Dirichlet character χ400(21,⋅)\chi_{400}(21,\cdot)

• Label: 400.21
• Modulus: $400$
• Conductor: $400$
• Order: $20$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$400$
Conductor:	$400$
Order:	$20$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 400.be

$\chi_{400}(21,\cdot)$ $\chi_{400}(61,\cdot)$ $\chi_{400}(141,\cdot)$ $\chi_{400}(181,\cdot)$ $\chi_{400}(221,\cdot)$ $\chi_{400}(261,\cdot)$ $\chi_{400}(341,\cdot)$ $\chi_{400}(381,\cdot)$

Related number fields

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

Values on generators

$(351,101,177)$ → $(1,i,e\left(\frac{3}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 400 }(21, a)$	$1$	$1$	$e\left(\frac{19}{20}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$

Gauss sum

Jacobi sum

Kloosterman sum