Dirichlet character χ1344(205,⋅)\chi_{1344}(205,\cdot)

• Label: 1344.205
• Modulus: $1344$
• Conductor: $448$
• Order: $48$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1344$
Conductor:	$448$
Order:	$48$
Real:	no
Primitive:	no, induced from $\chi_{448}(205,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 1344.cz

$\chi_{1344}(37,\cdot)$ $\chi_{1344}(109,\cdot)$ $\chi_{1344}(205,\cdot)$ $\chi_{1344}(277,\cdot)$ $\chi_{1344}(373,\cdot)$ $\chi_{1344}(445,\cdot)$ $\chi_{1344}(541,\cdot)$ $\chi_{1344}(613,\cdot)$ $\chi_{1344}(709,\cdot)$ $\chi_{1344}(781,\cdot)$ $\chi_{1344}(877,\cdot)$ $\chi_{1344}(949,\cdot)$ $\chi_{1344}(1045,\cdot)$ $\chi_{1344}(1117,\cdot)$ $\chi_{1344}(1213,\cdot)$ $\chi_{1344}(1285,\cdot)$

Related number fields

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

Values on generators

$(127,1093,449,577)$ → $(1,e\left(\frac{15}{16}\right),1,e\left(\frac{1}{3}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{ 1344 }(205, a)$	$1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{48}\right)$