Galois group: 35T22

• Label: 35T22
• Degree: $35$
• Order: $1260$
• Cyclic: no
• Abelian: no
• Solvable: no
• Primitive: no
• $p$-group: no
• Group: $C_7:\GL(2,4)$

Group invariants

Abstract group:		$C_7:\GL(2,4)$
Order:		$1260=2^{2} \cdot 3^{2} \cdot 5 \cdot 7$
Cyclic:		no
Abelian:		no
Solvable:		no
Nilpotency class:		not nilpotent

Group action invariants

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

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$3$:	$C_3$
$21$:	$C_7:C_3$
$60$:	$A_5$
$180$:	$\GL(2,4)$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $A_5$

Degree 7: $C_7:C_3$

Low degree siblings

42T197

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	$1^{35}$	$1$	$1$	$0$	$()$
2A	$2^{14},1^{7}$	$15$	$2$	$14$	$( 1, 4)( 2, 5)( 6,10)( 7, 9)(11,13)(12,15)(17,20)(18,19)(21,22)(23,24)(26,30)(27,28)(32,34)(33,35)$
3A1	$3^{10},1^{5}$	$7$	$3$	$20$	$( 1,28,24)( 2,30,21)( 3,29,25)( 4,27,23)( 5,26,22)( 6,15,34)( 7,13,35)( 8,14,31)( 9,11,33)(10,12,32)$
3A-1	$3^{10},1^{5}$	$7$	$3$	$20$	$( 1,24,28)( 2,21,30)( 3,25,29)( 4,23,27)( 5,22,26)( 6,34,15)( 7,35,13)( 8,31,14)( 9,33,11)(10,32,12)$
3B	$3^{7},1^{14}$	$20$	$3$	$14$	$( 1, 5, 3)( 7,10, 8)(12,14,13)(16,20,18)(22,25,24)(26,29,28)(31,35,32)$
3C1	$3^{11},1^{2}$	$140$	$3$	$22$	$( 1,20, 7)( 2,17, 8)( 3,19, 9)( 4,16, 6)( 5,18,10)(11,25,30)(12,22,26)(13,24,28)(14,21,27)(15,23,29)(31,34,33)$
3C-1	$3^{11},1^{2}$	$140$	$3$	$22$	$( 1, 7,20)( 2, 8,17)( 3, 9,19)( 4, 6,16)( 5,10,18)(11,30,25)(12,26,22)(13,28,24)(14,27,21)(15,29,23)(31,33,34)$
5A1	$5^{7}$	$12$	$5$	$28$	$( 1, 5, 3, 4, 2)( 6, 7,10, 8, 9)(11,15,13,12,14)(16,17,19,20,18)(21,24,22,25,23)(26,29,27,30,28)(31,33,34,35,32)$
5A2	$5^{7}$	$12$	$5$	$28$	$( 1, 4, 5, 2, 3)( 6, 8, 7, 9,10)(11,12,15,14,13)(16,20,17,18,19)(21,25,24,23,22)(26,30,29,28,27)(31,35,33,32,34)$
6A1	$6^{4},3^{2},2^{2},1$	$105$	$6$	$26$	$( 1, 9,20, 4, 7,17)( 2,10,19, 5, 6,18)( 3, 8,16)(11,28,23,13,27,24)(12,30,22,15,26,21)(14,29,25)(32,34)(33,35)$
6A-1	$6^{4},3^{2},2^{2},1$	$105$	$6$	$26$	$( 1,17, 7, 4,20, 9)( 2,18, 6, 5,19,10)( 3,16, 8)(11,24,27,13,23,28)(12,21,26,15,22,30)(14,25,29)(32,34)(33,35)$
7A1	$7^{5}$	$3$	$7$	$30$	$( 1,13,24,35, 7,20,28)( 2,15,21,34, 6,19,30)( 3,14,25,31, 8,16,29)( 4,11,23,33, 9,17,27)( 5,12,22,32,10,18,26)$
7A-1	$7^{5}$	$3$	$7$	$30$	$( 1,35,28,24,20,13, 7)( 2,34,30,21,19,15, 6)( 3,31,29,25,16,14, 8)( 4,33,27,23,17,11, 9)( 5,32,26,22,18,12,10)$
14A1	$14^{2},7$	$45$	$14$	$32$	$( 1,15,24,34, 7,19,28, 2,13,21,35, 6,20,30)( 3,12,25,32, 8,18,29, 5,14,22,31,10,16,26)( 4,11,23,33, 9,17,27)$
14A-1	$14^{2},7$	$45$	$14$	$32$	$( 1,19,35,15,28, 6,24, 2,20,34,13,30, 7,21)( 3,18,31,12,29,10,25, 5,16,32,14,26, 8,22)( 4,17,33,11,27, 9,23)$
15A1	$15^{2},5$	$84$	$15$	$32$	$( 1,22,29, 4,21,28, 5,25,27, 2,24,26, 3,23,30)( 6,35,12, 8,33,15, 7,32,14, 9,34,13,10,31,11)(16,17,19,20,18)$
15A-1	$15^{2},5$	$84$	$15$	$32$	$( 1,25,30, 5,23,28, 3,21,26, 4,24,29, 2,22,27)( 6,32,11, 7,31,15,10,33,13, 8,34,12, 9,35,14)(16,19,18,17,20)$
15A2	$15^{2},5$	$84$	$15$	$32$	$( 1,26,25, 4,30,24, 5,29,23, 2,28,22, 3,27,21)( 6,13,32, 8,11,34, 7,12,31, 9,15,35,10,14,33)(16,17,19,20,18)$
15A-2	$15^{2},5$	$84$	$15$	$32$	$( 1,29,21, 5,27,24, 3,30,22, 4,28,25, 2,26,23)( 6,12,33, 7,14,34,10,11,35, 8,15,32, 9,13,31)(16,19,18,17,20)$
21A1	$21,7^{2}$	$60$	$21$	$32$	$( 1, 8,12,20,25,26,35, 3,10,13,16,22,28,31, 5, 7,14,18,24,29,32)( 2, 6,15,19,21,30,34)( 4, 9,11,17,23,27,33)$
21A-1	$21,7^{2}$	$60$	$21$	$32$	$( 1,18,31,13,26, 8,24, 5,16,35,12,29, 7,22, 3,20,32,14,28,10,25)( 2,19,34,15,30, 6,21)( 4,17,33,11,27, 9,23)$
35A1	$35$	$36$	$35$	$34$	$( 1,26,19, 8,33,24,12, 2,29,17, 7,32,21,14, 4,28,18, 6,31,23,13, 5,30,16, 9,35,22,15, 3,27,20,10,34,25,11)$
35A-1	$35$	$36$	$35$	$34$	$( 1, 8,12,17,21,28,31, 5, 9,15,20,25,26,33, 2, 7,14,18,23,30,35, 3,10,11,19,24,29,32, 4, 6,13,16,22,27,34)$
35A2	$35$	$36$	$35$	$34$	$( 1,23, 8,30,12,35,17, 3,21,10,28,11,31,19, 5,24, 9,29,15,32,20, 4,25, 6,26,13,33,16, 2,22, 7,27,14,34,18)$
35A-2	$35$	$36$	$35$	$34$	$( 1,31,26,23,19,13, 8, 5,33,30,24,16,12, 9, 2,35,29,22,17,15, 7, 3,32,27,21,20,14,10, 4,34,28,25,18,11, 6)$

