Dirichlet character χ1176(23,⋅)\chi_{1176}(23,\cdot)

• Label: 1176.23
• Modulus: $1176$
• Conductor: $588$
• Order: $42$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$1176$
Conductor:	$588$
Order:	$42$
Real:	no
Primitive:	no, induced from $\chi_{588}(23,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 1176.cb

$\chi_{1176}(23,\cdot)$ $\chi_{1176}(95,\cdot)$ $\chi_{1176}(191,\cdot)$ $\chi_{1176}(359,\cdot)$ $\chi_{1176}(431,\cdot)$ $\chi_{1176}(527,\cdot)$ $\chi_{1176}(599,\cdot)$ $\chi_{1176}(695,\cdot)$ $\chi_{1176}(767,\cdot)$ $\chi_{1176}(935,\cdot)$ $\chi_{1176}(1031,\cdot)$ $\chi_{1176}(1103,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	Number field defined by a degree 42 polynomial

Values on generators

$(295,589,785,1081)$ → $(-1,1,-1,e\left(\frac{19}{21}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{ 1176 }(23, a)$	$1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{20}{21}\right)$