Dirichlet character χ319(20,⋅)\chi_{319}(20,\cdot)

• Label: 319.20
• Modulus: $319$
• Conductor: $319$
• Order: $35$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$319$
Conductor:	$319$
Order:	$35$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 319.s

$\chi_{319}(16,\cdot)$ $\chi_{319}(20,\cdot)$ $\chi_{319}(25,\cdot)$ $\chi_{319}(36,\cdot)$ $\chi_{319}(49,\cdot)$ $\chi_{319}(53,\cdot)$ $\chi_{319}(81,\cdot)$ $\chi_{319}(82,\cdot)$ $\chi_{319}(103,\cdot)$ $\chi_{319}(136,\cdot)$ $\chi_{319}(141,\cdot)$ $\chi_{319}(152,\cdot)$ $\chi_{319}(168,\cdot)$ $\chi_{319}(169,\cdot)$ $\chi_{319}(170,\cdot)$ $\chi_{319}(181,\cdot)$ $\chi_{319}(190,\cdot)$ $\chi_{319}(223,\cdot)$ $\chi_{319}(256,\cdot)$ $\chi_{319}(257,\cdot)$ $\chi_{319}(268,\cdot)$ $\chi_{319}(284,\cdot)$ $\chi_{319}(306,\cdot)$ $\chi_{319}(313,\cdot)$

Related number fields

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

Values on generators

$(233,89)$ → $(e\left(\frac{3}{5}\right),e\left(\frac{6}{7}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 319 }(20, a)$	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{5}{7}\right)$	$1$

Gauss sum

Jacobi sum

Kloosterman sum