Dirichlet character χ400(69,⋅)\chi_{400}(69,\cdot)

• Label: 400.69
• Modulus: $400$
• Conductor: $400$
• Order: $20$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$400$
Conductor:	$400$
Order:	$20$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 400.bl

$\chi_{400}(29,\cdot)$ $\chi_{400}(69,\cdot)$ $\chi_{400}(109,\cdot)$ $\chi_{400}(189,\cdot)$ $\chi_{400}(229,\cdot)$ $\chi_{400}(269,\cdot)$ $\chi_{400}(309,\cdot)$ $\chi_{400}(389,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	20.20.20971520000000000000000000000000000000000.1

Values on generators

$(351,101,177)$ → $(1,i,e\left(\frac{9}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 400 }(69, a)$	$1$	$1$	$e\left(\frac{1}{20}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{20}\right)$

Gauss sum

Jacobi sum

Kloosterman sum