Dirichlet character χ1224(1183,⋅)\chi_{1224}(1183,\cdot)

• Label: 1224.1183
• Modulus: $1224$
• Conductor: $612$
• Order: $48$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$1224$
Conductor:	$612$
Order:	$48$
Real:	no
Primitive:	no, induced from $\chi_{612}(571,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 1224.cv

$\chi_{1224}(7,\cdot)$ $\chi_{1224}(31,\cdot)$ $\chi_{1224}(79,\cdot)$ $\chi_{1224}(175,\cdot)$ $\chi_{1224}(295,\cdot)$ $\chi_{1224}(367,\cdot)$ $\chi_{1224}(439,\cdot)$ $\chi_{1224}(583,\cdot)$ $\chi_{1224}(607,\cdot)$ $\chi_{1224}(751,\cdot)$ $\chi_{1224}(823,\cdot)$ $\chi_{1224}(895,\cdot)$ $\chi_{1224}(1015,\cdot)$ $\chi_{1224}(1111,\cdot)$ $\chi_{1224}(1159,\cdot)$ $\chi_{1224}(1183,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{48})$
Fixed field:	Number field defined by a degree 48 polynomial

Values on generators

$(919,613,137,649)$ → $(-1,1,e\left(\frac{1}{3}\right),e\left(\frac{3}{16}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{ 1224 }(1183, a)$	$1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{41}{48}\right)$	$-1$