Galois group: 33T17

• Label: 33T17
• Degree: $33$
• Order: $1980$
• Cyclic: no
• Abelian: no
• Solvable: no
• Primitive: no
• $p$-group: no
• Group: $C_3\times \PSL(2,11)$

Group action invariants

Degree $n$:		$33$
Transitive number $t$:		$17$
Group:		$C_3\times \PSL(2,11)$
Parity:		$1$
Primitive:		no
$\card{\Aut(F/K)}$:		$3$
Generators:		(1,24,5,14,8)(2,23,4,13,7)(3,22,6,15,9)(10,17,25,21,31)(11,16,26,19,33)(12,18,27,20,32), (1,22,26,8,10,19,5,30,33,18,15,2,24,25,7,12,21,4,28,31,16,14,3,23,27,9,11,20,6,29,32,17,13)

Low degree resolvents

|G/N|	Galois groups for stem field(s)
$3$:	$C_3$
$660$:	$\PSL(2,11)$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: $\PSL(2,11)$

Low degree siblings

33T17, 36T3021

Siblings are shown with degree $\leq 47$

A number field with this Galois group has exactly one arithmetically equivalent field.

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 $	$1$	$1$	$()$
	$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $	$1$	$3$	$( 1, 2, 3)( 4, 6, 5)( 7, 9, 8)(10,12,11)(13,15,14)(16,17,18)(19,21,20) (22,24,23)(25,27,26)(28,29,30)(31,32,33)$
	$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $	$1$	$3$	$( 1, 3, 2)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,18,17)(19,20,21) (22,23,24)(25,26,27)(28,30,29)(31,33,32)$
	$ 6, 6, 6, 6, 3, 3, 3 $	$55$	$6$	$( 1, 2, 3)( 4,25, 5,26, 6,27)( 7,30, 8,29, 9,28)(10,14,11,15,12,13) (16,31,18,33,17,32)(19,21,20)(22,24,23)$
	$ 6, 6, 6, 6, 3, 3, 3 $	$55$	$6$	$( 1, 3, 2)( 4,27, 6,26, 5,25)( 7,28, 9,29, 8,30)(10,13,12,15,11,14) (16,32,17,33,18,31)(19,20,21)(22,23,24)$
	$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$55$	$2$	$( 4,26)( 5,27)( 6,25)( 7,29)( 8,28)( 9,30)(10,15)(11,13)(12,14)(16,33)(17,31) (18,32)$
	$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $	$110$	$3$	$( 1, 3, 2)( 4,14, 9)( 5,15, 7)( 6,13, 8)(10,26,28)(11,27,30)(12,25,29) (16,32,21)(17,33,20)(18,31,19)(22,23,24)$
	$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1 $	$110$	$3$	$( 4,13, 7)( 5,14, 8)( 6,15, 9)(10,25,30)(11,26,29)(12,27,28)(16,33,19) (17,31,21)(18,32,20)$
	$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $	$110$	$3$	$( 1, 2, 3)( 4,15, 8)( 5,13, 9)( 6,14, 7)(10,27,29)(11,25,28)(12,26,30) (16,31,20)(17,32,19)(18,33,21)(22,24,23)$
