Dirichlet character χ2240(923,⋅)\chi_{2240}(923,\cdot)

• Label: 2240.923
• Modulus: $2240$
• Conductor: $2240$
• Order: $16$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$2240$
Conductor:	$2240$
Order:	$16$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2240.ee

$\chi_{2240}(307,\cdot)$ $\chi_{2240}(363,\cdot)$ $\chi_{2240}(867,\cdot)$ $\chi_{2240}(923,\cdot)$ $\chi_{2240}(1427,\cdot)$ $\chi_{2240}(1483,\cdot)$ $\chi_{2240}(1987,\cdot)$ $\chi_{2240}(2043,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{16})$
Fixed field:	16.0.850734469462919174923747328000000000000.1

Values on generators

$(1471,1541,897,1921)$ → $(-1,e\left(\frac{9}{16}\right),-i,-1)$

First values

$a$	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{ 2240 }(923, a)$	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-1$