Dirichlet character χ847(216,⋅)\chi_{847}(216,\cdot)

• Label: 847.216
• Modulus: $847$
• Conductor: $847$
• Order: $110$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$847$
Conductor:	$847$
Order:	$110$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 847.ba

$\chi_{847}(6,\cdot)$ $\chi_{847}(13,\cdot)$ $\chi_{847}(41,\cdot)$ $\chi_{847}(62,\cdot)$ $\chi_{847}(83,\cdot)$ $\chi_{847}(90,\cdot)$ $\chi_{847}(139,\cdot)$ $\chi_{847}(160,\cdot)$ $\chi_{847}(167,\cdot)$ $\chi_{847}(195,\cdot)$ $\chi_{847}(216,\cdot)$ $\chi_{847}(237,\cdot)$ $\chi_{847}(244,\cdot)$ $\chi_{847}(272,\cdot)$ $\chi_{847}(293,\cdot)$ $\chi_{847}(314,\cdot)$ $\chi_{847}(321,\cdot)$ $\chi_{847}(349,\cdot)$ $\chi_{847}(370,\cdot)$ $\chi_{847}(391,\cdot)$ $\chi_{847}(398,\cdot)$ $\chi_{847}(426,\cdot)$ $\chi_{847}(447,\cdot)$ $\chi_{847}(468,\cdot)$ $\chi_{847}(503,\cdot)$ $\chi_{847}(545,\cdot)$ $\chi_{847}(552,\cdot)$ $\chi_{847}(580,\cdot)$ $\chi_{847}(601,\cdot)$ $\chi_{847}(622,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 110 polynomial (not computed)

Values on generators

$(122,365)$ → $(-1,e\left(\frac{47}{110}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{ 847 }(216, a)$	$1$	$1$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{36}{55}\right)$

Gauss sum

Jacobi sum

Kloosterman sum