Dirichlet character χ319(112,⋅)\chi_{319}(112,\cdot)

• Label: 319.112
• 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.u

$\chi_{319}(7,\cdot)$ $\chi_{319}(24,\cdot)$ $\chi_{319}(52,\cdot)$ $\chi_{319}(74,\cdot)$ $\chi_{319}(83,\cdot)$ $\chi_{319}(94,\cdot)$ $\chi_{319}(107,\cdot)$ $\chi_{319}(112,\cdot)$ $\chi_{319}(123,\cdot)$ $\chi_{319}(139,\cdot)$ $\chi_{319}(140,\cdot)$ $\chi_{319}(161,\cdot)$ $\chi_{319}(194,\cdot)$ $\chi_{319}(226,\cdot)$ $\chi_{319}(227,\cdot)$ $\chi_{319}(228,\cdot)$ $\chi_{319}(239,\cdot)$ $\chi_{319}(248,\cdot)$ $\chi_{319}(255,\cdot)$ $\chi_{319}(277,\cdot)$ $\chi_{319}(281,\cdot)$ $\chi_{319}(310,\cdot)$ $\chi_{319}(314,\cdot)$ $\chi_{319}(315,\cdot)$

Related number fields

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

Values on generators

$(233,89)$ → $(e\left(\frac{1}{10}\right),e\left(\frac{4}{7}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 319 }(112, a)$	$-1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{9}{14}\right)$	$1$

Gauss sum

Jacobi sum

Kloosterman sum