Malle's constant $a(G)$:     $1/14$

Character table

		1A	2A	3A1	3A-1	3B	3C1	3C-1	5A1	5A2	6A1	6A-1	7A1	7A-1	14A1	14A-1	15A1	15A-1	15A2	15A-2	21A1	21A-1	35A1	35A-1	35A2	35A-2
	Size	1	15	7	7	20	140	140	12	12	105	105	3	3	45	45	84	84	84	84	60	60	36	36	36	36
	2 P	1A	1A	3A-1	3A1	3B	3C-1	3C1	5A2	5A1	3A1	3A-1	7A1	7A-1	7A1	7A-1	15A2	15A-1	15A-2	15A1	21A1	21A-1	35A-1	35A2	35A1	35A-2
	3 P	1A	2A	1A	1A	1A	1A	1A	5A2	5A1	2A	2A	7A-1	7A1	14A-1	14A1	5A2	5A1	5A2	5A1	7A-1	7A1	35A1	35A-2	35A-1	35A2
	5 P	1A	2A	3A-1	3A1	3B	3C-1	3C1	1A	1A	6A-1	6A1	7A-1	7A1	14A-1	14A1	3A1	3A1	3A-1	3A-1	21A-1	21A1	7A1	7A-1	7A-1	7A1
	7 P	1A	2A	3A1	3A-1	3B	3C1	3C-1	5A2	5A1	6A1	6A-1	1A	1A	2A	2A	15A-2	15A1	15A2	15A-1	3B	3B	5A2	5A1	5A2	5A1
	Type
1260.61.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
1260.61.1b1	C	$1$	$1$	${\zeta }_3^{-1}$	${\zeta }_3$	$1$	${\zeta }_3^{-1}$	${\zeta }_3$	$1$	$1$	${\zeta }_3$	${\zeta }_3^{-1}$	$1$	$1$	$1$	$1$	${\zeta }_3$	${\zeta }_3^{-1}$	${\zeta }_3^{-1}$	${\zeta }_3$	$1$	$1$	$1$	$1$	$1$	$1$
1260.61.1b2	C	$1$	$1$	${\zeta }_3$	${\zeta }_3^{-1}$	$1$	${\zeta }_3$	${\zeta }_3^{-1}$	$1$	$1$	${\zeta }_3^{-1}$	${\zeta }_3$	$1$	$1$	$1$	$1$	${\zeta }_3^{-1}$	${\zeta }_3$	${\zeta }_3$	${\zeta }_3^{-1}$	$1$	$1$	$1$	$1$	$1$	$1$
1260.61.3a1	C	$3$	$3$	$0$	$0$	$3$	$0$	$0$	$3$	$3$	$0$	$0$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$	$0$	$0$	$0$	$0$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$
1260.61.3a2	C	$3$	$3$	$0$	$0$	$3$	$0$	$0$	$3$	$3$	$0$	$0$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$	$0$	$0$	$0$	$0$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$
1260.61.3b1	R	$3$	$-1$	$3$	$3$	$0$	$0$	$0$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-1$	$-1$	$3$	$3$	$-1$	$-1$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$0$	$0$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$
1260.61.3b2	R	$3$	$-1$	$3$	$3$	$0$	$0$	$0$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-1$	$-1$	$3$	$3$	$-1$	$-1$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$0$	$0$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$
