Galois group: 30T16

• Label: 30T16
• Degree: $30$
• Order: $90$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• pp-group: no
• Group: $C_3\times D_{15}$

Group invariants

Abstract group:		$C_3\times D_{15}$
Order:		$90=2 \cdot 3^{2} \cdot 5$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

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

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$
$3$:	$C_3$
$6$:	$S_3$, $C_6$
$10$:	$D_{5}$
$18$:	$S_3\times C_3$
$30$:	$D_{15}$, $D_5\times C_3$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: None

Degree 5: $D_{5}$

Degree 6: $S_3\times C_3$

Degree 10: $D_5$

Degree 15: None

Low degree siblings

45T5

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	$1^{30}$	$1$	$1$	$0$	$()$
2A	$2^{15}$	$15$	$2$	$15$	$( 1,29)( 2,30)( 3,28)( 4,26)( 5,27)( 6,25)( 7,22)( 8,23)( 9,24)(10,20)(11,21)(12,19)(13,17)(14,18)(15,16)$
3A1	$3^{10}$	$1$	$3$	$20$	$( 1, 3, 2)( 4, 6, 5)( 7, 9, 8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,27,26)(28,30,29)$
3A-1	$3^{10}$	$1$	$3$	$20$	$( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,17,18)(19,20,21)(22,23,24)(25,26,27)(28,29,30)$
3B	$3^{10}$	$2$	$3$	$20$	$( 1, 3, 2)( 4, 6, 5)( 7, 9, 8)(10,12,11)(13,15,14)(16,17,18)(19,20,21)(22,23,24)(25,26,27)(28,29,30)$
3C1	$3^{5},1^{15}$	$2$	$3$	$10$	$( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)$
3C-1	$3^{5},1^{15}$	$2$	$3$	$10$	$( 1, 3, 2)( 4, 6, 5)( 7, 9, 8)(10,12,11)(13,15,14)$
5A1	$5^{6}$	$2$	$5$	$24$	$( 1, 9,14, 4,10)( 2, 7,15, 5,11)( 3, 8,13, 6,12)(16,22,30,21,27)(17,23,28,19,25)(18,24,29,20,26)$
5A2	$5^{6}$	$2$	$5$	$24$	$( 1,14,10, 9, 4)( 2,15,11, 7, 5)( 3,13,12, 8, 6)(16,30,27,22,21)(17,28,25,23,19)(18,29,26,24,20)$
6A1	$6^{5}$	$15$	$6$	$25$	$( 1,28, 2,29, 3,30)( 4,25, 5,26, 6,27)( 7,24, 8,22, 9,23)(10,19,11,20,12,21)(13,16,14,17,15,18)$
6A-1	$6^{5}$	$15$	$6$	$25$	$( 1,30, 3,29, 2,28)( 4,27, 6,26, 5,25)( 7,23, 9,22, 8,24)(10,21,12,20,11,19)(13,18,15,17,14,16)$