	$ 15, 15, 3 $	$132$	$15$	$( 1, 2, 3)( 4,21,18,29,22, 5,19,17,28,23, 6,20,16,30,24)( 7,10,14,33,25, 8,11, 15,32,26, 9,12,13,31,27)$
	$ 15, 15, 3 $	$132$	$15$	$( 1, 3, 2)( 4,20,17,29,24, 6,19,18,30,23, 5,21,16,28,22)( 7,12,15,33,27, 9,11, 14,31,26, 8,10,13,32,25)$
	$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $	$132$	$5$	$( 4,19,16,29,23)( 5,20,18,28,24)( 6,21,17,30,22)( 7,11,13,33,26) ( 8,12,14,32,27)( 9,10,15,31,25)$
	$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $	$132$	$5$	$( 4,33,16,26,23)( 5,32,18,27,24)( 6,31,17,25,22)( 7,19,29,13,11) ( 8,20,28,14,12)( 9,21,30,15,10)$
	$ 15, 15, 3 $	$132$	$15$	$( 1, 2, 3)( 4,31,18,26,22, 5,33,17,27,23, 6,32,16,25,24)( 7,21,28,13,10, 8,19, 30,14,11, 9,20,29,15,12)$
	$ 15, 15, 3 $	$132$	$15$	$( 1, 3, 2)( 4,32,17,26,24, 6,33,18,25,23, 5,31,16,27,22)( 7,20,30,13,12, 9,19, 28,15,11, 8,21,29,14,10)$
	$ 6, 6, 6, 3, 3, 3, 2, 2, 2 $	$110$	$6$	$( 1,24)( 2,23)( 3,22)( 4,29, 7,26,13,11)( 5,28, 8,27,14,12)( 6,30, 9,25,15,10) (16,33,19)(17,31,21)(18,32,20)$
	$ 6, 6, 6, 6, 3, 3, 3 $	$110$	$6$	$( 1,23, 3,24, 2,22)( 4,30, 8,26,15,12)( 5,29, 9,27,13,10)( 6,28, 7,25,14,11) (16,31,20)(17,32,19)(18,33,21)$
	$ 6, 6, 6, 6, 3, 3, 3 $	$110$	$6$	$( 1,22, 2,24, 3,23)( 4,28, 9,26,14,10)( 5,30, 7,27,15,11)( 6,29, 8,25,13,12) (16,32,21)(17,33,20)(18,31,19)$
	$ 33 $	$60$	$33$	$( 1,22, 4,28,15,19,27, 9,16,32,10, 2,24, 6,29,14,21,26, 8,17,33,12, 3,23, 5, 30,13,20,25, 7,18,31,11)$
	$ 11, 11, 11 $	$60$	$11$	$( 1,24, 5,28,14,20,27, 8,18,32,12)( 2,23, 4,29,13,19,26, 7,16,33,11) ( 3,22, 6,30,15,21,25, 9,17,31,10)$
	$ 33 $	$60$	$33$	$( 1,23, 6,28,13,21,27, 7,17,32,11, 3,24, 4,30,14,19,25, 8,16,31,12, 2,22, 5, 29,15,20,26, 9,18,33,10)$
	$ 33 $	$60$	$33$	$( 1,23, 6,20,33,25,14,16,10, 8,29, 3,24, 4,21,32,26,15,18,11, 9,28, 2,22, 5, 19,31,27,13,17,12, 7,30)$
	$ 33 $	$60$	$33$	$( 1,22, 4,20,31,26,14,17,11, 8,30, 2,24, 6,19,32,25,13,18,10, 7,28, 3,23, 5, 21,33,27,15,16,12, 9,29)$
	$ 11, 11, 11 $	$60$	$11$	$( 1,24, 5,20,32,27,14,18,12, 8,28)( 2,23, 4,19,33,26,13,16,11, 7,29) ( 3,22, 6,21,31,25,15,17,10, 9,30)$

Group invariants

Order:		$1980=2^{2} \cdot 3^{2} \cdot 5 \cdot 11$
Cyclic:		no
Abelian:		no
Solvable:		no
Nilpotency class:		not nilpotent
Label:		1980.57
Character table:

