Dirichlet character χ400(23,⋅)\chi_{400}(23,\cdot)

• Label: 400.23
• Modulus: $400$
• Conductor: $200$
• Order: $20$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$400$
Conductor:	$200$
Order:	$20$
Real:	no
Primitive:	no, induced from $\chi_{200}(123,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 400.bh

$\chi_{400}(23,\cdot)$ $\chi_{400}(87,\cdot)$ $\chi_{400}(103,\cdot)$ $\chi_{400}(167,\cdot)$ $\chi_{400}(183,\cdot)$ $\chi_{400}(247,\cdot)$ $\chi_{400}(263,\cdot)$ $\chi_{400}(327,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	20.20.3125000000000000000000000000000000.1

Values on generators

$(351,101,177)$ → $(-1,-1,e\left(\frac{11}{20}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 400 }(23, a)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$

Gauss sum

Jacobi sum

Kloosterman sum