Dirichlet character χ200(73,⋅)\chi_{200}(73,\cdot)

• Label: 200.73
• Modulus: $200$
• Conductor: $25$
• Order: $20$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$200$
Conductor:	$25$
Order:	$20$
Real:	no
Primitive:	no, induced from $\chi_{25}(23,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 200.u

$\chi_{200}(17,\cdot)$ $\chi_{200}(33,\cdot)$ $\chi_{200}(73,\cdot)$ $\chi_{200}(97,\cdot)$ $\chi_{200}(113,\cdot)$ $\chi_{200}(137,\cdot)$ $\chi_{200}(153,\cdot)$ $\chi_{200}(177,\cdot)$

Related number fields

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

Values on generators

$(151,101,177)$ → $(1,1,e\left(\frac{11}{20}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 200 }(73, a)$	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{20}\right)$

Gauss sum

Jacobi sum

Kloosterman sum