Dirichlet character χ847(255,⋅)\chi_{847}(255,\cdot)

• Label: 847.255
• Modulus: $847$
• Conductor: $847$
• Order: $330$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$847$
Conductor:	$847$
Order:	$330$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 847.be

$\chi_{847}(17,\cdot)$ $\chi_{847}(19,\cdot)$ $\chi_{847}(24,\cdot)$ $\chi_{847}(52,\cdot)$ $\chi_{847}(61,\cdot)$ $\chi_{847}(68,\cdot)$ $\chi_{847}(73,\cdot)$ $\chi_{847}(96,\cdot)$ $\chi_{847}(101,\cdot)$ $\chi_{847}(117,\cdot)$ $\chi_{847}(129,\cdot)$ $\chi_{847}(138,\cdot)$ $\chi_{847}(145,\cdot)$ $\chi_{847}(150,\cdot)$ $\chi_{847}(171,\cdot)$ $\chi_{847}(173,\cdot)$ $\chi_{847}(178,\cdot)$ $\chi_{847}(194,\cdot)$ $\chi_{847}(206,\cdot)$ $\chi_{847}(222,\cdot)$ $\chi_{847}(227,\cdot)$ $\chi_{847}(248,\cdot)$ $\chi_{847}(250,\cdot)$ $\chi_{847}(255,\cdot)$ $\chi_{847}(271,\cdot)$ $\chi_{847}(283,\cdot)$ $\chi_{847}(292,\cdot)$ $\chi_{847}(299,\cdot)$ $\chi_{847}(304,\cdot)$ $\chi_{847}(325,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 330 polynomial (not computed)

Values on generators

$(122,365)$ → $(e\left(\frac{1}{6}\right),e\left(\frac{101}{110}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{ 847 }(255, a)$	$1$	$1$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{257}{330}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{13}{55}\right)$

Gauss sum

Jacobi sum

Kloosterman sum