Dirichlet character χ1197(1040,⋅)\chi_{1197}(1040,\cdot)

• Label: 1197.1040
• Modulus: $1197$
• Conductor: $1197$
• Order: $18$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1197$
Conductor:	$1197$
Order:	$18$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1197.fm

$\chi_{1197}(317,\cdot)$ $\chi_{1197}(725,\cdot)$ $\chi_{1197}(884,\cdot)$ $\chi_{1197}(914,\cdot)$ $\chi_{1197}(1040,\cdot)$ $\chi_{1197}(1136,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{9})$
Fixed field:	Number field defined by a degree 18 polynomial

Values on generators

$(533,514,1009)$ → $(e\left(\frac{5}{6}\right),e\left(\frac{2}{3}\right),e\left(\frac{7}{18}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$20$
$\chi_{ 1197 }(1040, a)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{6}\right)$