Dirichlet character χ800(229,⋅)\chi_{800}(229,\cdot)

• Label: 800.229
• 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.by

$\chi_{800}(29,\cdot)$ $\chi_{800}(69,\cdot)$ $\chi_{800}(109,\cdot)$ $\chi_{800}(189,\cdot)$ $\chi_{800}(229,\cdot)$ $\chi_{800}(269,\cdot)$ $\chi_{800}(309,\cdot)$ $\chi_{800}(389,\cdot)$ $\chi_{800}(429,\cdot)$ $\chi_{800}(469,\cdot)$ $\chi_{800}(509,\cdot)$ $\chi_{800}(589,\cdot)$ $\chi_{800}(629,\cdot)$ $\chi_{800}(669,\cdot)$ $\chi_{800}(709,\cdot)$ $\chi_{800}(789,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{40})$
Fixed field:	40.40.15474250491067253436239052800000000000000000000000000000000000000000000000000000000000000000000.1

Values on generators

$(351,101,577)$ → $(1,e\left(\frac{1}{8}\right),e\left(\frac{1}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 800 }(229, a)$	$1$	$1$	$e\left(\frac{3}{40}\right)$	$-i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{40}\right)$

Gauss sum

Jacobi sum

Kloosterman sum