Dirichlet character χ1200(533,⋅)\chi_{1200}(533,\cdot)

• Label: 1200.533
• Modulus: $1200$
• Conductor: $1200$
• Order: $20$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1200$
Conductor:	$1200$
Order:	$20$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1200.cm

$\chi_{1200}(53,\cdot)$ $\chi_{1200}(77,\cdot)$ $\chi_{1200}(317,\cdot)$ $\chi_{1200}(533,\cdot)$ $\chi_{1200}(773,\cdot)$ $\chi_{1200}(797,\cdot)$ $\chi_{1200}(1013,\cdot)$ $\chi_{1200}(1037,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	20.20.6191736422400000000000000000000000000000000000.1

Values on generators

$(751,901,401,577)$ → $(1,i,-1,e\left(\frac{3}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 1200 }(533, a)$	$1$	$1$	$i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$