Dirichlet character χ2156(1537,⋅)\chi_{2156}(1537,\cdot)

• Label: 2156.1537
• Modulus: $2156$
• Conductor: $77$
• Order: $30$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$2156$
Conductor:	$77$
Order:	$30$
Real:	no
Primitive:	no, induced from $\chi_{77}(74,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 2156.bo

$\chi_{2156}(557,\cdot)$ $\chi_{2156}(569,\cdot)$ $\chi_{2156}(765,\cdot)$ $\chi_{2156}(1157,\cdot)$ $\chi_{2156}(1537,\cdot)$ $\chi_{2156}(1733,\cdot)$ $\chi_{2156}(1745,\cdot)$ $\chi_{2156}(2125,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	30.0.1046076147688308987260717152173116396995512371.1

Values on generators

$(1079,1277,981)$ → $(1,e\left(\frac{2}{3}\right),e\left(\frac{3}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$13$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{ 2156 }(1537, a)$	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{5}\right)$