Dirichlet character χ9680(529,⋅)\chi_{9680}(529,\cdot)

• Label: 9680.529
• Modulus: $9680$
• Conductor: $605$
• Order: $22$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$9680$
Conductor:	$605$
Order:	$22$
Real:	no
Primitive:	no, induced from $\chi_{605}(529,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 9680.dk

$\chi_{9680}(529,\cdot)$ $\chi_{9680}(1409,\cdot)$ $\chi_{9680}(2289,\cdot)$ $\chi_{9680}(3169,\cdot)$ $\chi_{9680}(4049,\cdot)$ $\chi_{9680}(4929,\cdot)$ $\chi_{9680}(6689,\cdot)$ $\chi_{9680}(7569,\cdot)$ $\chi_{9680}(8449,\cdot)$ $\chi_{9680}(9329,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{11})$
Fixed field:	Number field defined by a degree 22 polynomial

Values on generators

$(3631,2421,1937,4721)$ → $(1,1,-1,e\left(\frac{3}{11}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 9680 }(529, a)$	$1$	$1$	$-1$	$e\left(\frac{9}{22}\right)$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$	$-1$	$e\left(\frac{7}{11}\right)$