Dirichlet character χ8800(7247,⋅)\chi_{8800}(7247,\cdot)

• Label: 8800.7247
• Modulus: $8800$
• Conductor: $2200$
• Order: $20$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$8800$
Conductor:	$2200$
Order:	$20$
Real:	no
Primitive:	no, induced from $\chi_{2200}(1747,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 8800.hz

$\chi_{8800}(3887,\cdot)$ $\chi_{8800}(4623,\cdot)$ $\chi_{8800}(5327,\cdot)$ $\chi_{8800}(5967,\cdot)$ $\chi_{8800}(7247,\cdot)$ $\chi_{8800}(8303,\cdot)$ $\chi_{8800}(8463,\cdot)$ $\chi_{8800}(8783,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	Number field defined by a degree 20 polynomial

Values on generators

$(2751,3301,4577,5601)$ → $(-1,-1,e\left(\frac{17}{20}\right),e\left(\frac{3}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 8800 }(7247, a)$	$1$	$1$	$-i$	$e\left(\frac{19}{20}\right)$	$-1$	$i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$i$	$e\left(\frac{2}{5}\right)$