Properties

Label 1.1077.2t1.a.a
Dimension $1$
Group $C_2$
Conductor $1077$
Root number $1$
Indicator $1$

Related objects

Learn more about

Basic invariants

Dimension: $1$
Group: $C_2$
Conductor: \(1077\)\(\medspace = 3 \cdot 359 \)
Frobenius-Schur indicator: $1$
Root number: $1$
Artin field: \(\Q(\sqrt{1077}) \)
Galois orbit size: $1$
Smallest permutation container: $C_2$
Parity: even
Dirichlet character: \(\displaystyle\left(\frac{1077}{\bullet}\right)\)
Projective image: $C_1$
Projective field: \(\Q\)

Defining polynomial

$f(x)$$=$\(x^{2} - x - 269\)  Toggle raw display.

The roots of $f$ are computed in $\Q_{ 29 }$ to precision 5.

Roots:
$r_{ 1 }$ $=$ \( 14 + 13\cdot 29 + 18\cdot 29^{2} + 28\cdot 29^{3} + 11\cdot 29^{4} +O(29^{5})\)  Toggle raw display
$r_{ 2 }$ $=$ \( 16 + 15\cdot 29 + 10\cdot 29^{2} + 17\cdot 29^{4} +O(29^{5})\)  Toggle raw display

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 value
$1$$1$$()$$1$
$1$$2$$(1,2)$$-1$

The blue line marks the conjugacy class containing complex conjugation.