Dirichlet character χ2156(353,⋅)\chi_{2156}(353,\cdot)

• Label: 2156.353
• Modulus: $2156$
• Conductor: $49$
• Order: $42$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$2156$
Conductor:	$49$
Order:	$42$
Real:	no
Primitive:	no, induced from $\chi_{49}(10,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 2156.br

$\chi_{2156}(45,\cdot)$ $\chi_{2156}(89,\cdot)$ $\chi_{2156}(353,\cdot)$ $\chi_{2156}(397,\cdot)$ $\chi_{2156}(661,\cdot)$ $\chi_{2156}(969,\cdot)$ $\chi_{2156}(1013,\cdot)$ $\chi_{2156}(1277,\cdot)$ $\chi_{2156}(1321,\cdot)$ $\chi_{2156}(1585,\cdot)$ $\chi_{2156}(1629,\cdot)$ $\chi_{2156}(1937,\cdot)$

Related number fields

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

Values on generators

$(1079,1277,981)$ → $(1,e\left(\frac{13}{42}\right),1)$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$13$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{ 2156 }(353, a)$	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{13}{14}\right)$