Dirichlet character χ223(17,⋅)\chi_{223}(17,\cdot)

• Label: 223.17
• Modulus: $223$
• Conductor: $223$
• Order: $37$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$223$
Conductor:	$223$
Order:	$37$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 223.e

$\chi_{223}(2,\cdot)$ $\chi_{223}(4,\cdot)$ $\chi_{223}(7,\cdot)$ $\chi_{223}(8,\cdot)$ $\chi_{223}(14,\cdot)$ $\chi_{223}(15,\cdot)$ $\chi_{223}(16,\cdot)$ $\chi_{223}(17,\cdot)$ $\chi_{223}(28,\cdot)$ $\chi_{223}(30,\cdot)$ $\chi_{223}(32,\cdot)$ $\chi_{223}(33,\cdot)$ $\chi_{223}(34,\cdot)$ $\chi_{223}(41,\cdot)$ $\chi_{223}(49,\cdot)$ $\chi_{223}(56,\cdot)$ $\chi_{223}(60,\cdot)$ $\chi_{223}(64,\cdot)$ $\chi_{223}(66,\cdot)$ $\chi_{223}(68,\cdot)$ $\chi_{223}(82,\cdot)$ $\chi_{223}(98,\cdot)$ $\chi_{223}(105,\cdot)$ $\chi_{223}(112,\cdot)$ $\chi_{223}(115,\cdot)$ $\chi_{223}(119,\cdot)$ $\chi_{223}(120,\cdot)$ $\chi_{223}(128,\cdot)$ $\chi_{223}(132,\cdot)$ $\chi_{223}(136,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{37})$
Fixed field:	Number field defined by a degree 37 polynomial

Values on generators

$3$ → $e\left(\frac{24}{37}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 223 }(17, a)$	$1$	$1$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{15}{37}\right)$

Gauss sum

Jacobi sum

Kloosterman sum