Dirichlet character χ8800(4701,⋅)\chi_{8800}(4701,\cdot)

• Label: 8800.4701
• Modulus: $8800$
• Conductor: $352$
• Order: $40$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8800$
Conductor:	$352$
Order:	$40$
Real:	no
Primitive:	no, induced from $\chi_{352}(125,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 8800.nn

$\chi_{8800}(301,\cdot)$ $\chi_{8800}(1301,\cdot)$ $\chi_{8800}(1501,\cdot)$ $\chi_{8800}(1901,\cdot)$ $\chi_{8800}(2501,\cdot)$ $\chi_{8800}(3501,\cdot)$ $\chi_{8800}(3701,\cdot)$ $\chi_{8800}(4101,\cdot)$ $\chi_{8800}(4701,\cdot)$ $\chi_{8800}(5701,\cdot)$ $\chi_{8800}(5901,\cdot)$ $\chi_{8800}(6301,\cdot)$ $\chi_{8800}(6901,\cdot)$ $\chi_{8800}(7901,\cdot)$ $\chi_{8800}(8101,\cdot)$ $\chi_{8800}(8501,\cdot)$

Related number fields

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

Values on generators

$(2751,3301,4577,5601)$ → $(1,e\left(\frac{3}{8}\right),1,e\left(\frac{1}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 8800 }(4701, a)$	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{21}{40}\right)$