Dirichlet character χ8800(4113,⋅)\chi_{8800}(4113,\cdot)

• Label: 8800.4113
• 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 $\chi_{2200}(813,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 8800.iw

$\chi_{8800}(1297,\cdot)$ $\chi_{8800}(2353,\cdot)$ $\chi_{8800}(4113,\cdot)$ $\chi_{8800}(4817,\cdot)$ $\chi_{8800}(5873,\cdot)$ $\chi_{8800}(6577,\cdot)$ $\chi_{8800}(7633,\cdot)$ $\chi_{8800}(8337,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	20.20.81054451878125000000000000000000000000000000.1

Values on generators

$(2751,3301,4577,5601)$ → $(1,-1,e\left(\frac{19}{20}\right),-1)$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 8800 }(4113, a)$	$1$	$1$	$e\left(\frac{3}{20}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$