Dirichlet character χ200(47,⋅)\chi_{200}(47,\cdot)

• Label: 200.47
• Modulus: $200$
• Conductor: $100$
• Order: $20$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$200$
Conductor:	$100$
Order:	$20$
Real:	no
Primitive:	no, induced from $\chi_{100}(47,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 200.w

$\chi_{200}(23,\cdot)$ $\chi_{200}(47,\cdot)$ $\chi_{200}(63,\cdot)$ $\chi_{200}(87,\cdot)$ $\chi_{200}(103,\cdot)$ $\chi_{200}(127,\cdot)$ $\chi_{200}(167,\cdot)$ $\chi_{200}(183,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	$\Q(\zeta_{100})^+$

Values on generators

$(151,101,177)$ → $(-1,1,e\left(\frac{17}{20}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 200 }(47, a)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{20}\right)$

Gauss sum

Jacobi sum

Kloosterman sum