Dirichlet character χ676(279,⋅)\chi_{676}(279,\cdot)

• Label: 676.279
• Modulus: $676$
• Conductor: $676$
• Order: $156$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$676$
Conductor:	$676$
Order:	$156$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 676.w

$\chi_{676}(7,\cdot)$ $\chi_{676}(11,\cdot)$ $\chi_{676}(15,\cdot)$ $\chi_{676}(59,\cdot)$ $\chi_{676}(63,\cdot)$ $\chi_{676}(67,\cdot)$ $\chi_{676}(71,\cdot)$ $\chi_{676}(111,\cdot)$ $\chi_{676}(115,\cdot)$ $\chi_{676}(119,\cdot)$ $\chi_{676}(123,\cdot)$ $\chi_{676}(163,\cdot)$ $\chi_{676}(167,\cdot)$ $\chi_{676}(171,\cdot)$ $\chi_{676}(175,\cdot)$ $\chi_{676}(215,\cdot)$ $\chi_{676}(219,\cdot)$ $\chi_{676}(223,\cdot)$ $\chi_{676}(227,\cdot)$ $\chi_{676}(267,\cdot)$ $\chi_{676}(271,\cdot)$ $\chi_{676}(275,\cdot)$ $\chi_{676}(279,\cdot)$ $\chi_{676}(323,\cdot)$ $\chi_{676}(327,\cdot)$ $\chi_{676}(331,\cdot)$ $\chi_{676}(371,\cdot)$ $\chi_{676}(375,\cdot)$ $\chi_{676}(379,\cdot)$ $\chi_{676}(383,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{156})$
Fixed field:	Number field defined by a degree 156 polynomial (not computed)

Values on generators

$(339,509)$ → $(-1,e\left(\frac{113}{156}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 676 }(279, a)$	$1$	$1$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{2}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum