Dirichlet character χ3800(2001,⋅)\chi_{3800}(2001,\cdot)

• Label: 3800.2001
• Modulus: $3800$
• Conductor: $19$
• Order: $9$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$3800$
Conductor:	$19$
Order:	$9$
Real:	no
Primitive:	no, induced from $\chi_{19}(6,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 3800.bp

$\chi_{3800}(1201,\cdot)$ $\chi_{3800}(1601,\cdot)$ $\chi_{3800}(2001,\cdot)$ $\chi_{3800}(2201,\cdot)$ $\chi_{3800}(2601,\cdot)$ $\chi_{3800}(3201,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{9})$
Fixed field:	$\Q(\zeta_{19})^+$

Values on generators

$(951,1901,1977,401)$ → $(1,1,1,e\left(\frac{7}{9}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3800 }(2001, a)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{9}\right)$