		1A	2A	3A1	3A-1	3B	3C1	3C-1	5A1	5A2	6A1	6A-1	6B	6C1	6C-1	11A1	11A-1	15A1	15A-1	15A2	15A-2	33A1	33A-1	33A5	33A-5
	Size	1	55	1	1	110	110	110	132	132	55	55	110	110	110	60	60	132	132	132	132	60	60	60	60
	2 P	1A	1A	3A-1	3A1	3C1	3B	3C-1	5A2	5A1	3A-1	3A1	3C-1	3B	3C1	11A-1	11A1	15A2	15A-1	15A-2	15A1	33A-1	33A1	33A-5	33A5
	3 P	1A	2A	1A	1A	1A	1A	1A	5A2	5A1	2A	2A	2A	2A	2A	11A1	11A-1	5A1	5A2	5A1	5A2	11A1	11A-1	11A1	11A-1
	5 P	1A	2A	3A-1	3A1	3C1	3B	3C-1	1A	1A	6A-1	6A1	6C1	6B	6C-1	11A1	11A-1	3A1	3A1	3A-1	3A-1	33A5	33A-5	33A1	33A-1
	11 P	1A	2A	3A-1	3A1	3C1	3B	3C-1	5A1	5A2	6A-1	6A1	6C1	6B	6C-1	1A	1A	15A-1	15A2	15A1	15A-2	3A1	3A-1	3A-1	3A1
	Type
1980.57.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
1980.57.1b1	C	$1$	$1$	${\zeta }_3^{-1}$	${\zeta }_3$	$1$	${\zeta }_3$	${\zeta }_3^{-1}$	$1$	$1$	${\zeta }_3^{-1}$	${\zeta }_3$	$1$	${\zeta }_3^{-1}$	${\zeta }_3$	$1$	$1$	${\zeta }_3$	${\zeta }_3^{-1}$	${\zeta }_3^{-1}$	${\zeta }_3$	${\zeta }_3$	${\zeta }_3^{-1}$	${\zeta }_3^{-1}$	${\zeta }_3$
1980.57.1b2	C	$1$	$1$	${\zeta }_3$	${\zeta }_3^{-1}$	$1$	${\zeta }_3^{-1}$	${\zeta }_3$	$1$	$1$	${\zeta }_3$	${\zeta }_3^{-1}$	$1$	${\zeta }_3$	${\zeta }_3^{-1}$	$1$	$1$	${\zeta }_3^{-1}$	${\zeta }_3$	${\zeta }_3$	${\zeta }_3^{-1}$	${\zeta }_3^{-1}$	${\zeta }_3$	${\zeta }_3$	${\zeta }_3^{-1}$
1980.57.5a1	C	$5$	$1$	$5$	$5$	$-1$	$-1$	$-1$	$0$	$0$	$1$	$1$	$1$	$1$	$1$	$-{\zeta }_{11}^{-2}-1-{\zeta }_{11}-{\zeta }_{11}^3-{\zeta }_{11}^4-{\zeta }_{11}^5$	${\zeta }_{11}^{-2}+{\zeta }_{11}+{\zeta }_{11}^3+{\zeta }_{11}^4+{\zeta }_{11}^5$	$0$	$0$	$0$	$0$	$-{\zeta }_{11}^{-2}-1-{\zeta }_{11}-{\zeta }_{11}^3-{\zeta }_{11}^4-{\zeta }_{11}^5$	${\zeta }_{11}^{-2}+{\zeta }_{11}+{\zeta }_{11}^3+{\zeta }_{11}^4+{\zeta }_{11}^5$	$-{\zeta }_{11}^{-2}-1-{\zeta }_{11}-{\zeta }_{11}^3-{\zeta }_{11}^4-{\zeta }_{11}^5$	${\zeta }_{11}^{-2}+{\zeta }_{11}+{\zeta }_{11}^3+{\zeta }_{11}^4+{\zeta }_{11}^5$
1980.57.5a2	C	$5$	$1$	$5$	$5$	$-1$	$-1$	$-1$	$0$	$0$	$1$	$1$	$1$	$1$	$1$	${\zeta }_{11}^{-2}+{\zeta }_{11}+{\zeta }_{11}^3+{\zeta }_{11}^4+{\zeta }_{11}^5$	$-{\zeta }_{11}^{-2}-1-{\zeta }_{11}-{\zeta }_{11}^3-{\zeta }_{11}^4-{\zeta }_{11}^5$	$0$	$0$	$0$	$0$	${\zeta }_{11}^{-2}+{\zeta }_{11}+{\zeta }_{11}^3+{\zeta }_{11}^4+{\zeta }_{11}^5$	$-{\zeta }_{11}^{-2}-1-{\zeta }_{11}-{\zeta }_{11}^3-{\zeta }_{11}^4-{\zeta }_{11}^5$	${\zeta }_{11}^{-2}+{\zeta }_{11}+{\zeta }_{11}^3+{\zeta }_{11}^4+{\zeta }_{11}^5$	$-{\zeta }_{11}^{-2}-1-{\zeta }_{11}-{\zeta }_{11}^3-{\zeta }_{11}^4-{\zeta }_{11}^5$
