Dirichlet character χ352(239,⋅)\chi_{352}(239,\cdot)

• Label: 352.239
• Modulus: $352$
• Conductor: $88$
• Order: $10$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$352$
Conductor:	$88$
Order:	$10$
Real:	no
Primitive:	no, induced from $\chi_{88}(19,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 352.s

$\chi_{352}(79,\cdot)$ $\chi_{352}(239,\cdot)$ $\chi_{352}(271,\cdot)$ $\chi_{352}(303,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{5})$
Fixed field:	10.10.77265229938688.1

Values on generators

$(287,133,321)$ → $(-1,-1,e\left(\frac{3}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 352 }(239, a)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$-1$

Gauss sum

Jacobi sum

Kloosterman sum