15A1	$15^{2}$	$2$	$15$	$28$	$( 1,15,12, 9, 5, 3,14,11, 8, 4, 2,13,10, 7, 6)(16,29,25,22,20,17,30,26,23,21,18,28,27,24,19)$
15A2	$15^{2}$	$2$	$15$	$28$	$( 1,12, 5,14, 8, 2,10, 6,15, 9, 3,11, 4,13, 7)(16,25,20,30,23,18,27,19,29,22,17,26,21,28,24)$
15A4	$15^{2}$	$2$	$15$	$28$	$( 1, 5, 8,10,15, 3, 4, 7,12,14, 2, 6, 9,11,13)(16,20,23,27,29,17,21,24,25,30,18,19,22,26,28)$
15A7	$15^{2}$	$2$	$15$	$28$	$( 1,11, 6,14, 7, 3,10, 5,13, 9, 2,12, 4,15, 8)(16,26,19,30,24,17,27,20,28,22,18,25,21,29,23)$
15B1	$15^{2}$	$2$	$15$	$28$	$( 1, 7,13, 4,11, 3, 9,15, 6,10, 2, 8,14, 5,12)(16,23,29,21,25,18,22,28,20,27,17,24,30,19,26)$
15B-1	$15^{2}$	$2$	$15$	$28$	$( 1, 8,15, 4,12, 2, 9,13, 5,10, 3, 7,14, 6,11)(16,24,28,21,26,17,22,29,19,27,18,23,30,20,25)$
15B2	$15^{2}$	$2$	$15$	$28$	$( 1,13,11, 9, 6, 2,14,12, 7, 4, 3,15,10, 8, 5)(16,29,25,22,20,17,30,26,23,21,18,28,27,24,19)$
15B-2	$15^{2}$	$2$	$15$	$28$	$( 1,15,12, 9, 5, 3,14,11, 8, 4, 2,13,10, 7, 6)(16,28,26,22,19,18,30,25,24,21,17,29,27,23,20)$
15C1	$15,5^{3}$	$2$	$15$	$26$	$( 1,13,11, 9, 6, 2,14,12, 7, 4, 3,15,10, 8, 5)(16,30,27,22,21)(17,28,25,23,19)(18,29,26,24,20)$
15C-1	$15,5^{3}$	$2$	$15$	$26$	$( 1,14,10, 9, 4)( 2,15,11, 7, 5)( 3,13,12, 8, 6)(16,28,26,22,19,18,30,25,24,21,17,29,27,23,20)$
15C2	$15,5^{3}$	$2$	$15$	$26$	$( 1,11, 6,14, 7, 3,10, 5,13, 9, 2,12, 4,15, 8)(16,27,21,30,22)(17,25,19,28,23)(18,26,20,29,24)$
15C-2	$15,5^{3}$	$2$	$15$	$26$	$( 1,10, 4,14, 9)( 2,11, 5,15, 7)( 3,12, 6,13, 8)(16,26,19,30,24,17,27,20,28,22,18,25,21,29,23)$
15C4	$15,5^{3}$	$2$	$15$	$26$	$( 1, 6, 7,10,13, 2, 4, 8,11,14, 3, 5, 9,12,15)(16,21,22,27,30)(17,19,23,25,28)(18,20,24,26,29)$
15C-4	$15,5^{3}$	$2$	$15$	$26$	$( 1, 4, 9,10,14)( 2, 5, 7,11,15)( 3, 6, 8,12,13)(16,19,24,27,28,18,21,23,26,30,17,20,22,25,29)$
15C7	$15,5^{3}$	$2$	$15$	$26$	$( 1,12, 5,14, 8, 2,10, 6,15, 9, 3,11, 4,13, 7)(16,27,21,30,22)(17,25,19,28,23)(18,26,20,29,24)$
15C-7	$15,5^{3}$	$2$	$15$	$26$	$( 1,10, 4,14, 9)( 2,11, 5,15, 7)( 3,12, 6,13, 8)(16,25,20,30,23,18,27,19,29,22,17,26,21,28,24)$

