Dirichlet character χ1640(427,⋅)\chi_{1640}(427,\cdot)

• Label: 1640.427
• Modulus: $1640$
• Conductor: $1640$
• Order: $40$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1640$
Conductor:	$1640$
Order:	$40$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1640.dw

$\chi_{1640}(67,\cdot)$ $\chi_{1640}(147,\cdot)$ $\chi_{1640}(227,\cdot)$ $\chi_{1640}(347,\cdot)$ $\chi_{1640}(403,\cdot)$ $\chi_{1640}(427,\cdot)$ $\chi_{1640}(507,\cdot)$ $\chi_{1640}(563,\cdot)$ $\chi_{1640}(603,\cdot)$ $\chi_{1640}(643,\cdot)$ $\chi_{1640}(867,\cdot)$ $\chi_{1640}(1243,\cdot)$ $\chi_{1640}(1283,\cdot)$ $\chi_{1640}(1323,\cdot)$ $\chi_{1640}(1347,\cdot)$ $\chi_{1640}(1483,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{40})$
Fixed field:	40.0.850100520307178141323742388002497873911873722563896105590771728372465664000000000000000000000000000000.1

Values on generators

$(1231,821,657,1441)$ → $(-1,-1,i,e\left(\frac{33}{40}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 1640 }(427, a)$	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{37}{40}\right)$	$i$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{8}\right)$