Dirichlet character χ8112(6239,⋅)\chi_{8112}(6239,\cdot)

• Label: 8112.6239
• Modulus: $8112$
• Conductor: $2028$
• Order: $26$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8112$
Conductor:	$2028$
Order:	$26$
Real:	no
Primitive:	no, induced from $\chi_{2028}(155,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 8112.df

$\chi_{8112}(623,\cdot)$ $\chi_{8112}(1247,\cdot)$ $\chi_{8112}(1871,\cdot)$ $\chi_{8112}(2495,\cdot)$ $\chi_{8112}(3119,\cdot)$ $\chi_{8112}(3743,\cdot)$ $\chi_{8112}(4367,\cdot)$ $\chi_{8112}(4991,\cdot)$ $\chi_{8112}(5615,\cdot)$ $\chi_{8112}(6239,\cdot)$ $\chi_{8112}(6863,\cdot)$ $\chi_{8112}(7487,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{13})$
Fixed field:	26.26.409808027834211389172943903711535494765866720064678008376474736787456.1

Values on generators

$(5071,6085,2705,3889)$ → $(-1,1,-1,e\left(\frac{5}{26}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{ 8112 }(6239, a)$	$1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{15}{26}\right)$	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{4}{13}\right)$