1980.57.5b1	C	$5$	$1$	$5{\zeta }_{33}^{-11}$	$5{\zeta }_{33}^{11}$	$-1$	$-{\zeta }_{33}^{11}$	$-{\zeta }_{33}^{-11}$	$0$	$0$	${\zeta }_{33}^{-11}$	${\zeta }_{33}^{11}$	$1$	${\zeta }_{33}^{-11}$	${\zeta }_{33}^{11}$	$-1-{\zeta }_{33}^3+{\zeta }_{33}^5-{\zeta }_{33}^9-{\zeta }_{33}^{12}-{\zeta }_{33}^{15}+{\zeta }_{33}^{16}$	${\zeta }_{33}^3-{\zeta }_{33}^5+{\zeta }_{33}^9+{\zeta }_{33}^{12}+{\zeta }_{33}^{15}-{\zeta }_{33}^{16}$	$0$	$0$	$0$	$0$	${\zeta }_{33}^{-16}-{\zeta }_{33}^{-14}+1+{\zeta }_{33}^3-{\zeta }_{33}^5+{\zeta }_{33}^6-{\zeta }_{33}^7+{\zeta }_{33}^9-{\zeta }_{33}^{10}+{\zeta }_{33}^{12}-{\zeta }_{33}^{13}+{\zeta }_{33}^{15}-{\zeta }_{33}^{16}$	${\zeta }_{33}^{-16}-{\zeta }_{33}^{-14}+1+{\zeta }_{33}^6-{\zeta }_{33}^7-{\zeta }_{33}^{10}+{\zeta }_{33}^{11}-{\zeta }_{33}^{13}$	$-{\zeta }_{33}^{-16}+{\zeta }_{33}^{-14}-{\zeta }_{33}^6+{\zeta }_{33}^7+{\zeta }_{33}^{10}+{\zeta }_{33}^{13}$	$-{\zeta }_{33}^{-16}+{\zeta }_{33}^{-14}-1-{\zeta }_{33}^3+{\zeta }_{33}^5-{\zeta }_{33}^6+{\zeta }_{33}^7-{\zeta }_{33}^9+{\zeta }_{33}^{10}-{\zeta }_{33}^{11}-{\zeta }_{33}^{12}+{\zeta }_{33}^{13}-{\zeta }_{33}^{15}+{\zeta }_{33}^{16}$
1980.57.5b2	C	$5$	$1$	$5{\zeta }_{33}^{11}$	$5{\zeta }_{33}^{-11}$	$-1$	$-{\zeta }_{33}^{-11}$	$-{\zeta }_{33}^{11}$	$0$	$0$	${\zeta }_{33}^{11}$	${\zeta }_{33}^{-11}$	$1$	${\zeta }_{33}^{11}$	${\zeta }_{33}^{-11}$	${\zeta }_{33}^3-{\zeta }_{33}^5+{\zeta }_{33}^9+{\zeta }_{33}^{12}+{\zeta }_{33}^{15}-{\zeta }_{33}^{16}$	$-1-{\zeta }_{33}^3+{\zeta }_{33}^5-{\zeta }_{33}^9-{\zeta }_{33}^{12}-{\zeta }_{33}^{15}+{\zeta }_{33}^{16}$	$0$	$0$	$0$	$0$	${\zeta }_{33}^{-16}-{\zeta }_{33}^{-14}+1+{\zeta }_{33}^6-{\zeta }_{33}^7-{\zeta }_{33}^{10}+{\zeta }_{33}^{11}-{\zeta }_{33}^{13}$	${\zeta }_{33}^{-16}-{\zeta }_{33}^{-14}+1+{\zeta }_{33}^3-{\zeta }_{33}^5+{\zeta }_{33}^6-{\zeta }_{33}^7+{\zeta }_{33}^9-{\zeta }_{33}^{10}+{\zeta }_{33}^{12}-{\zeta }_{33}^{13}+{\zeta }_{33}^{15}-{\zeta }_{33}^{16}$	$-{\zeta }_{33}^{-16}+{\zeta }_{33}^{-14}-1-{\zeta }_{33}^3+{\zeta }_{33}^5-{\zeta }_{33}^6+{\zeta }_{33}^7-{\zeta }_{33}^9+{\zeta }_{33}^{10}-{\zeta }_{33}^{11}-{\zeta }_{33}^{12}+{\zeta }_{33}^{13}-{\zeta }_{33}^{15}+{\zeta }_{33}^{16}$	$-{\zeta }_{33}^{-16}+{\zeta }_{33}^{-14}-{\zeta }_{33}^6+{\zeta }_{33}^7+{\zeta }_{33}^{10}+{\zeta }_{33}^{13}$
