Dirichlet character χ525(257,⋅)\chi_{525}(257,\cdot)

• Label: 525.257
• Modulus: $525$
• Conductor: $105$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$525$
Conductor:	$105$
Order:	$12$
Real:	no
Primitive:	no, induced from $\chi_{105}(47,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 525.be

$\chi_{525}(68,\cdot)$ $\chi_{525}(143,\cdot)$ $\chi_{525}(257,\cdot)$ $\chi_{525}(332,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.0.402196204142578125.1

Values on generators

$(176,127,451)$ → $(-1,i,e\left(\frac{5}{6}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$17$	$19$	$22$	$23$
$\chi_{ 525 }(257, a)$	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{11}{12}\right)$

Gauss sum

Jacobi sum

Kloosterman sum