Properties

Label 1.2e2_29.2t1.1
Dimension 1
Group $C_2$
Conductor $ 2^{2} \cdot 29 $
Frobenius-Schur indicator 1

Related objects

Learn more about

Basic invariants

Dimension:$1$
Group:$C_2$
Conductor:$116= 2^{2} \cdot 29 $
Artin number field: Splitting field of $f= x^{2} + 29 $ over $\Q$
Size of Galois orbit: 1
Smallest containing permutation representation: $C_2$
Parity: Odd

Galois action

Roots of defining polynomial

The roots of $f$ are computed in $\Q_{ 3 }$ to precision 5.
Roots:
$r_{ 1 }$ $=$ $ 1 + 3 + 2\cdot 3^{2} + 3^{3} +O\left(3^{ 5 }\right)$
$r_{ 2 }$ $=$ $ 2 + 3 + 3^{3} + 2\cdot 3^{4} +O\left(3^{ 5 }\right)$

Generators of the action on the roots $ r_{ 1 }, r_{ 2 } $

Cycle notation
$(1,2)$

Character values on conjugacy classes

SizeOrderAction on $ r_{ 1 }, r_{ 2 } $ Character values
$c1$
$1$ $1$ $()$ $1$
$1$ $2$ $(1,2)$ $-1$
The blue line marks the conjugacy class containing complex conjugation.