Dirichlet character χ400(33,⋅)\chi_{400}(33,\cdot)

• Label: 400.33
• Modulus: $400$
• Conductor: $25$
• Order: $20$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$400$
Conductor:	$25$
Order:	$20$
Real:	no
Primitive:	no, induced from $\chi_{25}(8,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 400.bg

$\chi_{400}(17,\cdot)$ $\chi_{400}(33,\cdot)$ $\chi_{400}(97,\cdot)$ $\chi_{400}(113,\cdot)$ $\chi_{400}(177,\cdot)$ $\chi_{400}(273,\cdot)$ $\chi_{400}(337,\cdot)$ $\chi_{400}(353,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	Number field defined by a degree 20 polynomial

Values on generators

$(351,101,177)$ → $(1,1,e\left(\frac{3}{20}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 400 }(33, a)$	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$

Gauss sum

Jacobi sum

Kloosterman sum