Dirichlet character χ1296(17,⋅)\chi_{1296}(17,\cdot)

• Label: 1296.17
• Modulus: $1296$
• Conductor: $27$
• Order: $18$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$1296$
Conductor:	$27$
Order:	$18$
Real:	no
Primitive:	no, induced from $\chi_{27}(23,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 1296.bc

$\chi_{1296}(17,\cdot)$ $\chi_{1296}(305,\cdot)$ $\chi_{1296}(449,\cdot)$ $\chi_{1296}(737,\cdot)$ $\chi_{1296}(881,\cdot)$ $\chi_{1296}(1169,\cdot)$

Related number fields

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

Values on generators

$(1135,325,1217)$ → $(1,1,e\left(\frac{11}{18}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{ 1296 }(17, a)$	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$