Dirichlet character χ284(261,⋅)\chi_{284}(261,\cdot)

• Label: 284.261
• Modulus: $284$
• Conductor: $71$
• Order: $7$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$284$
Conductor:	$71$
Order:	$7$
Real:	no
Primitive:	no, induced from $\chi_{71}(48,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 284.f

$\chi_{284}(37,\cdot)$ $\chi_{284}(45,\cdot)$ $\chi_{284}(101,\cdot)$ $\chi_{284}(233,\cdot)$ $\chi_{284}(245,\cdot)$ $\chi_{284}(261,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{7})$
Fixed field:	7.7.128100283921.1

Values on generators

$(143,149)$ → $(1,e\left(\frac{5}{7}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 284 }(261, a)$	$1$	$1$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$

Gauss sum

Jacobi sum

Kloosterman sum