Dirichlet character χ1760(1557,⋅)\chi_{1760}(1557,\cdot)

• Label: 1760.1557
• Modulus: $1760$
• Conductor: $1760$
• Order: $40$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1760$
Conductor:	$1760$
Order:	$40$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1760.ds

$\chi_{1760}(13,\cdot)$ $\chi_{1760}(117,\cdot)$ $\chi_{1760}(173,\cdot)$ $\chi_{1760}(277,\cdot)$ $\chi_{1760}(413,\cdot)$ $\chi_{1760}(437,\cdot)$ $\chi_{1760}(677,\cdot)$ $\chi_{1760}(733,\cdot)$ $\chi_{1760}(893,\cdot)$ $\chi_{1760}(997,\cdot)$ $\chi_{1760}(1053,\cdot)$ $\chi_{1760}(1157,\cdot)$ $\chi_{1760}(1293,\cdot)$ $\chi_{1760}(1317,\cdot)$ $\chi_{1760}(1557,\cdot)$ $\chi_{1760}(1613,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{40})$
Fixed field:	40.40.1314880012449506220994309247746612403564809108378301093397843089030698237952000000000000000000000000000000.2

Values on generators

$(991,1541,1057,321)$ → $(1,e\left(\frac{5}{8}\right),i,e\left(\frac{9}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 1760 }(1557, a)$	$1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{27}{40}\right)$