Dirichlet character χ1200(163,⋅)\chi_{1200}(163,\cdot)

• Label: 1200.163
• Modulus: $1200$
• Conductor: $400$
• Order: $20$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1200$
Conductor:	$400$
Order:	$20$
Real:	no
Primitive:	no, induced from $\chi_{400}(163,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 1200.ct

$\chi_{1200}(163,\cdot)$ $\chi_{1200}(187,\cdot)$ $\chi_{1200}(403,\cdot)$ $\chi_{1200}(427,\cdot)$ $\chi_{1200}(667,\cdot)$ $\chi_{1200}(883,\cdot)$ $\chi_{1200}(1123,\cdot)$ $\chi_{1200}(1147,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	20.20.104857600000000000000000000000000000000000.2

Values on generators

$(751,901,401,577)$ → $(-1,-i,1,e\left(\frac{19}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 1200 }(163, a)$	$1$	$1$	$-i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$