Dirichlet character χ100(71,⋅)\chi_{100}(71,\cdot)

• Label: 100.71
• Modulus: $100$
• Conductor: $100$
• Order: $10$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$100$
Conductor:	$100$
Order:	$10$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 100.j

$\chi_{100}(11,\cdot)$ $\chi_{100}(31,\cdot)$ $\chi_{100}(71,\cdot)$ $\chi_{100}(91,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{5})$
Fixed field:	10.0.156250000000000.1

Values on generators

$(51,77)$ → $(-1,e\left(\frac{3}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 100 }(71, a)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$

Gauss sum

Jacobi sum

Kloosterman sum