LMFDB - Galois group: 41T2

Show commands: Magma

magma: G := TransitiveGroup(41, 2);

Group action invariants

Degree $n$:	$41$	magma: t, n := TransitiveGroupIdentification(G); n;
Transitive number $t$:	$2$	magma: t, n := TransitiveGroupIdentification(G); t;
Group:	$D_{41}$
Parity:	$1$	magma: IsEven(G);
Primitive:	yes	magma: IsPrimitive(G);
magma: NilpotencyClass(G);
$\card{\Aut(F/K)}$:	$1$	magma: Order(Centralizer(SymmetricGroup(n), G));
Generators:	(1,40)(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)	magma: Generators(G);

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

\|G/N\|	Galois groups for stem field(s)
$2$:	$C_2$

Subfields

Prime degree - none

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	$1^{41}$	$1$	$1$	$0$	$()$
2A	$2^{20},1$	$41$	$2$	$20$	$( 2,41)( 3,40)( 4,39)( 5,38)( 6,37)( 7,36)( 8,35)( 9,34)(10,33)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)$
41A1	$41$	$2$	$41$	$40$	$( 1,30,18, 6,35,23,11,40,28,16, 4,33,21, 9,38,26,14, 2,31,19, 7,36,24,12,41,29,17, 5,34,22,10,39,27,15, 3,32,20, 8,37,25,13)$
41A2	$41$	$2$	$41$	$40$	$( 1,26,10,35,19, 3,28,12,37,21, 5,30,14,39,23, 7,32,16,41,25, 9,34,18, 2,27,11,36,20, 4,29,13,38,22, 6,31,15,40,24, 8,33,17)$
41A3	$41$	$2$	$41$	$40$	$( 1,22, 2,23, 3,24, 4,25, 5,26, 6,27, 7,28, 8,29, 9,30,10,31,11,32,12,33,13,34,14,35,15,36,16,37,17,38,18,39,19,40,20,41,21)$
41A4	$41$	$2$	$41$	$40$	$( 1,18,35,11,28, 4,21,38,14,31, 7,24,41,17,34,10,27, 3,20,37,13,30, 6,23,40,16,33, 9,26, 2,19,36,12,29, 5,22,39,15,32, 8,25)$
41A5	$41$	$2$	$41$	$40$	$( 1,14,27,40,12,25,38,10,23,36, 8,21,34, 6,19,32, 4,17,30, 2,15,28,41,13,26,39,11,24,37, 9,22,35, 7,20,33, 5,18,31, 3,16,29)$
41A6	$41$	$2$	$41$	$40$	$( 1,10,19,28,37, 5,14,23,32,41, 9,18,27,36, 4,13,22,31,40, 8,17,26,35, 3,12,21,30,39, 7,16,25,34, 2,11,20,29,38, 6,15,24,33)$
41A7	$41$	$2$	$41$	$40$	$( 1, 6,11,16,21,26,31,36,41, 5,10,15,20,25,30,35,40, 4, 9,14,19,24,29,34,39, 3, 8,13,18,23,28,33,38, 2, 7,12,17,22,27,32,37)$
41A8	$41$	$2$	$41$	$40$	$( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)$
41A9	$41$	$2$	$41$	$40$	$( 1,39,36,33,30,27,24,21,18,15,12, 9, 6, 3,41,38,35,32,29,26,23,20,17,14,11, 8, 5, 2,40,37,34,31,28,25,22,19,16,13,10, 7, 4)$
41A10	$41$	$2$	$41$	$40$	$( 1,35,28,21,14, 7,41,34,27,20,13, 6,40,33,26,19,12, 5,39,32,25,18,11, 4,38,31,24,17,10, 3,37,30,23,16, 9, 2,36,29,22,15, 8)$
41A11	$41$	$2$	$41$	$40$	$( 1,31,20, 9,39,28,17, 6,36,25,14, 3,33,22,11,41,30,19, 8,38,27,16, 5,35,24,13, 2,32,21,10,40,29,18, 7,37,26,15, 4,34,23,12)$
41A12	$41$	$2$	$41$	$40$	$( 1,27,12,38,23, 8,34,19, 4,30,15,41,26,11,37,22, 7,33,18, 3,29,14,40,25,10,36,21, 6,32,17, 2,28,13,39,24, 9,35,20, 5,31,16)$
41A13	$41$	$2$	$41$	$40$	$( 1,23, 4,26, 7,29,10,32,13,35,16,38,19,41,22, 3,25, 6,28, 9,31,12,34,15,37,18,40,21, 2,24, 5,27, 8,30,11,33,14,36,17,39,20)$
41A14	$41$	$2$	$41$	$40$	$( 1,19,37,14,32, 9,27, 4,22,40,17,35,12,30, 7,25, 2,20,38,15,33,10,28, 5,23,41,18,36,13,31, 8,26, 3,21,39,16,34,11,29, 6,24)$
41A15	$41$	$2$	$41$	$40$	$( 1,15,29, 2,16,30, 3,17,31, 4,18,32, 5,19,33, 6,20,34, 7,21,35, 8,22,36, 9,23,37,10,24,38,11,25,39,12,26,40,13,27,41,14,28)$
41A16	$41$	$2$	$41$	$40$	$( 1,11,21,31,41,10,20,30,40, 9,19,29,39, 8,18,28,38, 7,17,27,37, 6,16,26,36, 5,15,25,35, 4,14,24,34, 3,13,23,33, 2,12,22,32)$
41A17	$41$	$2$	$41$	$40$	$( 1, 7,13,19,25,31,37, 2, 8,14,20,26,32,38, 3, 9,15,21,27,33,39, 4,10,16,22,28,34,40, 5,11,17,23,29,35,41, 6,12,18,24,30,36)$
41A18	$41$	$2$	$41$	$40$	$( 1, 3, 5, 7, 9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41, 2, 4, 6, 8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40)$
41A19	$41$	$2$	$41$	$40$	$( 1,38,34,30,26,22,18,14,10, 6, 2,39,35,31,27,23,19,15,11, 7, 3,40,36,32,28,24,20,16,12, 8, 4,41,37,33,29,25,21,17,13, 9, 5)$
41A20	$41$	$2$	$41$	$40$	$( 1,34,26,18,10, 2,35,27,19,11, 3,36,28,20,12, 4,37,29,21,13, 5,38,30,22,14, 6,39,31,23,15, 7,40,32,24,16, 8,41,33,25,17, 9)$

