Dirichlet character χ319(171,⋅)\chi_{319}(171,\cdot)

• Label: 319.171
• Modulus: $319$
• Conductor: $319$
• Order: $140$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$319$
Conductor:	$319$
Order:	$140$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 319.x

$\chi_{319}(2,\cdot)$ $\chi_{319}(8,\cdot)$ $\chi_{319}(18,\cdot)$ $\chi_{319}(19,\cdot)$ $\chi_{319}(39,\cdot)$ $\chi_{319}(40,\cdot)$ $\chi_{319}(50,\cdot)$ $\chi_{319}(61,\cdot)$ $\chi_{319}(68,\cdot)$ $\chi_{319}(72,\cdot)$ $\chi_{319}(73,\cdot)$ $\chi_{319}(79,\cdot)$ $\chi_{319}(84,\cdot)$ $\chi_{319}(85,\cdot)$ $\chi_{319}(90,\cdot)$ $\chi_{319}(95,\cdot)$ $\chi_{319}(101,\cdot)$ $\chi_{319}(105,\cdot)$ $\chi_{319}(106,\cdot)$ $\chi_{319}(118,\cdot)$ $\chi_{319}(127,\cdot)$ $\chi_{319}(134,\cdot)$ $\chi_{319}(156,\cdot)$ $\chi_{319}(160,\cdot)$ $\chi_{319}(171,\cdot)$ $\chi_{319}(172,\cdot)$ $\chi_{319}(182,\cdot)$ $\chi_{319}(184,\cdot)$ $\chi_{319}(189,\cdot)$ $\chi_{319}(193,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{140})$
Fixed field:	Number field defined by a degree 140 polynomial (not computed)

Values on generators

$(233,89)$ → $(e\left(\frac{9}{10}\right),e\left(\frac{19}{28}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 319 }(171, a)$	$1$	$1$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{3}{28}\right)$	$-i$

Gauss sum

Jacobi sum

Kloosterman sum