Dirichlet character χ344(41,⋅)\chi_{344}(41,\cdot)

• Label: 344.41
• Modulus: $344$
• Conductor: $43$
• Order: $7$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$344$
Conductor:	$43$
Order:	$7$
Real:	no
Primitive:	no, induced from $\chi_{43}(41,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 344.q

$\chi_{344}(41,\cdot)$ $\chi_{344}(97,\cdot)$ $\chi_{344}(121,\cdot)$ $\chi_{344}(145,\cdot)$ $\chi_{344}(193,\cdot)$ $\chi_{344}(305,\cdot)$

Related number fields

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

Values on generators

$(87,173,89)$ → $(1,1,e\left(\frac{1}{7}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 344 }(41, a)$	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$

Gauss sum

Jacobi sum

Kloosterman sum