Dirichlet character χ215(11,⋅)\chi_{215}(11,\cdot)

• Label: 215.11
• Modulus: $215$
• Conductor: $43$
• Order: $7$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$215$
Conductor:	$43$
Order:	$7$
Real:	no
Primitive:	no, induced from $\chi_{43}(11,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 215.k

$\chi_{215}(11,\cdot)$ $\chi_{215}(16,\cdot)$ $\chi_{215}(21,\cdot)$ $\chi_{215}(41,\cdot)$ $\chi_{215}(121,\cdot)$ $\chi_{215}(176,\cdot)$

Related number fields

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

Values on generators

$(87,46)$ → $(1,e\left(\frac{5}{7}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 215 }(11, a)$	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$

Gauss sum

Jacobi sum

Kloosterman sum