Dirichlet character χ2352(1123,⋅)\chi_{2352}(1123,\cdot)

• Label: 2352.1123
• Modulus: $2352$
• Conductor: $784$
• Order: $84$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2352$
Conductor:	$784$
Order:	$84$
Real:	no
Primitive:	no, induced from $\chi_{784}(339,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 2352.dn

$\chi_{2352}(115,\cdot)$ $\chi_{2352}(187,\cdot)$ $\chi_{2352}(283,\cdot)$ $\chi_{2352}(355,\cdot)$ $\chi_{2352}(451,\cdot)$ $\chi_{2352}(523,\cdot)$ $\chi_{2352}(691,\cdot)$ $\chi_{2352}(787,\cdot)$ $\chi_{2352}(859,\cdot)$ $\chi_{2352}(955,\cdot)$ $\chi_{2352}(1027,\cdot)$ $\chi_{2352}(1123,\cdot)$ $\chi_{2352}(1291,\cdot)$ $\chi_{2352}(1363,\cdot)$ $\chi_{2352}(1459,\cdot)$ $\chi_{2352}(1531,\cdot)$ $\chi_{2352}(1627,\cdot)$ $\chi_{2352}(1699,\cdot)$ $\chi_{2352}(1867,\cdot)$ $\chi_{2352}(1963,\cdot)$ $\chi_{2352}(2035,\cdot)$ $\chi_{2352}(2131,\cdot)$ $\chi_{2352}(2203,\cdot)$ $\chi_{2352}(2299,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

$(1471,1765,785,2257)$ → $(-1,-i,1,e\left(\frac{31}{42}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{ 2352 }(1123, a)$	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{84}\right)$