1260.61.3c1	C	$3$	$-1$	$3{\zeta }_{15}^{-5}$	$3{\zeta }_{15}^5$	$0$	$0$	$0$	$-{\zeta }_{15}^{-3}-{\zeta }_{15}^3$	$-{\zeta }_{15}^{-6}-{\zeta }_{15}^6$	$-{\zeta }_{15}^5$	$-{\zeta }_{15}^{-5}$	$3$	$3$	$-1$	$-1$	$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4+{\zeta }_{15}^5-{\zeta }_{15}^7$	$-1+{\zeta }_{15}+{\zeta }_{15}^4-{\zeta }_{15}^5$	$-{\zeta }_{15}-{\zeta }_{15}^4$	$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4+{\zeta }_{15}^7$	$0$	$0$	$-{\zeta }_{15}^{-6}-{\zeta }_{15}^6$	$-{\zeta }_{15}^{-6}-{\zeta }_{15}^6$	$-{\zeta }_{15}^{-3}-{\zeta }_{15}^3$	$-{\zeta }_{15}^{-3}-{\zeta }_{15}^3$
1260.61.3c2	C	$3$	$-1$	$3{\zeta }_{15}^5$	$3{\zeta }_{15}^{-5}$	$0$	$0$	$0$	$-{\zeta }_{15}^{-3}-{\zeta }_{15}^3$	$-{\zeta }_{15}^{-6}-{\zeta }_{15}^6$	$-{\zeta }_{15}^{-5}$	$-{\zeta }_{15}^5$	$3$	$3$	$-1$	$-1$	$-1+{\zeta }_{15}+{\zeta }_{15}^4-{\zeta }_{15}^5$	$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4+{\zeta }_{15}^5-{\zeta }_{15}^7$	$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4+{\zeta }_{15}^7$	$-{\zeta }_{15}-{\zeta }_{15}^4$	$0$	$0$	$-{\zeta }_{15}^{-6}-{\zeta }_{15}^6$	$-{\zeta }_{15}^{-6}-{\zeta }_{15}^6$	$-{\zeta }_{15}^{-3}-{\zeta }_{15}^3$	$-{\zeta }_{15}^{-3}-{\zeta }_{15}^3$
1260.61.3c3	C	$3$	$-1$	$3{\zeta }_{15}^{-5}$	$3{\zeta }_{15}^5$	$0$	$0$	$0$	$-{\zeta }_{15}^{-6}-{\zeta }_{15}^6$	$-{\zeta }_{15}^{-3}-{\zeta }_{15}^3$	$-{\zeta }_{15}^5$	$-{\zeta }_{15}^{-5}$	$3$	$3$	$-1$	$-1$	$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4+{\zeta }_{15}^7$	$-{\zeta }_{15}-{\zeta }_{15}^4$	$-1+{\zeta }_{15}+{\zeta }_{15}^4-{\zeta }_{15}^5$	$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4+{\zeta }_{15}^5-{\zeta }_{15}^7$	$0$	$0$	$-{\zeta }_{15}^{-3}-{\zeta }_{15}^3$	$-{\zeta }_{15}^{-3}-{\zeta }_{15}^3$	$-{\zeta }_{15}^{-6}-{\zeta }_{15}^6$	$-{\zeta }_{15}^{-6}-{\zeta }_{15}^6$
1260.61.3c4	C	$3$	$-1$	$3{\zeta }_{15}^5$	$3{\zeta }_{15}^{-5}$	$0$	$0$	$0$	$-{\zeta }_{15}^{-6}-{\zeta }_{15}^6$	$-{\zeta }_{15}^{-3}-{\zeta }_{15}^3$	$-{\zeta }_{15}^{-5}$	$-{\zeta }_{15}^5$	$3$	$3$	$-1$	$-1$	$-{\zeta }_{15}-{\zeta }_{15}^4$	$-1+{\zeta }_{15}+{\zeta }_{15}^2-{\zeta }_{15}^3+{\zeta }_{15}^4+{\zeta }_{15}^7$	$1-{\zeta }_{15}-{\zeta }_{15}^2+{\zeta }_{15}^3-{\zeta }_{15}^4+{\zeta }_{15}^5-{\zeta }_{15}^7$	$-1+{\zeta }_{15}+{\zeta }_{15}^4-{\zeta }_{15}^5$	$0$	$0$	$-{\zeta }_{15}^{-3}-{\zeta }_{15}^3$	$-{\zeta }_{15}^{-3}-{\zeta }_{15}^3$	$-{\zeta }_{15}^{-6}-{\zeta }_{15}^6$	$-{\zeta }_{15}^{-6}-{\zeta }_{15}^6$
