Dirichlet character χ8043(340,⋅)\chi_{8043}(340,\cdot)

• Label: 8043.340
• Modulus: $8043$
• Conductor: $2681$
• Order: $1146$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$8043$
Conductor:	$2681$
Order:	$1146$
Real:	no
Primitive:	no, induced from $\chi_{2681}(340,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 8043.bd

$\chi_{8043}(37,\cdot)$ $\chi_{8043}(79,\cdot)$ $\chi_{8043}(88,\cdot)$ $\chi_{8043}(109,\cdot)$ $\chi_{8043}(151,\cdot)$ $\chi_{8043}(163,\cdot)$ $\chi_{8043}(214,\cdot)$ $\chi_{8043}(247,\cdot)$ $\chi_{8043}(310,\cdot)$ $\chi_{8043}(319,\cdot)$ $\chi_{8043}(340,\cdot)$ $\chi_{8043}(352,\cdot)$ $\chi_{8043}(394,\cdot)$ $\chi_{8043}(403,\cdot)$ $\chi_{8043}(424,\cdot)$ $\chi_{8043}(436,\cdot)$ $\chi_{8043}(457,\cdot)$ $\chi_{8043}(466,\cdot)$ $\chi_{8043}(478,\cdot)$ $\chi_{8043}(487,\cdot)$ $\chi_{8043}(508,\cdot)$ $\chi_{8043}(541,\cdot)$ $\chi_{8043}(550,\cdot)$ $\chi_{8043}(562,\cdot)$ $\chi_{8043}(571,\cdot)$ $\chi_{8043}(592,\cdot)$ $\chi_{8043}(604,\cdot)$ $\chi_{8043}(613,\cdot)$ $\chi_{8043}(697,\cdot)$ $\chi_{8043}(709,\cdot)$ ...

Related number fields

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

Values on generators

$(5363,2299,6133)$ → $(1,e\left(\frac{2}{3}\right),e\left(\frac{43}{382}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{ 8043 }(340, a)$	$-1$	$1$	$e\left(\frac{239}{573}\right)$	$e\left(\frac{478}{573}\right)$	$e\left(\frac{511}{1146}\right)$	$e\left(\frac{48}{191}\right)$	$e\left(\frac{989}{1146}\right)$	$e\left(\frac{401}{1146}\right)$	$e\left(\frac{259}{382}\right)$	$e\left(\frac{383}{573}\right)$	$e\left(\frac{130}{573}\right)$	$e\left(\frac{554}{573}\right)$