1980.57.5b3	C	$5$	$1$	$5{\zeta }_{33}^{-11}$	$5{\zeta }_{33}^{11}$	$-1$	$-{\zeta }_{33}^{11}$	$-{\zeta }_{33}^{-11}$	$0$	$0$	${\zeta }_{33}^{-11}$	${\zeta }_{33}^{11}$	$1$	${\zeta }_{33}^{-11}$	${\zeta }_{33}^{11}$	${\zeta }_{33}^3-{\zeta }_{33}^5+{\zeta }_{33}^9+{\zeta }_{33}^{12}+{\zeta }_{33}^{15}-{\zeta }_{33}^{16}$	$-1-{\zeta }_{33}^3+{\zeta }_{33}^5-{\zeta }_{33}^9-{\zeta }_{33}^{12}-{\zeta }_{33}^{15}+{\zeta }_{33}^{16}$	$0$	$0$	$0$	$0$	$-{\zeta }_{33}^{-16}+{\zeta }_{33}^{-14}-1-{\zeta }_{33}^3+{\zeta }_{33}^5-{\zeta }_{33}^6+{\zeta }_{33}^7-{\zeta }_{33}^9+{\zeta }_{33}^{10}-{\zeta }_{33}^{11}-{\zeta }_{33}^{12}+{\zeta }_{33}^{13}-{\zeta }_{33}^{15}+{\zeta }_{33}^{16}$	$-{\zeta }_{33}^{-16}+{\zeta }_{33}^{-14}-{\zeta }_{33}^6+{\zeta }_{33}^7+{\zeta }_{33}^{10}+{\zeta }_{33}^{13}$	${\zeta }_{33}^{-16}-{\zeta }_{33}^{-14}+1+{\zeta }_{33}^6-{\zeta }_{33}^7-{\zeta }_{33}^{10}+{\zeta }_{33}^{11}-{\zeta }_{33}^{13}$	${\zeta }_{33}^{-16}-{\zeta }_{33}^{-14}+1+{\zeta }_{33}^3-{\zeta }_{33}^5+{\zeta }_{33}^6-{\zeta }_{33}^7+{\zeta }_{33}^9-{\zeta }_{33}^{10}+{\zeta }_{33}^{12}-{\zeta }_{33}^{13}+{\zeta }_{33}^{15}-{\zeta }_{33}^{16}$
1980.57.5b4	C	$5$	$1$	$5{\zeta }_{33}^{11}$	$5{\zeta }_{33}^{-11}$	$-1$	$-{\zeta }_{33}^{-11}$	$-{\zeta }_{33}^{11}$	$0$	$0$	${\zeta }_{33}^{11}$	${\zeta }_{33}^{-11}$	$1$	${\zeta }_{33}^{11}$	${\zeta }_{33}^{-11}$	$-1-{\zeta }_{33}^3+{\zeta }_{33}^5-{\zeta }_{33}^9-{\zeta }_{33}^{12}-{\zeta }_{33}^{15}+{\zeta }_{33}^{16}$	${\zeta }_{33}^3-{\zeta }_{33}^5+{\zeta }_{33}^9+{\zeta }_{33}^{12}+{\zeta }_{33}^{15}-{\zeta }_{33}^{16}$	$0$	$0$	$0$	$0$	$-{\zeta }_{33}^{-16}+{\zeta }_{33}^{-14}-{\zeta }_{33}^6+{\zeta }_{33}^7+{\zeta }_{33}^{10}+{\zeta }_{33}^{13}$	$-{\zeta }_{33}^{-16}+{\zeta }_{33}^{-14}-1-{\zeta }_{33}^3+{\zeta }_{33}^5-{\zeta }_{33}^6+{\zeta }_{33}^7-{\zeta }_{33}^9+{\zeta }_{33}^{10}-{\zeta }_{33}^{11}-{\zeta }_{33}^{12}+{\zeta }_{33}^{13}-{\zeta }_{33}^{15}+{\zeta }_{33}^{16}$	${\zeta }_{33}^{-16}-{\zeta }_{33}^{-14}+1+{\zeta }_{33}^3-{\zeta }_{33}^5+{\zeta }_{33}^6-{\zeta }_{33}^7+{\zeta }_{33}^9-{\zeta }_{33}^{10}+{\zeta }_{33}^{12}-{\zeta }_{33}^{13}+{\zeta }_{33}^{15}-{\zeta }_{33}^{16}$	${\zeta }_{33}^{-16}-{\zeta }_{33}^{-14}+1+{\zeta }_{33}^6-{\zeta }_{33}^7-{\zeta }_{33}^{10}+{\zeta }_{33}^{11}-{\zeta }_{33}^{13}$
