Dirichlet character χ1089(1024,⋅)\chi_{1089}(1024,\cdot)

• Label: 1089.1024
• Modulus: $1089$
• Conductor: $1089$
• Order: $33$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1089$
Conductor:	$1089$
Order:	$33$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1089.u

$\chi_{1089}(34,\cdot)$ $\chi_{1089}(67,\cdot)$ $\chi_{1089}(133,\cdot)$ $\chi_{1089}(166,\cdot)$ $\chi_{1089}(232,\cdot)$ $\chi_{1089}(265,\cdot)$ $\chi_{1089}(331,\cdot)$ $\chi_{1089}(430,\cdot)$ $\chi_{1089}(463,\cdot)$ $\chi_{1089}(529,\cdot)$ $\chi_{1089}(562,\cdot)$ $\chi_{1089}(628,\cdot)$ $\chi_{1089}(661,\cdot)$ $\chi_{1089}(760,\cdot)$ $\chi_{1089}(826,\cdot)$ $\chi_{1089}(859,\cdot)$ $\chi_{1089}(925,\cdot)$ $\chi_{1089}(958,\cdot)$ $\chi_{1089}(1024,\cdot)$ $\chi_{1089}(1057,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{33})$
Fixed field:	Number field defined by a degree 33 polynomial

Values on generators

$(848,244)$ → $(e\left(\frac{2}{3}\right),e\left(\frac{1}{11}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{ 1089 }(1024, a)$	$1$	$1$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{5}{11}\right)$