Dirichlet character χ8043(76,⋅)\chi_{8043}(76,\cdot)

• Label: 8043.76
• Modulus: $8043$
• Conductor: $2681$
• Order: $382$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$8043$
Conductor:	$2681$
Order:	$382$
Real:	no
Primitive:	no, induced from $\chi_{2681}(76,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 8043.s

$\chi_{8043}(34,\cdot)$ $\chi_{8043}(55,\cdot)$ $\chi_{8043}(76,\cdot)$ $\chi_{8043}(139,\cdot)$ $\chi_{8043}(202,\cdot)$ $\chi_{8043}(223,\cdot)$ $\chi_{8043}(265,\cdot)$ $\chi_{8043}(286,\cdot)$ $\chi_{8043}(370,\cdot)$ $\chi_{8043}(391,\cdot)$ $\chi_{8043}(412,\cdot)$ $\chi_{8043}(433,\cdot)$ $\chi_{8043}(454,\cdot)$ $\chi_{8043}(475,\cdot)$ $\chi_{8043}(496,\cdot)$ $\chi_{8043}(517,\cdot)$ $\chi_{8043}(643,\cdot)$ $\chi_{8043}(706,\cdot)$ $\chi_{8043}(727,\cdot)$ $\chi_{8043}(769,\cdot)$ $\chi_{8043}(790,\cdot)$ $\chi_{8043}(853,\cdot)$ $\chi_{8043}(874,\cdot)$ $\chi_{8043}(895,\cdot)$ $\chi_{8043}(916,\cdot)$ $\chi_{8043}(937,\cdot)$ $\chi_{8043}(958,\cdot)$ $\chi_{8043}(979,\cdot)$ $\chi_{8043}(1042,\cdot)$ $\chi_{8043}(1105,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{191})$
Fixed field:	Number field defined by a degree 382 polynomial (not computed)

Values on generators

$(5363,2299,6133)$ → $(1,-1,e\left(\frac{8}{191}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{ 8043 }(76, a)$	$-1$	$1$	$e\left(\frac{117}{191}\right)$	$e\left(\frac{43}{191}\right)$	$e\left(\frac{207}{382}\right)$	$e\left(\frac{160}{191}\right)$	$e\left(\frac{59}{382}\right)$	$e\left(\frac{53}{191}\right)$	$e\left(\frac{163}{382}\right)$	$e\left(\frac{86}{191}\right)$	$e\left(\frac{13}{382}\right)$	$e\left(\frac{361}{382}\right)$