Dirichlet character χ9680(613,⋅)\chi_{9680}(613,\cdot)

• Label: 9680.613
• Modulus: $9680$
• Conductor: $9680$
• Order: $220$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$9680$
Conductor:	$9680$
Order:	$220$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 9680.fh

$\chi_{9680}(237,\cdot)$ $\chi_{9680}(293,\cdot)$ $\chi_{9680}(453,\cdot)$ $\chi_{9680}(557,\cdot)$ $\chi_{9680}(613,\cdot)$ $\chi_{9680}(853,\cdot)$ $\chi_{9680}(877,\cdot)$ $\chi_{9680}(1117,\cdot)$ $\chi_{9680}(1173,\cdot)$ $\chi_{9680}(1333,\cdot)$ $\chi_{9680}(1437,\cdot)$ $\chi_{9680}(1493,\cdot)$ $\chi_{9680}(1597,\cdot)$ $\chi_{9680}(1733,\cdot)$ $\chi_{9680}(1757,\cdot)$ $\chi_{9680}(1997,\cdot)$ $\chi_{9680}(2053,\cdot)$ $\chi_{9680}(2213,\cdot)$ $\chi_{9680}(2317,\cdot)$ $\chi_{9680}(2373,\cdot)$ $\chi_{9680}(2477,\cdot)$ $\chi_{9680}(2613,\cdot)$ $\chi_{9680}(2637,\cdot)$ $\chi_{9680}(2933,\cdot)$ $\chi_{9680}(3093,\cdot)$ $\chi_{9680}(3197,\cdot)$ $\chi_{9680}(3253,\cdot)$ $\chi_{9680}(3357,\cdot)$ $\chi_{9680}(3493,\cdot)$ $\chi_{9680}(3517,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{220})$
Fixed field:	Number field defined by a degree 220 polynomial (not computed)

Values on generators

$(3631,2421,1937,4721)$ → $(1,i,-i,e\left(\frac{3}{110}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 9680 }(613, a)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{157}{220}\right)$