Artin representation 5.3e6_71e4.6t12.1c1

• Label: 5.3e6_71e4.6t12.1c1
• Dimension: 5
• Group: $A_5$
• Conductor: $ 3^{6} \cdot 71^{4}$
• Root number: 1
• Frobenius-Schur indicator: 1

Basic invariants

Dimension:	$5$
Group:	$A_5$
Conductor:	$18525115449= 3^{6} \cdot 71^{4} $
Artin number field:	Splitting field of $f= x^{5} - x^{4} + x^{3} - 9 x + 12 $ over $\Q$
Size of Galois orbit:	1
Smallest containing permutation representation:	$\PSL(2,5)$
Parity:	Even
Determinant:	1.1.1t1.1c1

Galois action

Roots of defining polynomial

The roots of $f$ are computed in $\Q_{ 101 }$ to precision 5.

Roots:

$r_{ 1 }$	$=$	$ 4 + 17\cdot 101 + 12\cdot 101^{2} + 26\cdot 101^{3} + 87\cdot 101^{4} +O\left(101^{ 5 }\right)$
$r_{ 2 }$	$=$	$ 23 + 48\cdot 101 + 11\cdot 101^{2} + 95\cdot 101^{3} + 33\cdot 101^{4} +O\left(101^{ 5 }\right)$
$r_{ 3 }$	$=$	$ 36 + 68\cdot 101 + 80\cdot 101^{2} + 13\cdot 101^{3} +O\left(101^{ 5 }\right)$
$r_{ 4 }$	$=$	$ 49 + 14\cdot 101 + 25\cdot 101^{2} + 57\cdot 101^{3} + 85\cdot 101^{4} +O\left(101^{ 5 }\right)$
$r_{ 5 }$	$=$	$ 91 + 53\cdot 101 + 72\cdot 101^{2} + 9\cdot 101^{3} + 96\cdot 101^{4} +O\left(101^{ 5 }\right)$

Generators of the action on the roots $r_1, \ldots, r_{ 5 }$

Cycle notation

$(1,2,3)$

$(3,4,5)$

Character values on conjugacy classes

Size	Order	Action on $r_1, \ldots, r_{ 5 }$	Character value
$1$	$1$	$()$	$5$
$15$	$2$	$(1,2)(3,4)$	$1$
$20$	$3$	$(1,2,3)$	$-1$
$12$	$5$	$(1,2,3,4,5)$	$0$
$12$	$5$	$(1,3,4,5,2)$	$0$

The blue line marks the conjugacy class containing complex conjugation.