Dirichlet character χ2760(401,⋅)\chi_{2760}(401,\cdot)

• Label: 2760.401
• Modulus: $2760$
• Conductor: $69$
• Order: $22$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2760$
Conductor:	$69$
Order:	$22$
Real:	no
Primitive:	no, induced from $\chi_{69}(56,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 2760.cn

$\chi_{2760}(281,\cdot)$ $\chi_{2760}(401,\cdot)$ $\chi_{2760}(521,\cdot)$ $\chi_{2760}(641,\cdot)$ $\chi_{2760}(881,\cdot)$ $\chi_{2760}(1121,\cdot)$ $\chi_{2760}(1601,\cdot)$ $\chi_{2760}(1721,\cdot)$ $\chi_{2760}(2081,\cdot)$ $\chi_{2760}(2321,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{11})$
Fixed field:	$\Q(\zeta_{69})^+$

Values on generators

$(2071,1381,1841,1657,1201)$ → $(1,1,-1,1,e\left(\frac{3}{22}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 2760 }(401, a)$	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{15}{22}\right)$