Dirichlet character χ352(5,⋅)\chi_{352}(5,\cdot)

• Label: 352.5
• Modulus: $352$
• Conductor: $352$
• Order: $40$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$352$
Conductor:	$352$
Order:	$40$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 352.bf

$\chi_{352}(5,\cdot)$ $\chi_{352}(37,\cdot)$ $\chi_{352}(53,\cdot)$ $\chi_{352}(69,\cdot)$ $\chi_{352}(93,\cdot)$ $\chi_{352}(125,\cdot)$ $\chi_{352}(141,\cdot)$ $\chi_{352}(157,\cdot)$ $\chi_{352}(181,\cdot)$ $\chi_{352}(213,\cdot)$ $\chi_{352}(229,\cdot)$ $\chi_{352}(245,\cdot)$ $\chi_{352}(269,\cdot)$ $\chi_{352}(301,\cdot)$ $\chi_{352}(317,\cdot)$ $\chi_{352}(333,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{40})$
Fixed field:	40.40.96430685261162182749113906515642066253992366248338958954046471967872161601814528.1

Values on generators

$(287,133,321)$ → $(1,e\left(\frac{1}{8}\right),e\left(\frac{2}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 352 }(5, a)$	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{5}{8}\right)$	$-i$

Gauss sum

Jacobi sum

Kloosterman sum