1260.61.4a	R	$4$	$0$	$4$	$4$	$1$	$1$	$1$	$-1$	$-1$	$0$	$0$	$4$	$4$	$0$	$0$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$
1260.61.4b1	C	$4$	$0$	$4{\zeta }_3^{-1}$	$4{\zeta }_3$	$1$	${\zeta }_3^{-1}$	${\zeta }_3$	$-1$	$-1$	$0$	$0$	$4$	$4$	$0$	$0$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$	$1$	$1$	$-1$	$-1$	$-1$	$-1$
1260.61.4b2	C	$4$	$0$	$4{\zeta }_3$	$4{\zeta }_3^{-1}$	$1$	${\zeta }_3$	${\zeta }_3^{-1}$	$-1$	$-1$	$0$	$0$	$4$	$4$	$0$	$0$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$	$1$	$1$	$-1$	$-1$	$-1$	$-1$
1260.61.5a	R	$5$	$1$	$5$	$5$	$-1$	$-1$	$-1$	$0$	$0$	$1$	$1$	$5$	$5$	$1$	$1$	$0$	$0$	$0$	$0$	$-1$	$-1$	$0$	$0$	$0$	$0$
1260.61.5b1	C	$5$	$1$	$5{\zeta }_3^{-1}$	$5{\zeta }_3$	$-1$	$-{\zeta }_3^{-1}$	$-{\zeta }_3$	$0$	$0$	${\zeta }_3$	${\zeta }_3^{-1}$	$5$	$5$	$1$	$1$	$0$	$0$	$0$	$0$	$-1$	$-1$	$0$	$0$	$0$	$0$
1260.61.5b2	C	$5$	$1$	$5{\zeta }_3$	$5{\zeta }_3^{-1}$	$-1$	$-{\zeta }_3$	$-{\zeta }_3^{-1}$	$0$	$0$	${\zeta }_3^{-1}$	${\zeta }_3$	$5$	$5$	$1$	$1$	$0$	$0$	$0$	$0$	$-1$	$-1$	$0$	$0$	$0$	$0$
1260.61.9a1	C	$9$	$-3$	$0$	$0$	$0$	$0$	$0$	$-3{\zeta }_{35}^{-7}-3{\zeta }_{35}^7$	$-3{\zeta }_{35}^{-14}-3{\zeta }_{35}^{14}$	$0$	$0$	$-3{\zeta }_{35}^{-15}-3-3{\zeta }_{35}^5-3{\zeta }_{35}^{10}$	$3{\zeta }_{35}^{-15}+3{\zeta }_{35}^5+3{\zeta }_{35}^{10}$	${\zeta }_{35}^{-15}+1+{\zeta }_{35}^5+{\zeta }_{35}^{10}$	$-{\zeta }_{35}^{-15}-{\zeta }_{35}^5-{\zeta }_{35}^{10}$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_{35}^{-13}-{\zeta }_{35}^4+{\zeta }_{35}^8-{\zeta }_{35}^9-{\zeta }_{35}^{11}+{\zeta }_{35}^{15}-{\zeta }_{35}^{16}$	${\zeta }_{35}^{-14}-{\zeta }_{35}^{-13}+{\zeta }_{35}^4-{\zeta }_{35}^8+{\zeta }_{35}^9+{\zeta }_{35}^{11}+{\zeta }_{35}^{14}-{\zeta }_{35}^{15}+{\zeta }_{35}^{16}$	$-{\zeta }_{35}^{-13}+{\zeta }_{35}^{-10}+{\zeta }_{35}^{-5}+{\zeta }_{35}^4-{\zeta }_{35}^8+{\zeta }_{35}^9+{\zeta }_{35}^{11}+{\zeta }_{35}^{16}$	$-{\zeta }_{35}^{-14}+{\zeta }_{35}^{-13}-{\zeta }_{35}^{-10}-{\zeta }_{35}^{-5}-1-{\zeta }_{35}^4+{\zeta }_{35}^8-{\zeta }_{35}^9-{\zeta }_{35}^{11}-{\zeta }_{35}^{14}-{\zeta }_{35}^{16}$