Malle's constant $a(G)$:     $1/10$

Character table

1A

2A

3A1

3A-1

3B

3C1

3C-1

5A1

5A2

6A1

6A-1

15A1

15A2

15A4

15A7

15B1

15B-1

15B2

15B-2

15C1

15C-1

15C2

15C-2

15C4

15C-4

15C7

15C-7

Size

1

15

1

1

2

2

2

2

2

15

15

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2 P

1A

1A

3A-1

3A1

3B

3C-1

3C1

5A2

5A1

3A-1

3A1

15A2

15A4

15A7

15A1

15B2

15B-2

15B1

15B-1

15C2

15C-2

15C4

15C-4

15C-7

15C7

15C-1

15C1

3 P

1A

2A

1A

1A

1A

1A

1A

5A2

5A1

2A

2A

5A1

5A2

5A1

5A2

5A2

5A2

5A1

5A1

5A1

5A1

5A2

5A2

5A1

5A1

5A2

5A2

5 P

1A

2A

3A-1

3A1

3B

3C-1

3C1

1A

1A

6A-1

6A1

3B

3B

3B

3B

3A1

3A-1

3A-1

3A1

3C1

3C-1

3C-1

3C1

3C1

3C-1

3C1

3C-1

Type

90.7.1a

R

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

90.7.1b

R

$1$

$-1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$-1$

$-1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

90.7.1c1

C

$1$

$1$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

$1$

${\zeta }_3^{-1}$

$1$

$1$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

$1$

$1$

${\zeta }_3$

$1$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

$1$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

90.7.1c2

C

$1$

$1$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

$1$

${\zeta }_3$

$1$

$1$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

$1$

$1$

${\zeta }_3^{-1}$

$1$

${\zeta }_3$

${\zeta }_3$

$1$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

90.7.1d1

C

$1$

$-1$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

$1$

${\zeta }_3^{-1}$

$1$

$1$

$-{\zeta }_3^{-1}$

$-{\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

$1$

$1$

${\zeta }_3$

$1$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

$1$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

90.7.1d2

C

$1$

$-1$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

$1$

${\zeta }_3$

$1$

$1$

$-{\zeta }_3$

$-{\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3$

${\zeta }_3^{-1}$

$1$

$1$

${\zeta }_3^{-1}$

$1$

${\zeta }_3$

${\zeta }_3$

$1$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

${\zeta }_3^{-1}$

${\zeta }_3^{-1}$

${\zeta }_3$

90.7.2a

R

$2$

$0$

$2$

$2$

$-1$

$-1$

$-1$

$2$

$2$

$0$

$0$

$-1$

$-1$

$2$

$-1$

$-1$

$-1$

$-1$

$2$

$-1$

$-1$

$2$

$-1$

$-1$

$-1$

$-1$

$2$

90.7.2b1

R

$2$

$0$

$2$

$2$

$2$

$2$

$2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

$0$

$0$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

90.7.2b2

R

$2$

$0$

$2$

$2$

$2$

$2$

$2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

$0$

$0$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-2}+{\zeta }_5^2$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-1}+{\zeta }_5$

${\zeta }_5^{-2}+{\zeta }_5^2$

90.7.2c1

C

$2$

$0$

$2{\zeta }_3^{-1}$

$2{\zeta }_3$

$-{\zeta }_3$

$-1$

$-{\zeta }_3^{-1}$

$2$

$2$

$0$

$0$

$-{\zeta }_3^{-1}$

$-{\zeta }_3^{-1}$

$2{\zeta }_3$

$-1$

$-1$

$-{\zeta }_3$

$-1$

$2{\zeta }_3^{-1}$

$-{\zeta }_3^{-1}$

$-1$

$2{\zeta }_3$

$-{\zeta }_3$

$-{\zeta }_3^{-1}$

$-{\zeta }_3$

$-{\zeta }_3$

$2{\zeta }_3^{-1}$

90.7.2c2

C

$2$

$0$

$2{\zeta }_3$

$2{\zeta }_3^{-1}$

$-{\zeta }_3^{-1}$

$-1$

$-{\zeta }_3$

$2$

$2$

$0$

$0$

$-{\zeta }_3$

$-{\zeta }_3$

$2{\zeta }_3^{-1}$

$-1$

$-1$

$-{\zeta }_3^{-1}$

$-1$

$2{\zeta }_3$

$-{\zeta }_3$

$-1$

$2{\zeta }_3^{-1}$

$-{\zeta }_3^{-1}$

$-{\zeta }_3$

$-{\zeta }_3^{-1}$

$-{\zeta }_3^{-1}$

$2{\zeta }_3$

90.7.2d1

R

$2$

$0$

$2$

$2$

$-1$

$-1$

$-1$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

$0$

$0$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

90.7.2d2

R

$2$

$0$

$2$

$2$

$-1$

$-1$

$-1$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

$0$

$0$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

90.7.2d3

R

$2$

$0$

$2$

$2$

$-1$

$-1$

$-1$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

$0$

$0$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

90.7.2d4

R

$2$

$0$

$2$

$2$

$-1$

$-1$

$-1$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

$0$

$0$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

90.7.2e1

C

$2$

$0$

$2{\zeta }_{15}^{-5}$

$2{\zeta }_{15}^5$

$2{\zeta }_{15}^5$

$2$

$2{\zeta }_{15}^{-5}$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

$0$

$0$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

${\zeta }_{15}+{\zeta }_{15}^4$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}+{\zeta }_{15}^4$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

${\zeta }_{15}+{\zeta }_{15}^4$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

90.7.2e2

C

$2$

$0$

$2{\zeta }_{15}^5$

$2{\zeta }_{15}^{-5}$

$2{\zeta }_{15}^{-5}$

$2$

$2{\zeta }_{15}^5$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

$0$

$0$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

${\zeta }_{15}+{\zeta }_{15}^4$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

