Dirichlet character χ704(393,⋅)\chi_{704}(393,\cdot)

• Label: 704.393
• Modulus: $704$
• Conductor: $352$
• Order: $40$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$704$
Conductor:	$352$
Order:	$40$
Real:	no
Primitive:	no, induced from $\chi_{352}(349,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 704.bi

$\chi_{704}(41,\cdot)$ $\chi_{704}(57,\cdot)$ $\chi_{704}(73,\cdot)$ $\chi_{704}(105,\cdot)$ $\chi_{704}(217,\cdot)$ $\chi_{704}(233,\cdot)$ $\chi_{704}(249,\cdot)$ $\chi_{704}(281,\cdot)$ $\chi_{704}(393,\cdot)$ $\chi_{704}(409,\cdot)$ $\chi_{704}(425,\cdot)$ $\chi_{704}(457,\cdot)$ $\chi_{704}(569,\cdot)$ $\chi_{704}(585,\cdot)$ $\chi_{704}(601,\cdot)$ $\chi_{704}(633,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{40})$
Fixed field:	40.0.1411841662908675517629776705295515492024702234241930698046194396081616318012166504448.1

Values on generators

$(639,133,321)$ → $(1,e\left(\frac{3}{8}\right),e\left(\frac{3}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 704 }(393, a)$	$-1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{8}\right)$	$i$

Gauss sum

Jacobi sum

Kloosterman sum