Dirichlet character χ1472(413,⋅)\chi_{1472}(413,\cdot)

• Label: 1472.413
• Modulus: $1472$
• Conductor: $1472$
• Order: $16$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1472$
Conductor:	$1472$
Order:	$16$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1472.s

$\chi_{1472}(45,\cdot)$ $\chi_{1472}(229,\cdot)$ $\chi_{1472}(413,\cdot)$ $\chi_{1472}(597,\cdot)$ $\chi_{1472}(781,\cdot)$ $\chi_{1472}(965,\cdot)$ $\chi_{1472}(1149,\cdot)$ $\chi_{1472}(1333,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{16})$
Fixed field:	16.0.47336086032831043196344263117897728.1

Values on generators

$(1151,645,833)$ → $(1,e\left(\frac{11}{16}\right),-1)$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 1472 }(413, a)$	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$i$	$-i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$