Dirichlet character χ209(169,⋅)\chi_{209}(169,\cdot)

• Label: 209.169
• Modulus: $209$
• Conductor: $209$
• Order: $45$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$209$
Conductor:	$209$
Order:	$45$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 209.u

$\chi_{209}(4,\cdot)$ $\chi_{209}(5,\cdot)$ $\chi_{209}(9,\cdot)$ $\chi_{209}(16,\cdot)$ $\chi_{209}(25,\cdot)$ $\chi_{209}(36,\cdot)$ $\chi_{209}(42,\cdot)$ $\chi_{209}(47,\cdot)$ $\chi_{209}(80,\cdot)$ $\chi_{209}(81,\cdot)$ $\chi_{209}(82,\cdot)$ $\chi_{209}(92,\cdot)$ $\chi_{209}(93,\cdot)$ $\chi_{209}(104,\cdot)$ $\chi_{209}(119,\cdot)$ $\chi_{209}(130,\cdot)$ $\chi_{209}(137,\cdot)$ $\chi_{209}(157,\cdot)$ $\chi_{209}(158,\cdot)$ $\chi_{209}(168,\cdot)$ $\chi_{209}(169,\cdot)$ $\chi_{209}(180,\cdot)$ $\chi_{209}(196,\cdot)$ $\chi_{209}(207,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{45})$
Fixed field:	45.45.43679806300610465846484971330073185012597520004657724600953543350870941304329239684756561.1

Values on generators

$(134,78)$ → $(e\left(\frac{1}{5}\right),e\left(\frac{5}{9}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 209 }(169, a)$	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum