Dirichlet character χ8043(509,⋅)\chi_{8043}(509,\cdot)

• Label: 8043.509
• Modulus: $8043$
• Conductor: $8043$
• Order: $1146$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8043$
Conductor:	$8043$
Order:	$1146$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8043.bb

$\chi_{8043}(17,\cdot)$ $\chi_{8043}(38,\cdot)$ $\chi_{8043}(68,\cdot)$ $\chi_{8043}(101,\cdot)$ $\chi_{8043}(110,\cdot)$ $\chi_{8043}(143,\cdot)$ $\chi_{8043}(152,\cdot)$ $\chi_{8043}(173,\cdot)$ $\chi_{8043}(185,\cdot)$ $\chi_{8043}(206,\cdot)$ $\chi_{8043}(227,\cdot)$ $\chi_{8043}(248,\cdot)$ $\chi_{8043}(278,\cdot)$ $\chi_{8043}(353,\cdot)$ $\chi_{8043}(395,\cdot)$ $\chi_{8043}(404,\cdot)$ $\chi_{8043}(425,\cdot)$ $\chi_{8043}(437,\cdot)$ $\chi_{8043}(446,\cdot)$ $\chi_{8043}(458,\cdot)$ $\chi_{8043}(467,\cdot)$ $\chi_{8043}(479,\cdot)$ $\chi_{8043}(509,\cdot)$ $\chi_{8043}(521,\cdot)$ $\chi_{8043}(530,\cdot)$ $\chi_{8043}(551,\cdot)$ $\chi_{8043}(572,\cdot)$ $\chi_{8043}(584,\cdot)$ $\chi_{8043}(626,\cdot)$ $\chi_{8043}(635,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{573})$
Fixed field:	Number field defined by a degree 1146 polynomial (not computed)

Values on generators

$(5363,2299,6133)$ → $(-1,e\left(\frac{5}{6}\right),e\left(\frac{183}{191}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{ 8043 }(509, a)$	$1$	$1$	$e\left(\frac{635}{1146}\right)$	$e\left(\frac{62}{573}\right)$	$e\left(\frac{358}{573}\right)$	$e\left(\frac{253}{382}\right)$	$e\left(\frac{205}{1146}\right)$	$e\left(\frac{637}{1146}\right)$	$e\left(\frac{219}{382}\right)$	$e\left(\frac{124}{573}\right)$	$e\left(\frac{458}{573}\right)$	$e\left(\frac{827}{1146}\right)$