Dirichlet character χ8800(4311,⋅)\chi_{8800}(4311,\cdot)

• Label: 8800.4311
• 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 $\chi_{4400}(1011,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 8800.gw

$\chi_{8800}(791,\cdot)$ $\chi_{8800}(1671,\cdot)$ $\chi_{8800}(3431,\cdot)$ $\chi_{8800}(4311,\cdot)$ $\chi_{8800}(5191,\cdot)$ $\chi_{8800}(6071,\cdot)$ $\chi_{8800}(7831,\cdot)$ $\chi_{8800}(8711,\cdot)$

Related number fields

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

Values on generators

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

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 8800 }(4311, a)$	$1$	$1$	$e\left(\frac{7}{20}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$