${\zeta }_{15}+{\zeta }_{15}^4$

${\zeta }_{15}+{\zeta }_{15}^4$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

90.7.2e3

C

$2$

$0$

$2{\zeta }_{15}^{-5}$

$2{\zeta }_{15}^5$

$2{\zeta }_{15}^5$

$2$

$2{\zeta }_{15}^{-5}$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

$0$

$0$

${\zeta }_{15}+{\zeta }_{15}^4$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

${\zeta }_{15}+{\zeta }_{15}^4$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

${\zeta }_{15}+{\zeta }_{15}^4$

90.7.2e4

C

$2$

$0$

$2{\zeta }_{15}^5$

$2{\zeta }_{15}^{-5}$

$2{\zeta }_{15}^{-5}$

$2$

$2{\zeta }_{15}^5$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

$0$

$0$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}+{\zeta }_{15}^4$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}+{\zeta }_{15}^4$

${\zeta }_{15}+{\zeta }_{15}^4$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

90.7.2f1

C

$2$

$0$

$2{\zeta }_{15}^{-5}$

$2{\zeta }_{15}^5$

$-{\zeta }_{15}^5$

$-1$

$-{\zeta }_{15}^{-5}$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

$0$

$0$

$-1+{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5$

$1-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4+2{\zeta }_{15}^6-{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^3+{\zeta }_{15}^7$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}+{\zeta }_{15}^4$

${\zeta }_{15}^2+{\zeta }_{15}^3$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^4+{\zeta }_{15}^5-2{\zeta }_{15}^7$

$-1-{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-2{\zeta }_{15}^6+{\zeta }_{15}^7$

${\zeta }_{15}^4+{\zeta }_{15}^6$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-{\zeta }_{15}^6+{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

90.7.2f2

C

$2$

$0$

$2{\zeta }_{15}^5$

$2{\zeta }_{15}^{-5}$

$-{\zeta }_{15}^{-5}$

$-1$

$-{\zeta }_{15}^5$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

$0$

$0$

${\zeta }_{15}^3+{\zeta }_{15}^7$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-{\zeta }_{15}^6+{\zeta }_{15}^7$

${\zeta }_{15}+{\zeta }_{15}^4$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

$-1+{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^4+{\zeta }_{15}^5-2{\zeta }_{15}^7$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

${\zeta }_{15}^2+{\zeta }_{15}^3$

${\zeta }_{15}^4+{\zeta }_{15}^6$

$-1-{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-2{\zeta }_{15}^6+{\zeta }_{15}^7$

$1-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4+2{\zeta }_{15}^6-{\zeta }_{15}^7$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

90.7.2f3

C

$2$

$0$

$2{\zeta }_{15}^{-5}$

$2{\zeta }_{15}^5$

$-{\zeta }_{15}^5$

$-1$

$-{\zeta }_{15}^{-5}$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

$0$

$0$

${\zeta }_{15}^2+{\zeta }_{15}^3$

$-1-{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-2{\zeta }_{15}^6+{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

$1-{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^4+{\zeta }_{15}^5-2{\zeta }_{15}^7$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}+{\zeta }_{15}^4$

$-1+{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

${\zeta }_{15}^3+{\zeta }_{15}^7$

$1-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4+2{\zeta }_{15}^6-{\zeta }_{15}^7$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-{\zeta }_{15}^6+{\zeta }_{15}^7$

${\zeta }_{15}^4+{\zeta }_{15}^6$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

90.7.2f4

C

$2$

$0$

$2{\zeta }_{15}^5$

$2{\zeta }_{15}^{-5}$

$-{\zeta }_{15}^{-5}$

$-1$

$-{\zeta }_{15}^5$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

$0$

$0$

$1-{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^4+{\zeta }_{15}^5-2{\zeta }_{15}^7$

${\zeta }_{15}^4+{\zeta }_{15}^6$

${\zeta }_{15}+{\zeta }_{15}^4$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}^2+{\zeta }_{15}^3$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

${\zeta }_{15}^3+{\zeta }_{15}^7$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

$-1+{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-{\zeta }_{15}^6+{\zeta }_{15}^7$

