}+{\zeta }_{39}^4-{\zeta }_{39}^6-{\zeta }_{39}^{19}$	$-{\zeta }_{39}^{-17}+{\zeta }_{39}^7-{\zeta }_{39}^9+{\zeta }_{39}^{17}+{\zeta }_{39}^{19}$	${\zeta }_{39}^{-19}-{\zeta }_{39}^{-17}+{\zeta }_{39}^{-16}-1+{\zeta }_{39}+{\zeta }_{39}^2-{\zeta }_{39}^3+2{\zeta }_{39}^5-{\zeta }_{39}^6+2{\zeta }_{39}^8-{\zeta }_{39}^9+{\zeta }_{39}^{11}-{\zeta }_{39}^{12}-{\zeta }_{39}^{13}+{\zeta }_{39}^{14}-{\zeta }_{39}^{16}+{\zeta }_{39}^{17}-{\zeta }_{39}^{19}$	$-{\zeta }_{39}^{-19}-{\zeta }_{39}^{-18}+{\zeta }_{39}^{-17}-{\zeta }_{39}^{-16}+1-{\zeta }_{39}^2+{\zeta }_{39}^3-2{\zeta }_{39}^5+{\zeta }_{39}^6-2{\zeta }_{39}^8+{\zeta }_{39}^9-{\zeta }_{39}^{11}+{\zeta }_{39}^{13}+{\zeta }_{39}^{16}-{\zeta }_{39}^{17}-{\zeta }_{39}^{18}+{\zeta }_{39}^{19}$