Dirichlet character χ209(138,⋅)\chi_{209}(138,\cdot)

• Label: 209.138
• Modulus: $209$
• Conductor: $209$
• Order: $90$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$209$
Conductor:	$209$
Order:	$90$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 209.v

$\chi_{209}(6,\cdot)$ $\chi_{209}(17,\cdot)$ $\chi_{209}(24,\cdot)$ $\chi_{209}(28,\cdot)$ $\chi_{209}(35,\cdot)$ $\chi_{209}(61,\cdot)$ $\chi_{209}(62,\cdot)$ $\chi_{209}(63,\cdot)$ $\chi_{209}(73,\cdot)$ $\chi_{209}(74,\cdot)$ $\chi_{209}(85,\cdot)$ $\chi_{209}(101,\cdot)$ $\chi_{209}(112,\cdot)$ $\chi_{209}(118,\cdot)$ $\chi_{209}(123,\cdot)$ $\chi_{209}(138,\cdot)$ $\chi_{209}(139,\cdot)$ $\chi_{209}(149,\cdot)$ $\chi_{209}(150,\cdot)$ $\chi_{209}(156,\cdot)$ $\chi_{209}(161,\cdot)$ $\chi_{209}(194,\cdot)$ $\chi_{209}(195,\cdot)$ $\chi_{209}(206,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{45})$
Fixed field:	Number field defined by a degree 90 polynomial

Values on generators

$(134,78)$ → $(e\left(\frac{9}{10}\right),e\left(\frac{8}{9}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 209 }(138, a)$	$-1$	$1$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum