Dirichlet character χ8800(5063,⋅)\chi_{8800}(5063,\cdot)

• Label: 8800.5063
• Modulus: $8800$
• Conductor: $4400$
• Order: $20$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$8800$
Conductor:	$4400$
Order:	$20$
Real:	no
Primitive:	no, induced from $\chi_{4400}(3963,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 8800.ks

$\chi_{8800}(247,\cdot)$ $\chi_{8800}(3623,\cdot)$ $\chi_{8800}(4887,\cdot)$ $\chi_{8800}(5063,\cdot)$ $\chi_{8800}(5703,\cdot)$ $\chi_{8800}(6983,\cdot)$ $\chi_{8800}(8567,\cdot)$ $\chi_{8800}(8727,\cdot)$

Related number fields

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

Values on generators

$(2751,3301,4577,5601)$ → $(-1,i,e\left(\frac{19}{20}\right),e\left(\frac{4}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 8800 }(5063, a)$	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$-i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$i$