Dirichlet character χ784(165,⋅)\chi_{784}(165,\cdot)

• Label: 784.165
• Modulus: $784$
• Conductor: $112$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$784$
Conductor:	$112$
Order:	$12$
Real:	no
Primitive:	no, induced from $\chi_{112}(53,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 784.x

$\chi_{784}(165,\cdot)$ $\chi_{784}(373,\cdot)$ $\chi_{784}(557,\cdot)$ $\chi_{784}(765,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.12.49519263525896192.1

Values on generators

$(687,197,689)$ → $(1,i,e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{ 784 }(165, a)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Gauss sum

Jacobi sum

Kloosterman sum