Dirichlet character χ100(87,⋅)\chi_{100}(87,\cdot)

• Label: 100.87
• Modulus: $100$
• Conductor: $100$
• Order: $20$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$100$
Conductor:	$100$
Order:	$20$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 100.l

$\chi_{100}(3,\cdot)$ $\chi_{100}(23,\cdot)$ $\chi_{100}(27,\cdot)$ $\chi_{100}(47,\cdot)$ $\chi_{100}(63,\cdot)$ $\chi_{100}(67,\cdot)$ $\chi_{100}(83,\cdot)$ $\chi_{100}(87,\cdot)$

Related number fields

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

Values on generators

$(51,77)$ → $(-1,e\left(\frac{9}{20}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 100 }(87, a)$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$-i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{20}\right)$

Gauss sum

Jacobi sum

Kloosterman sum