1260.61.9a2	C	$9$	$-3$	$0$	$0$	$0$	$0$	$0$	$-3{\zeta }_{35}^{-7}-3{\zeta }_{35}^7$	$-3{\zeta }_{35}^{-14}-3{\zeta }_{35}^{14}$	$0$	$0$	$3{\zeta }_{35}^{-15}+3{\zeta }_{35}^5+3{\zeta }_{35}^{10}$	$-3{\zeta }_{35}^{-15}-3-3{\zeta }_{35}^5-3{\zeta }_{35}^{10}$	$-{\zeta }_{35}^{-15}-{\zeta }_{35}^5-{\zeta }_{35}^{10}$	${\zeta }_{35}^{-15}+1+{\zeta }_{35}^5+{\zeta }_{35}^{10}$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_{35}^{-14}-{\zeta }_{35}^{-13}+{\zeta }_{35}^4-{\zeta }_{35}^8+{\zeta }_{35}^9+{\zeta }_{35}^{11}+{\zeta }_{35}^{14}-{\zeta }_{35}^{15}+{\zeta }_{35}^{16}$	${\zeta }_{35}^{-13}-{\zeta }_{35}^4+{\zeta }_{35}^8-{\zeta }_{35}^9-{\zeta }_{35}^{11}+{\zeta }_{35}^{15}-{\zeta }_{35}^{16}$	$-{\zeta }_{35}^{-14}+{\zeta }_{35}^{-13}-{\zeta }_{35}^{-10}-{\zeta }_{35}^{-5}-1-{\zeta }_{35}^4+{\zeta }_{35}^8-{\zeta }_{35}^9-{\zeta }_{35}^{11}-{\zeta }_{35}^{14}-{\zeta }_{35}^{16}$	$-{\zeta }_{35}^{-13}+{\zeta }_{35}^{-10}+{\zeta }_{35}^{-5}+{\zeta }_{35}^4-{\zeta }_{35}^8+{\zeta }_{35}^9+{\zeta }_{35}^{11}+{\zeta }_{35}^{16}$
1260.61.9a3	C	$9$	$-3$	$0$	$0$	$0$	$0$	$0$	$-3{\zeta }_{35}^{-14}-3{\zeta }_{35}^{14}$	$-3{\zeta }_{35}^{-7}-3{\zeta }_{35}^7$	$0$	$0$	$-3{\zeta }_{35}^{-15}-3-3{\zeta }_{35}^5-3{\zeta }_{35}^{10}$	$3{\zeta }_{35}^{-15}+3{\zeta }_{35}^5+3{\zeta }_{35}^{10}$	${\zeta }_{35}^{-15}+1+{\zeta }_{35}^5+{\zeta }_{35}^{10}$	$-{\zeta }_{35}^{-15}-{\zeta }_{35}^5-{\zeta }_{35}^{10}$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_{35}^{-13}+{\zeta }_{35}^{-10}+{\zeta }_{35}^{-5}+{\zeta }_{35}^4-{\zeta }_{35}^8+{\zeta }_{35}^9+{\zeta }_{35}^{11}+{\zeta }_{35}^{16}$	$-{\zeta }_{35}^{-14}+{\zeta }_{35}^{-13}-{\zeta }_{35}^{-10}-{\zeta }_{35}^{-5}-1-{\zeta }_{35}^4+{\zeta }_{35}^8-{\zeta }_{35}^9-{\zeta }_{35}^{11}-{\zeta }_{35}^{14}-{\zeta }_{35}^{16}$	${\zeta }_{35}^{-13}-{\zeta }_{35}^4+{\zeta }_{35}^8-{\zeta }_{35}^9-{\zeta }_{35}^{11}+{\zeta }_{35}^{15}-{\zeta }_{35}^{16}$	${\zeta }_{35}^{-14}-{\zeta }_{35}^{-13}+{\zeta }_{35}^4-{\zeta }_{35}^8+{\zeta }_{35}^9+{\zeta }_{35}^{11}+{\zeta }_{35}^{14}-{\zeta }_{35}^{15}+{\zeta }_{35}^{16}$
