Dirichlet character χ5760(3791,⋅)\chi_{5760}(3791,\cdot)

• Label: 5760.3791
• Modulus: $5760$
• Conductor: $288$
• Order: $24$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$5760$
Conductor:	$288$
Order:	$24$
Real:	no
Primitive:	no, induced from $\chi_{288}(11,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 5760.es

$\chi_{5760}(911,\cdot)$ $\chi_{5760}(1391,\cdot)$ $\chi_{5760}(2351,\cdot)$ $\chi_{5760}(2831,\cdot)$ $\chi_{5760}(3791,\cdot)$ $\chi_{5760}(4271,\cdot)$ $\chi_{5760}(5231,\cdot)$ $\chi_{5760}(5711,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{24})$
Fixed field:	24.24.1486465269728735333725176976133731985582456832.1

Values on generators

$(2431,901,641,3457)$ → $(-1,e\left(\frac{5}{8}\right),e\left(\frac{1}{6}\right),1)$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 5760 }(3791, a)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{12}\right)$