Dirichlet character χ2156(1009,⋅)\chi_{2156}(1009,\cdot)

• Label: 2156.1009
• Modulus: $2156$
• Conductor: $539$
• Order: $70$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$2156$
Conductor:	$539$
Order:	$70$
Real:	no
Primitive:	no, induced from $\chi_{539}(470,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 2156.cd

$\chi_{2156}(29,\cdot)$ $\chi_{2156}(57,\cdot)$ $\chi_{2156}(85,\cdot)$ $\chi_{2156}(281,\cdot)$ $\chi_{2156}(337,\cdot)$ $\chi_{2156}(365,\cdot)$ $\chi_{2156}(645,\cdot)$ $\chi_{2156}(673,\cdot)$ $\chi_{2156}(701,\cdot)$ $\chi_{2156}(897,\cdot)$ $\chi_{2156}(953,\cdot)$ $\chi_{2156}(1009,\cdot)$ $\chi_{2156}(1205,\cdot)$ $\chi_{2156}(1261,\cdot)$ $\chi_{2156}(1289,\cdot)$ $\chi_{2156}(1317,\cdot)$ $\chi_{2156}(1513,\cdot)$ $\chi_{2156}(1597,\cdot)$ $\chi_{2156}(1625,\cdot)$ $\chi_{2156}(1821,\cdot)$ $\chi_{2156}(1877,\cdot)$ $\chi_{2156}(1905,\cdot)$ $\chi_{2156}(1933,\cdot)$ $\chi_{2156}(2129,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{35})$
Fixed field:	Number field defined by a degree 70 polynomial

Values on generators

$(1079,1277,981)$ → $(1,e\left(\frac{3}{7}\right),e\left(\frac{3}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$13$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{ 2156 }(1009, a)$	$-1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{17}{35}\right)$