Dirichlet character χ2640(709,⋅)\chi_{2640}(709,\cdot)

• Label: 2640.709
• Modulus: $2640$
• Conductor: $880$
• Order: $20$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2640$
Conductor:	$880$
Order:	$20$
Real:	no
Primitive:	no, induced from $\chi_{880}(709,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 2640.eo

$\chi_{2640}(229,\cdot)$ $\chi_{2640}(709,\cdot)$ $\chi_{2640}(829,\cdot)$ $\chi_{2640}(949,\cdot)$ $\chi_{2640}(1549,\cdot)$ $\chi_{2640}(2029,\cdot)$ $\chi_{2640}(2149,\cdot)$ $\chi_{2640}(2269,\cdot)$

Related number fields

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

Values on generators

$(991,661,881,1057,1201)$ → $(1,i,1,-1,e\left(\frac{2}{5}\right))$

First values

$a$	$-1$	$1$	$7$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 2640 }(709, a)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$