Dirichlet character χ1232(19,⋅)\chi_{1232}(19,\cdot)

• Label: 1232.19
• Modulus: $1232$
• Conductor: $1232$
• Order: $60$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1232$
Conductor:	$1232$
Order:	$60$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1232.dr

$\chi_{1232}(19,\cdot)$ $\chi_{1232}(171,\cdot)$ $\chi_{1232}(227,\cdot)$ $\chi_{1232}(283,\cdot)$ $\chi_{1232}(299,\cdot)$ $\chi_{1232}(523,\cdot)$ $\chi_{1232}(563,\cdot)$ $\chi_{1232}(579,\cdot)$ $\chi_{1232}(635,\cdot)$ $\chi_{1232}(787,\cdot)$ $\chi_{1232}(843,\cdot)$ $\chi_{1232}(899,\cdot)$ $\chi_{1232}(915,\cdot)$ $\chi_{1232}(1139,\cdot)$ $\chi_{1232}(1179,\cdot)$ $\chi_{1232}(1195,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{60})$
Fixed field:	Number field defined by a degree 60 polynomial

Values on generators

$(463,309,353,673)$ → $(-1,-i,e\left(\frac{5}{6}\right),e\left(\frac{3}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$13$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{ 1232 }(19, a)$	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{20}\right)$