Dirichlet character χ3744(2767,⋅)\chi_{3744}(2767,\cdot)

• Label: 3744.2767
• Modulus: $3744$
• Conductor: $936$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$3744$
Conductor:	$936$
Order:	$12$
Real:	no
Primitive:	no, induced from $\chi_{936}(427,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 3744.gx

$\chi_{3744}(943,\cdot)$ $\chi_{3744}(2671,\cdot)$ $\chi_{3744}(2767,\cdot)$ $\chi_{3744}(3343,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.12.20223525773472118256959488.1

Values on generators

$(703,2341,2081,2017)$ → $(-1,-1,e\left(\frac{1}{3}\right),e\left(\frac{7}{12}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{ 3744 }(2767, a)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$