Dirichlet character χ4400(131,⋅)\chi_{4400}(131,\cdot)

• Label: 4400.131
• Modulus: $4400$
• Conductor: $4400$
• Order: $20$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4400$
Conductor:	$4400$
Order:	$20$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4400.gg

$\chi_{4400}(131,\cdot)$ $\chi_{4400}(571,\cdot)$ $\chi_{4400}(1011,\cdot)$ $\chi_{4400}(1891,\cdot)$ $\chi_{4400}(2331,\cdot)$ $\chi_{4400}(2771,\cdot)$ $\chi_{4400}(3211,\cdot)$ $\chi_{4400}(4091,\cdot)$

Related number fields

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

Values on generators

$(2751,3301,177,1201)$ → $(-1,-i,e\left(\frac{2}{5}\right),-1)$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 4400 }(131, a)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$