Dirichlet character χ2200(3,⋅)\chi_{2200}(3,\cdot)

• Label: 2200.3
• Modulus: $2200$
• Conductor: $2200$
• Order: $20$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2200$
Conductor:	$2200$
Order:	$20$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2200.gd

$\chi_{2200}(3,\cdot)$ $\chi_{2200}(27,\cdot)$ $\chi_{2200}(163,\cdot)$ $\chi_{2200}(1147,\cdot)$ $\chi_{2200}(1467,\cdot)$ $\chi_{2200}(1523,\cdot)$ $\chi_{2200}(2083,\cdot)$ $\chi_{2200}(2187,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	Number field defined by a degree 20 polynomial

Values on generators

$(551,1101,177,1201)$ → $(-1,-1,e\left(\frac{7}{20}\right),e\left(\frac{4}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 2200 }(3, a)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$