Dirichlet character χ4140(19,⋅)\chi_{4140}(19,\cdot)

• Label: 4140.19
• Modulus: $4140$
• Conductor: $460$
• Order: $22$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4140$
Conductor:	$460$
Order:	$22$
Real:	no
Primitive:	no, induced from $\chi_{460}(19,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 4140.cg

$\chi_{4140}(19,\cdot)$ $\chi_{4140}(199,\cdot)$ $\chi_{4140}(379,\cdot)$ $\chi_{4140}(559,\cdot)$ $\chi_{4140}(1279,\cdot)$ $\chi_{4140}(1459,\cdot)$ $\chi_{4140}(1999,\cdot)$ $\chi_{4140}(2179,\cdot)$ $\chi_{4140}(2719,\cdot)$ $\chi_{4140}(3079,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{11})$
Fixed field:	22.22.8083780427918435509708715954790400000000000.1

Values on generators

$(2071,461,1657,3961)$ → $(-1,1,-1,e\left(\frac{15}{22}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 4140 }(19, a)$	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{22}\right)$