Dirichlet character χ319(35,⋅)\chi_{319}(35,\cdot)

• Label: 319.35
• Modulus: $319$
• Conductor: $319$
• Order: $70$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$319$
Conductor:	$319$
Order:	$70$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 319.v

$\chi_{319}(6,\cdot)$ $\chi_{319}(13,\cdot)$ $\chi_{319}(35,\cdot)$ $\chi_{319}(51,\cdot)$ $\chi_{319}(62,\cdot)$ $\chi_{319}(63,\cdot)$ $\chi_{319}(96,\cdot)$ $\chi_{319}(129,\cdot)$ $\chi_{319}(138,\cdot)$ $\chi_{319}(149,\cdot)$ $\chi_{319}(150,\cdot)$ $\chi_{319}(151,\cdot)$ $\chi_{319}(167,\cdot)$ $\chi_{319}(178,\cdot)$ $\chi_{319}(183,\cdot)$ $\chi_{319}(216,\cdot)$ $\chi_{319}(237,\cdot)$ $\chi_{319}(238,\cdot)$ $\chi_{319}(266,\cdot)$ $\chi_{319}(270,\cdot)$ $\chi_{319}(283,\cdot)$ $\chi_{319}(294,\cdot)$ $\chi_{319}(299,\cdot)$ $\chi_{319}(303,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{35})$
Fixed field:	Number field defined by a degree 70 polynomial

Values on generators

$(233,89)$ → $(e\left(\frac{1}{10}\right),e\left(\frac{3}{14}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 319 }(35, a)$	$-1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{3}{7}\right)$	$-1$

Gauss sum

Jacobi sum

Kloosterman sum