1260.61.9a4	C	$9$	$-3$	$0$	$0$	$0$	$0$	$0$	$-3{\zeta }_{35}^{-14}-3{\zeta }_{35}^{14}$	$-3{\zeta }_{35}^{-7}-3{\zeta }_{35}^7$	$0$	$0$	$3{\zeta }_{35}^{-15}+3{\zeta }_{35}^5+3{\zeta }_{35}^{10}$	$-3{\zeta }_{35}^{-15}-3-3{\zeta }_{35}^5-3{\zeta }_{35}^{10}$	$-{\zeta }_{35}^{-15}-{\zeta }_{35}^5-{\zeta }_{35}^{10}$	${\zeta }_{35}^{-15}+1+{\zeta }_{35}^5+{\zeta }_{35}^{10}$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_{35}^{-14}+{\zeta }_{35}^{-13}-{\zeta }_{35}^{-10}-{\zeta }_{35}^{-5}-1-{\zeta }_{35}^4+{\zeta }_{35}^8-{\zeta }_{35}^9-{\zeta }_{35}^{11}-{\zeta }_{35}^{14}-{\zeta }_{35}^{16}$	$-{\zeta }_{35}^{-13}+{\zeta }_{35}^{-10}+{\zeta }_{35}^{-5}+{\zeta }_{35}^4-{\zeta }_{35}^8+{\zeta }_{35}^9+{\zeta }_{35}^{11}+{\zeta }_{35}^{16}$	${\zeta }_{35}^{-14}-{\zeta }_{35}^{-13}+{\zeta }_{35}^4-{\zeta }_{35}^8+{\zeta }_{35}^9+{\zeta }_{35}^{11}+{\zeta }_{35}^{14}-{\zeta }_{35}^{15}+{\zeta }_{35}^{16}$	${\zeta }_{35}^{-13}-{\zeta }_{35}^4+{\zeta }_{35}^8-{\zeta }_{35}^9-{\zeta }_{35}^{11}+{\zeta }_{35}^{15}-{\zeta }_{35}^{16}$
1260.61.12a1	C	$12$	$0$	$0$	$0$	$3$	$0$	$0$	$-3$	$-3$	$0$	$0$	$-4{\zeta }_7^{-3}-4-4{\zeta }_7-4{\zeta }_7^2$	$4{\zeta }_7^{-3}+4{\zeta }_7+4{\zeta }_7^2$	$0$	$0$	$0$	$0$	$0$	$0$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$	${\zeta }_7^{-3}+1+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+1+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-{\zeta }_7-{\zeta }_7^2$
1260.61.12a2	C	$12$	$0$	$0$	$0$	$3$	$0$	$0$	$-3$	$-3$	$0$	$0$	$4{\zeta }_7^{-3}+4{\zeta }_7+4{\zeta }_7^2$	$-4{\zeta }_7^{-3}-4-4{\zeta }_7-4{\zeta }_7^2$	$0$	$0$	$0$	$0$	$0$	$0$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$	$-{\zeta }_7^{-3}-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+1+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+1+{\zeta }_7+{\zeta }_7^2$
1260.61.15a1	C	$15$	$3$	$0$	$0$	$-3$	$0$	$0$	$0$	$0$	$0$	$0$	$-5{\zeta }_7^{-3}-5-5{\zeta }_7-5{\zeta }_7^2$	$5{\zeta }_7^{-3}+5{\zeta }_7+5{\zeta }_7^2$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$	$0$	$0$	$0$	$0$	${\zeta }_7^{-3}+1+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-{\zeta }_7-{\zeta }_7^2$	$0$	$0$	$0$	$0$
1260.61.15a2	C	$15$	$3$	$0$	$0$	$-3$	$0$	$0$	$0$	$0$	$0$	$0$	$5{\zeta }_7^{-3}+5{\zeta }_7+5{\zeta }_7^2$	$-5{\zeta }_7^{-3}-5-5{\zeta }_7-5{\zeta }_7^2$	${\zeta }_7^{-3}+{\zeta }_7+{\zeta }_7^2$	$-{\zeta }_7^{-3}-1-{\zeta }_7-{\zeta }_7^2$	$0$	$0$	$0$	$0$	$-{\zeta }_7^{-3}-{\zeta }_7-{\zeta }_7^2$	${\zeta }_7^{-3}+1+{\zeta }_7+{\zeta }_7^2$	$0$	$0$	$0$	$0$

Regular extensions

Data not computed