Dirichlet character χ7225(4493,⋅)\chi_{7225}(4493,\cdot)

• Label: 7225.4493
• Modulus: $7225$
• Conductor: $85$
• Order: $16$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$7225$
Conductor:	$85$
Order:	$16$
Real:	no
Primitive:	no, induced from $\chi_{85}(73,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 7225.s

$\chi_{7225}(643,\cdot)$ $\chi_{7225}(907,\cdot)$ $\chi_{7225}(2443,\cdot)$ $\chi_{7225}(3682,\cdot)$ $\chi_{7225}(3832,\cdot)$ $\chi_{7225}(4493,\cdot)$ $\chi_{7225}(6293,\cdot)$ $\chi_{7225}(6607,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{16})$
Fixed field:	16.16.698833752810013621337890625.2

Values on generators

$(2602,2026)$ → $(-i,e\left(\frac{5}{16}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 7225 }(4493, a)$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-1$