Properties

Label 2.4872.3t2.a.a
Dimension 22
Group S3S_3
Conductor 48724872
Root number 11
Indicator 11

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Basic invariants

Dimension: 22
Group: S3S_3
Conductor: 48724872=233729\medspace = 2^{3} \cdot 3 \cdot 7 \cdot 29
Frobenius-Schur indicator: 11
Root number: 11
Artin stem field: Galois closure of 3.1.4872.1
Galois orbit size: 11
Smallest permutation container: S3S_3
Parity: odd
Determinant: 1.4872.2t1.b.a
Projective image: S3S_3
Projective stem field: Galois closure of 3.1.4872.1

Defining polynomial

f(x)f(x)== x3x2+2x14 x^{3} - x^{2} + 2x - 14 Copy content Toggle raw display .

The roots of ff are computed in Q71\Q_{ 71 } to precision 5.

Roots:
r1r_{ 1 } == 41+3471+51712+44713+28714+O(715) 41 + 34\cdot 71 + 51\cdot 71^{2} + 44\cdot 71^{3} + 28\cdot 71^{4} +O(71^{5}) Copy content Toggle raw display
r2r_{ 2 } == 45+3871+712+17713+34714+O(715) 45 + 38\cdot 71 + 71^{2} + 17\cdot 71^{3} + 34\cdot 71^{4} +O(71^{5}) Copy content Toggle raw display
r3r_{ 3 } == 57+6871+17712+9713+8714+O(715) 57 + 68\cdot 71 + 17\cdot 71^{2} + 9\cdot 71^{3} + 8\cdot 71^{4} +O(71^{5}) Copy content Toggle raw display

Generators of the action on the roots r1,r2,r3 r_{ 1 }, r_{ 2 }, r_{ 3 }

Cycle notation
(1,2,3)(1,2,3)
(1,2)(1,2)

Character values on conjugacy classes

SizeOrderAction on r1,r2,r3 r_{ 1 }, r_{ 2 }, r_{ 3 } Character valueComplex conjugation
1111()()22
3322(1,2)(1,2)00
2233(1,2,3)(1,2,3)1-1