$1-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4+2{\zeta }_{15}^6-{\zeta }_{15}^7$

$-1-{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-2{\zeta }_{15}^6+{\zeta }_{15}^7$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

90.7.2f5

C

$2$

$0$

$2{\zeta }_{15}^{-5}$

$2{\zeta }_{15}^5$

$-{\zeta }_{15}^5$

$-1$

$-{\zeta }_{15}^{-5}$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

$0$

$0$

$-1-{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-2{\zeta }_{15}^6+{\zeta }_{15}^7$

$-1+{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^4+{\zeta }_{15}^6$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

$1-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4+2{\zeta }_{15}^6-{\zeta }_{15}^7$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-{\zeta }_{15}^6+{\zeta }_{15}^7$

${\zeta }_{15}^2+{\zeta }_{15}^3$

$1-{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^4+{\zeta }_{15}^5-2{\zeta }_{15}^7$

${\zeta }_{15}^3+{\zeta }_{15}^7$

${\zeta }_{15}+{\zeta }_{15}^4$

90.7.2f6

C

$2$

$0$

$2{\zeta }_{15}^5$

$2{\zeta }_{15}^{-5}$

$-{\zeta }_{15}^{-5}$

$-1$

$-{\zeta }_{15}^5$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

$0$

$0$

${\zeta }_{15}^4+{\zeta }_{15}^6$

${\zeta }_{15}^3+{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

$-1-{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-2{\zeta }_{15}^6+{\zeta }_{15}^7$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-{\zeta }_{15}^6+{\zeta }_{15}^7$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

${\zeta }_{15}+{\zeta }_{15}^4$

$1-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4+2{\zeta }_{15}^6-{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^4+{\zeta }_{15}^5-2{\zeta }_{15}^7$

${\zeta }_{15}^2+{\zeta }_{15}^3$

$-1+{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

90.7.2f7

C

$2$

$0$

$2{\zeta }_{15}^{-5}$

$2{\zeta }_{15}^5$

$-{\zeta }_{15}^5$

$-1$

$-{\zeta }_{15}^{-5}$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

$0$

$0$

$1-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4+2{\zeta }_{15}^6-{\zeta }_{15}^7$

${\zeta }_{15}^2+{\zeta }_{15}^3$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-{\zeta }_{15}^6+{\zeta }_{15}^7$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

$-1-{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-2{\zeta }_{15}^6+{\zeta }_{15}^7$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

${\zeta }_{15}^4+{\zeta }_{15}^6$

$-1+{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5$

${\zeta }_{15}^3+{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^4+{\zeta }_{15}^5-2{\zeta }_{15}^7$

${\zeta }_{15}+{\zeta }_{15}^4$

90.7.2f8

C

$2$

$0$

$2{\zeta }_{15}^5$

$2{\zeta }_{15}^{-5}$

$-{\zeta }_{15}^{-5}$

$-1$

$-{\zeta }_{15}^5$

${\zeta }_{15}^{-3}+{\zeta }_{15}^3$

${\zeta }_{15}^{-6}+{\zeta }_{15}^6$

$0$

$0$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-{\zeta }_{15}^6+{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^4+{\zeta }_{15}^5-2{\zeta }_{15}^7$

$1-{\zeta }_{15}-{\zeta }_{15}^4+{\zeta }_{15}^5$

${\zeta }_{15}^{-2}+{\zeta }_{15}^2$

${\zeta }_{15}^{-7}+{\zeta }_{15}^7$

$1-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4+2{\zeta }_{15}^6-{\zeta }_{15}^7$

${\zeta }_{15}^{-4}+{\zeta }_{15}^4$

$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5+{\zeta }_{15}^7$

${\zeta }_{15}^4+{\zeta }_{15}^6$

${\zeta }_{15}^{-1}+{\zeta }_{15}$

${\zeta }_{15}+{\zeta }_{15}^4$

$-1-{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3-2{\zeta }_{15}^6+{\zeta }_{15}^7$

${\zeta }_{15}^3+{\zeta }_{15}^7$

$-1+{\zeta }_{15}-{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4-{\zeta }_{15}^5$

${\zeta }_{15}^2+{\zeta }_{15}^3$

$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4-{\zeta }_{15}^7$

Regular extensions

Data not computed