Dirichlet character χ352(215,⋅)\chi_{352}(215,\cdot)

• Label: 352.215
• Modulus: $352$
• Conductor: $176$
• Order: $20$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$352$
Conductor:	$176$
Order:	$20$
Real:	no
Primitive:	no, induced from $\chi_{176}(83,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 352.bb

$\chi_{352}(7,\cdot)$ $\chi_{352}(39,\cdot)$ $\chi_{352}(151,\cdot)$ $\chi_{352}(167,\cdot)$ $\chi_{352}(183,\cdot)$ $\chi_{352}(215,\cdot)$ $\chi_{352}(327,\cdot)$ $\chi_{352}(343,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	20.20.200317132330035063121671003054276608.1

Values on generators

$(287,133,321)$ → $(-1,-i,e\left(\frac{9}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 352 }(215, a)$	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$i$	$1$

Gauss sum

Jacobi sum

Kloosterman sum