Dirichlet character χ2352(1865,⋅)\chi_{2352}(1865,\cdot)

• Label: 2352.1865
• Modulus: $2352$
• Conductor: $1176$
• Order: $42$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$2352$
Conductor:	$1176$
Order:	$42$
Real:	no
Primitive:	no, induced from $\chi_{1176}(101,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 2352.da

$\chi_{2352}(89,\cdot)$ $\chi_{2352}(185,\cdot)$ $\chi_{2352}(425,\cdot)$ $\chi_{2352}(761,\cdot)$ $\chi_{2352}(857,\cdot)$ $\chi_{2352}(1193,\cdot)$ $\chi_{2352}(1433,\cdot)$ $\chi_{2352}(1529,\cdot)$ $\chi_{2352}(1769,\cdot)$ $\chi_{2352}(1865,\cdot)$ $\chi_{2352}(2105,\cdot)$ $\chi_{2352}(2201,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	42.42.11402108177106104552822037830207017370882719938852769609842060849495301710065603498954056531968.1

Values on generators

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

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{ 2352 }(1865, a)$	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{42}\right)$