magma: ConjugacyClasses(G);

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

Group invariants

Order:	$82=2 \cdot 41$	magma: Order(G);
Cyclic:	no	magma: IsCyclic(G);
Abelian:	no	magma: IsAbelian(G);
Solvable:	yes	magma: IsSolvable(G);
Nilpotency class:	not nilpotent
Label:	82.1	magma: IdentifyGroup(G);
Character table:

Size

41A6

41A8

41A10

41A12

41A14

41A16

41A18

41A20

41A19

41A17

41A15

41A13

41A11

41A9

41A7

41A5

41A3

41A1

41A2

41A4

41 P

41A15

41A20

41A16

41A11

41A6

41A1

41A4

41A9

41A14

41A19

41A17

41A12

41A7

41A2

41A3

41A8

41A13

41A18

41A5

41A10

Type

82.1.1a

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

82.1.1b

1

- 1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

82.1.2a1

2

0

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 10} + ζ_{41}^{10}

82.1.2a2

2

0

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 11} + ζ_{41}^{11}

82.1.2a3

2

0

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 9} + ζ_{41}^{9}

82.1.2a4

2

0

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 12} + ζ_{41}^{12}

82.1.2a5

2

0

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 8} + ζ_{41}^{8}

82.1.2a6

2

0

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 13} + ζ_{41}^{13}

82.1.2a7

2

0

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 7} + ζ_{41}^{7}

82.1.2a8

2

0

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 14} + ζ_{41}^{14}

82.1.2a9

2

0

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 6} + ζ_{41}^{6}

82.1.2a10

2

0

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 15} + ζ_{41}^{15}

82.1.2a11

2

0

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 5} + ζ_{41}^{5}

82.1.2a12

2

0

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 16} + ζ_{41}^{16}

82.1.2a13

2

0

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 4} + ζ_{41}^{4}

82.1.2a14

2

0

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 17} + ζ_{41}^{17}

82.1.2a15

2

0

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 3} + ζ_{41}^{3}

82.1.2a16

2

0

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 18} + ζ_{41}^{18}

82.1.2a17

2

0

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 2} + ζ_{41}^{2}

82.1.2a18

2

0

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 19} + ζ_{41}^{19}

82.1.2a19

2

0

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 20} + ζ_{41}^{20}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 1} + ζ_{41}

82.1.2a20

2

0

ζ_{41}^{- 1} + ζ_{41}

ζ_{41}^{- 2} + ζ_{41}^{2}

ζ_{41}^{- 3} + ζ_{41}^{3}

ζ_{41}^{- 4} + ζ_{41}^{4}

ζ_{41}^{- 5} + ζ_{41}^{5}

ζ_{41}^{- 6} + ζ_{41}^{6}

ζ_{41}^{- 7} + ζ_{41}^{7}

ζ_{41}^{- 8} + ζ_{41}^{8}

ζ_{41}^{- 9} + ζ_{41}^{9}

ζ_{41}^{- 10} + ζ_{41}^{10}

ζ_{41}^{- 11} + ζ_{41}^{11}

ζ_{41}^{- 12} + ζ_{41}^{12}

ζ_{41}^{- 13} + ζ_{41}^{13}

ζ_{41}^{- 14} + ζ_{41}^{14}

ζ_{41}^{- 15} + ζ_{41}^{15}

ζ_{41}^{- 16} + ζ_{41}^{16}

ζ_{41}^{- 17} + ζ_{41}^{17}

ζ_{41}^{- 18} + ζ_{41}^{18}

ζ_{41}^{- 19} + ζ_{41}^{19}

ζ_{41}^{- 20} + ζ_{41}^{20}

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	41T2
Degree	$41$
Order	$82$
Cyclic	no
Abelian	no
Solvable	yes
Primitive	yes
$p$-group	no
Group:	$D_{41}$