Properties

Label 1.5241.2t1.a
Dimension $1$
Group $C_2$
Conductor $5241$
Indicator $1$

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Basic invariants

Dimension:$1$
Group:$C_2$
Conductor:\(5241\)\(\medspace = 3 \cdot 1747 \)
Frobenius-Schur indicator: $1$
Root number: $1$
Artin number field: Galois closure of \(\Q(\sqrt{5241}) \)
Galois orbit size: $1$
Smallest permutation container: $C_2$
Parity: even
Projective image: $C_1$
Projective field: \(\Q\)

Galois action

Roots of defining polynomial

The roots of $f$ are computed in $\Q_{ 5 }$ to precision 5.
Roots:
$r_{ 1 }$ $=$ \( 3\cdot 5 + 5^{2} + 2\cdot 5^{3} + 2\cdot 5^{4} +O(5^{5})\)  Toggle raw display
$r_{ 2 }$ $=$ \( 1 + 2\cdot 5 + 3\cdot 5^{2} + 2\cdot 5^{3} + 2\cdot 5^{4} +O(5^{5})\)  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 values
$c1$
$1$ $1$ $()$ $1$
$1$ $2$ $(1,2)$ $-1$
The blue line marks the conjugacy class containing complex conjugation.