Dirichlet character χ1176(989,⋅)\chi_{1176}(989,\cdot)

• Label: 1176.989
• Modulus: $1176$
• Conductor: $1176$
• Order: $42$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1176$
Conductor:	$1176$
Order:	$42$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1176.ck

$\chi_{1176}(53,\cdot)$ $\chi_{1176}(149,\cdot)$ $\chi_{1176}(221,\cdot)$ $\chi_{1176}(317,\cdot)$ $\chi_{1176}(389,\cdot)$ $\chi_{1176}(485,\cdot)$ $\chi_{1176}(653,\cdot)$ $\chi_{1176}(725,\cdot)$ $\chi_{1176}(821,\cdot)$ $\chi_{1176}(893,\cdot)$ $\chi_{1176}(989,\cdot)$ $\chi_{1176}(1061,\cdot)$

Related number fields

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

Values on generators

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

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{ 1176 }(989, a)$	$-1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{42}\right)$