Dirichlet character χ1632(1397,⋅)\chi_{1632}(1397,\cdot)

• Label: 1632.1397
• Modulus: $1632$
• Conductor: $1632$
• Order: $16$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1632$
Conductor:	$1632$
Order:	$16$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1632.dw

$\chi_{1632}(5,\cdot)$ $\chi_{1632}(125,\cdot)$ $\chi_{1632}(317,\cdot)$ $\chi_{1632}(653,\cdot)$ $\chi_{1632}(1253,\cdot)$ $\chi_{1632}(1397,\cdot)$ $\chi_{1632}(1421,\cdot)$ $\chi_{1632}(1493,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{16})$
Fixed field:	16.16.86609112753862292411929816663129369608192.2

Values on generators

$(511,613,545,1057)$ → $(1,e\left(\frac{5}{8}\right),-1,e\left(\frac{1}{16}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{ 1632 }(1397, a)$	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$