Dirichlet character χ441(226,⋅)\chi_{441}(226,\cdot)

• Label: 441.226
• Modulus: $441$
• Conductor: $7$
• Order: $3$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$441$
Conductor:	$7$
Order:	$3$
Real:	no
Primitive:	no, induced from $\chi_{7}(2,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 441.e

$\chi_{441}(226,\cdot)$ $\chi_{441}(361,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	$\Q(\zeta_{7})^+$

Values on generators

$(344,199)$ → $(1,e\left(\frac{1}{3}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{ 441 }(226, a)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum