Dirichlet character χ225(196,⋅)\chi_{225}(196,\cdot)

• Label: 225.196
• Modulus: $225$
• Conductor: $225$
• Order: $15$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$225$
Conductor:	$225$
Order:	$15$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 225.q

$\chi_{225}(16,\cdot)$ $\chi_{225}(31,\cdot)$ $\chi_{225}(61,\cdot)$ $\chi_{225}(106,\cdot)$ $\chi_{225}(121,\cdot)$ $\chi_{225}(166,\cdot)$ $\chi_{225}(196,\cdot)$ $\chi_{225}(211,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	Number field defined by a degree 15 polynomial

Values on generators

$(101,127)$ → $(e\left(\frac{2}{3}\right),e\left(\frac{3}{5}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 225 }(196, a)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$

Gauss sum

Jacobi sum

Kloosterman sum