Dirichlet character χ847(747,⋅)\chi_{847}(747,\cdot)

• Label: 847.747
• Modulus: $847$
• Conductor: $847$
• Order: $66$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$847$
Conductor:	$847$
Order:	$66$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 847.x

$\chi_{847}(10,\cdot)$ $\chi_{847}(54,\cdot)$ $\chi_{847}(87,\cdot)$ $\chi_{847}(131,\cdot)$ $\chi_{847}(164,\cdot)$ $\chi_{847}(208,\cdot)$ $\chi_{847}(285,\cdot)$ $\chi_{847}(318,\cdot)$ $\chi_{847}(395,\cdot)$ $\chi_{847}(439,\cdot)$ $\chi_{847}(472,\cdot)$ $\chi_{847}(516,\cdot)$ $\chi_{847}(549,\cdot)$ $\chi_{847}(593,\cdot)$ $\chi_{847}(626,\cdot)$ $\chi_{847}(670,\cdot)$ $\chi_{847}(703,\cdot)$ $\chi_{847}(747,\cdot)$ $\chi_{847}(780,\cdot)$ $\chi_{847}(824,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{33})$
Fixed field:	Number field defined by a degree 66 polynomial

Values on generators

$(122,365)$ → $(e\left(\frac{5}{6}\right),e\left(\frac{19}{22}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{ 847 }(747, a)$	$1$	$1$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{8}{11}\right)$

Gauss sum

Jacobi sum

Kloosterman sum