Properties

Label 1.14731.2t1.a.a
Dimension $1$
Group $C_2$
Conductor $14731$
Root number $1$
Indicator $1$

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Basic invariants

Dimension: $1$
Group: $C_2$
Conductor: \(14731\)
Frobenius-Schur indicator: $1$
Root number: $1$
Artin number field: Galois closure of \(\Q(\sqrt{-14731}) \)
Galois orbit size: $1$
Smallest permutation container: $C_2$
Parity: odd
Dirichlet character: \(\displaystyle\left(\frac{-14731}{\bullet}\right)\)
Projective image: $C_1$
Projective field: \(\Q\)

Defining polynomial

$f(x)$$=$$ x^{2} - x + 3683 $.

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

Roots:
$r_{ 1 }$ $=$ $ 2 + 5 + 2\cdot 5^{2} + 3\cdot 5^{4} +O\left(5^{ 5 }\right)$
$r_{ 2 }$ $=$ $ 4 + 3\cdot 5 + 2\cdot 5^{2} + 4\cdot 5^{3} + 5^{4} +O\left(5^{ 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 value
$1$$1$$()$$1$
$1$$2$$(1,2)$$-1$

The blue line marks the conjugacy class containing complex conjugation.