Dirichlet character χ3848(1205,⋅)\chi_{3848}(1205,\cdot)

• Label: 3848.1205
• Modulus: $3848$
• Conductor: $3848$
• Order: $18$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$3848$
Conductor:	$3848$
Order:	$18$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3848.ib

$\chi_{3848}(965,\cdot)$ $\chi_{3848}(1101,\cdot)$ $\chi_{3848}(1205,\cdot)$ $\chi_{3848}(2213,\cdot)$ $\chi_{3848}(2245,\cdot)$ $\chi_{3848}(3149,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{9})$
Fixed field:	Number field defined by a degree 18 polynomial

Values on generators

$(2887,1925,1185,2185)$ → $(1,-1,e\left(\frac{2}{3}\right),e\left(\frac{11}{18}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 3848 }(1205, a)$	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$	$-1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{6}\right)$