Dirichlet character χ800(667,⋅)\chi_{800}(667,\cdot)

• Label: 800.667
• Modulus: $800$
• Conductor: $800$
• Order: $40$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$800$
Conductor:	$800$
Order:	$40$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 800.cd

$\chi_{800}(3,\cdot)$ $\chi_{800}(27,\cdot)$ $\chi_{800}(83,\cdot)$ $\chi_{800}(163,\cdot)$ $\chi_{800}(187,\cdot)$ $\chi_{800}(267,\cdot)$ $\chi_{800}(323,\cdot)$ $\chi_{800}(347,\cdot)$ $\chi_{800}(403,\cdot)$ $\chi_{800}(427,\cdot)$ $\chi_{800}(483,\cdot)$ $\chi_{800}(563,\cdot)$ $\chi_{800}(587,\cdot)$ $\chi_{800}(667,\cdot)$ $\chi_{800}(723,\cdot)$ $\chi_{800}(747,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{40})$
Fixed field:	40.40.386856262276681335905976320000000000000000000000000000000000000000000000000000000000000000000000.1

Values on generators

$(351,101,577)$ → $(-1,e\left(\frac{1}{8}\right),e\left(\frac{13}{20}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 800 }(667, a)$	$1$	$1$	$e\left(\frac{17}{40}\right)$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{40}\right)$

Gauss sum

Jacobi sum

Kloosterman sum