Properties

 Label 1.155.2t1.a Dimension $1$ Group $C_2$ Conductor $155$ Indicator $1$

Related objects

Basic invariants

 Dimension: $1$ Group: $C_2$ Conductor: $$155$$$$\medspace = 5 \cdot 31$$ Frobenius-Schur indicator: $1$ Root number: $1$ Artin number field: Galois closure of $$\Q(\sqrt{-155})$$ Galois orbit size: $1$ Smallest permutation container: $C_2$ Parity: odd Projective image: $C_1$ Projective field: $$\Q$$

Galois action

Roots of defining polynomial

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

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

 Cycle notation $(1,2)$

Character values on conjugacy classes

 Size Order Action 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.