Dirichlet character χ200(133,⋅)\chi_{200}(133,\cdot)

• Label: 200.133
• Modulus: $200$
• Conductor: $200$
• Order: $20$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$200$
Conductor:	$200$
Order:	$20$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 200.x

$\chi_{200}(13,\cdot)$ $\chi_{200}(37,\cdot)$ $\chi_{200}(53,\cdot)$ $\chi_{200}(77,\cdot)$ $\chi_{200}(117,\cdot)$ $\chi_{200}(133,\cdot)$ $\chi_{200}(173,\cdot)$ $\chi_{200}(197,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	20.0.3125000000000000000000000000000000.1

Values on generators

$(151,101,177)$ → $(1,-1,e\left(\frac{3}{20}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 200 }(133, a)$	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{20}\right)$

Gauss sum

Jacobi sum

Kloosterman sum