1980.57.10a	R	$10$	$2$	$10$	$10$	$1$	$1$	$1$	$0$	$0$	$2$	$2$	$-1$	$-1$	$-1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$-1$	$-1$	$-1$	$-1$
1980.57.10b	R	$10$	$-2$	$10$	$10$	$1$	$1$	$1$	$0$	$0$	$-2$	$-2$	$1$	$1$	$1$	$-1$	$-1$	$0$	$0$	$0$	$0$	$-1$	$-1$	$-1$	$-1$
1980.57.10c1	C	$10$	$2$	$10{\zeta }_3^{-1}$	$10{\zeta }_3$	$1$	${\zeta }_3$	${\zeta }_3^{-1}$	$0$	$0$	$2{\zeta }_3^{-1}$	$2{\zeta }_3$	$-1$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$	$-1$	$-1$	$0$	$0$	$0$	$0$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$
1980.57.10c2	C	$10$	$2$	$10{\zeta }_3$	$10{\zeta }_3^{-1}$	$1$	${\zeta }_3^{-1}$	${\zeta }_3$	$0$	$0$	$2{\zeta }_3$	$2{\zeta }_3^{-1}$	$-1$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$	$-1$	$-1$	$0$	$0$	$0$	$0$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$
1980.57.10d1	C	$10$	$-2$	$10{\zeta }_3^{-1}$	$10{\zeta }_3$	$1$	${\zeta }_3$	${\zeta }_3^{-1}$	$0$	$0$	$-2{\zeta }_3^{-1}$	$-2{\zeta }_3$	$1$	${\zeta }_3^{-1}$	${\zeta }_3$	$-1$	$-1$	$0$	$0$	$0$	$0$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$
1980.57.10d2	C	$10$	$-2$	$10{\zeta }_3$	$10{\zeta }_3^{-1}$	$1$	${\zeta }_3^{-1}$	${\zeta }_3$	$0$	$0$	$-2{\zeta }_3$	$-2{\zeta }_3^{-1}$	$1$	${\zeta }_3$	${\zeta }_3^{-1}$	$-1$	$-1$	$0$	$0$	$0$	$0$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$
1980.57.11a	R	$11$	$-1$	$11$	$11$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$-1$	$0$	$0$	$1$	$1$	$1$	$1$	$0$	$0$	$0$	$0$
1980.57.11b1	C	$11$	$-1$	$11{\zeta }_3^{-1}$	$11{\zeta }_3$	$-1$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$	$1$	$1$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$	$-1$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$	$0$	$0$	${\zeta }_3$	${\zeta }_3^{-1}$	${\zeta }_3^{-1}$	${\zeta }_3$	$0$	$0$	$0$	$0$
1980.57.11b2	C	$11$	$-1$	$11{\zeta }_3$	$11{\zeta }_3^{-1}$	$-1$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$	$1$	$1$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$	$-1$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$	$0$	$0$	${\zeta }_3^{-1}$	${\zeta }_3$	${\zeta }_3$	${\zeta }_3^{-1}$	$0$	$0$	$0$	$0$
