Dirichlet character χ1760(1437,⋅)\chi_{1760}(1437,\cdot)

• Label: 1760.1437
• 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.eg

$\chi_{1760}(237,\cdot)$ $\chi_{1760}(293,\cdot)$ $\chi_{1760}(453,\cdot)$ $\chi_{1760}(557,\cdot)$ $\chi_{1760}(613,\cdot)$ $\chi_{1760}(717,\cdot)$ $\chi_{1760}(853,\cdot)$ $\chi_{1760}(877,\cdot)$ $\chi_{1760}(1117,\cdot)$ $\chi_{1760}(1173,\cdot)$ $\chi_{1760}(1333,\cdot)$ $\chi_{1760}(1437,\cdot)$ $\chi_{1760}(1493,\cdot)$ $\chi_{1760}(1597,\cdot)$ $\chi_{1760}(1733,\cdot)$ $\chi_{1760}(1757,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{40})$
Fixed field:	40.40.1314880012449506220994309247746612403564809108378301093397843089030698237952000000000000000000000000000000.1

Values on generators

$(991,1541,1057,321)$ → $(1,e\left(\frac{3}{8}\right),i,e\left(\frac{7}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 1760 }(1437, a)$	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{21}{40}\right)$