Dirichlet character χ3800(77,⋅)\chi_{3800}(77,\cdot)

• Label: 3800.77
• Modulus: $3800$
• Conductor: $200$
• Order: $20$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3800$
Conductor:	$200$
Order:	$20$
Real:	no
Primitive:	no, induced from $\chi_{200}(77,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 3800.dk

$\chi_{3800}(77,\cdot)$ $\chi_{3800}(533,\cdot)$ $\chi_{3800}(837,\cdot)$ $\chi_{3800}(1597,\cdot)$ $\chi_{3800}(2053,\cdot)$ $\chi_{3800}(2813,\cdot)$ $\chi_{3800}(3117,\cdot)$ $\chi_{3800}(3573,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	20.0.3125000000000000000000000000000000.1

Values on generators

$(951,1901,1977,401)$ → $(1,-1,e\left(\frac{1}{20}\right),1)$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3800 }(77, a)$	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{5}\right)$