Dirichlet character orbit 7225.m

• Label: 7225.m
• Modulus: $7225$
• Conductor: $17$
• Order: $8$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$7225$
Conductor:	$17$
Order:	$8$
Real:	no
Primitive:	no, induced from 17.d
Minimal:	no
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{8})$
Fixed field:	$\Q(\zeta_{17})^+$

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{7225}(1001,\cdot)$	$1$	$1$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$
$\chi_{7225}(4201,\cdot)$	$1$	$1$	$i$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$
$\chi_{7225}(5601,\cdot)$	$1$	$1$	$-i$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$
$\chi_{7225}(6826,\cdot)$	$1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$