1980.57.12a1	R	$12$	$0$	$12$	$12$	$0$	$0$	$0$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$0$	$0$	$0$	$0$	$0$	$1$	$1$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	$1$	$1$	$1$	$1$
1980.57.12a2	R	$12$	$0$	$12$	$12$	$0$	$0$	$0$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$0$	$0$	$0$	$0$	$0$	$1$	$1$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	$1$	$1$	$1$	$1$
1980.57.12b1	C	$12$	$0$	$12{\zeta }_{15}^{-5}$	$12{\zeta }_{15}^5$	$0$	$0$	$0$	${\zeta }_{15}^{-6}+{\zeta }_{15}^6$	${\zeta }_{15}^{-3}+{\zeta }_{15}^3$	$0$	$0$	$0$	$0$	$0$	$1$	$1$	$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$	$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$	${\zeta }_{15}+{\zeta }_{15}^4$	$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$	${\zeta }_{15}^5$	${\zeta }_{15}^{-5}$	${\zeta }_{15}^{-5}$	${\zeta }_{15}^5$
1980.57.12b2	C	$12$	$0$	$12{\zeta }_{15}^5$	$12{\zeta }_{15}^{-5}$	$0$	$0$	$0$	${\zeta }_{15}^{-6}+{\zeta }_{15}^6$	${\zeta }_{15}^{-3}+{\zeta }_{15}^3$	$0$	$0$	$0$	$0$	$0$	$1$	$1$	$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$	$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$	$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$	${\zeta }_{15}+{\zeta }_{15}^4$	${\zeta }_{15}^{-5}$	${\zeta }_{15}^5$	${\zeta }_{15}^5$	${\zeta }_{15}^{-5}$
1980.57.12b3	C	$12$	$0$	$12{\zeta }_{15}^{-5}$	$12{\zeta }_{15}^5$	$0$	$0$	$0$	${\zeta }_{15}^{-3}+{\zeta }_{15}^3$	${\zeta }_{15}^{-6}+{\zeta }_{15}^6$	$0$	$0$	$0$	$0$	$0$	$1$	$1$	$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$	${\zeta }_{15}+{\zeta }_{15}^4$	$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$	$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$	${\zeta }_{15}^5$	${\zeta }_{15}^{-5}$	${\zeta }_{15}^{-5}$	${\zeta }_{15}^5$
1980.57.12b4	C	$12$	$0$	$12{\zeta }_{15}^5$	$12{\zeta }_{15}^{-5}$	$0$	$0$	$0$	${\zeta }_{15}^{-3}+{\zeta }_{15}^3$	${\zeta }_{15}^{-6}+{\zeta }_{15}^6$	$0$	$0$	$0$	$0$	$0$	$1$	$1$	${\zeta }_{15}+{\zeta }_{15}^4$	$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$	$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$	$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$	${\zeta }_{15}^{-5}$	${\zeta }_{15}^5$	${\zeta }_{15}^5$	${\zeta }_{15}^{-5}$