Dirichlet character χ200(21,⋅)\chi_{200}(21,\cdot)

• Label: 200.21
• Modulus: $200$
• Conductor: $200$
• Order: $10$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$200$
Conductor:	$200$
Order:	$10$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 200.t

$\chi_{200}(21,\cdot)$ $\chi_{200}(61,\cdot)$ $\chi_{200}(141,\cdot)$ $\chi_{200}(181,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{5})$
Fixed field:	10.10.5000000000000000.1

Values on generators

$(151,101,177)$ → $(1,-1,e\left(\frac{3}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 200 }(21, a)$	$1$	$1$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$

Gauss sum

Jacobi sum

Kloosterman sum