Dirichlet character χ441(251,⋅)\chi_{441}(251,\cdot)

• Label: 441.251
• Modulus: $441$
• Conductor: $147$
• Order: $14$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$441$
Conductor:	$147$
Order:	$14$
Real:	no
Primitive:	no, induced from $\chi_{147}(104,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 441.w

$\chi_{441}(62,\cdot)$ $\chi_{441}(125,\cdot)$ $\chi_{441}(188,\cdot)$ $\chi_{441}(251,\cdot)$ $\chi_{441}(314,\cdot)$ $\chi_{441}(377,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{7})$
Fixed field:	14.14.2932917071205091238064909.1

Values on generators

$(344,199)$ → $(-1,e\left(\frac{9}{14}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{ 441 }(251, a)$	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$-1$

Gauss sum

Jacobi sum

Kloosterman sum