Dirichlet character χ169(139,⋅)\chi_{169}(139,\cdot)

• Label: 169.139
• Modulus: $169$
• Conductor: $169$
• Order: $39$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$169$
Conductor:	$169$
Order:	$39$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 169.i

$\chi_{169}(3,\cdot)$ $\chi_{169}(9,\cdot)$ $\chi_{169}(16,\cdot)$ $\chi_{169}(29,\cdot)$ $\chi_{169}(35,\cdot)$ $\chi_{169}(42,\cdot)$ $\chi_{169}(48,\cdot)$ $\chi_{169}(55,\cdot)$ $\chi_{169}(61,\cdot)$ $\chi_{169}(68,\cdot)$ $\chi_{169}(74,\cdot)$ $\chi_{169}(81,\cdot)$ $\chi_{169}(87,\cdot)$ $\chi_{169}(94,\cdot)$ $\chi_{169}(100,\cdot)$ $\chi_{169}(107,\cdot)$ $\chi_{169}(113,\cdot)$ $\chi_{169}(120,\cdot)$ $\chi_{169}(126,\cdot)$ $\chi_{169}(133,\cdot)$ $\chi_{169}(139,\cdot)$ $\chi_{169}(152,\cdot)$ $\chi_{169}(159,\cdot)$ $\chi_{169}(165,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 39 polynomial

Values on generators

$2$ → $e\left(\frac{14}{39}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 169 }(139, a)$	$1$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{38}{39}\right)$

Gauss sum

Jacobi sum

Kloosterman sum