Dirichlet character χ8800(7493,⋅)\chi_{8800}(7493,\cdot)

• Label: 8800.7493
• Modulus: $8800$
• Conductor: $1760$
• Order: $40$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8800$
Conductor:	$1760$
Order:	$40$
Real:	no
Primitive:	no, induced from $\chi_{1760}(453,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 8800.ow

$\chi_{8800}(293,\cdot)$ $\chi_{8800}(557,\cdot)$ $\chi_{8800}(1493,\cdot)$ $\chi_{8800}(1757,\cdot)$ $\chi_{8800}(3093,\cdot)$ $\chi_{8800}(3357,\cdot)$ $\chi_{8800}(3493,\cdot)$ $\chi_{8800}(3757,\cdot)$ $\chi_{8800}(4693,\cdot)$ $\chi_{8800}(4957,\cdot)$ $\chi_{8800}(5893,\cdot)$ $\chi_{8800}(6157,\cdot)$ $\chi_{8800}(7493,\cdot)$ $\chi_{8800}(7757,\cdot)$ $\chi_{8800}(7893,\cdot)$ $\chi_{8800}(8157,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{40})$
Fixed field:	40.40.1314880012449506220994309247746612403564809108378301093397843089030698237952000000000000000000000000000000.1

Values on generators

$(2751,3301,4577,5601)$ → $(1,e\left(\frac{1}{8}\right),-i,e\left(\frac{1}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 8800 }(7493, a)$	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{23}{40}\right)$