Dirichlet character χ43(21,⋅)\chi_{43}(21,\cdot)

• Label: 43.21
• Modulus: $43$
• Conductor: $43$
• Order: $7$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$43$
Conductor:	$43$
Order:	$7$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 43.e

$\chi_{43}(4,\cdot)$ $\chi_{43}(11,\cdot)$ $\chi_{43}(16,\cdot)$ $\chi_{43}(21,\cdot)$ $\chi_{43}(35,\cdot)$ $\chi_{43}(41,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{7})$
Fixed field:	7.7.6321363049.1

Values on generators

$3$ → $e\left(\frac{6}{7}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 43 }(21, a)$	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$

Gauss sum

Jacobi sum

Kloosterman sum