Dirichlet character χ1312(1051,⋅)\chi_{1312}(1051,\cdot)

• Label: 1312.1051
• Modulus: $1312$
• Conductor: $1312$
• Order: $40$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1312$
Conductor:	$1312$
Order:	$40$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1312.cs

$\chi_{1312}(275,\cdot)$ $\chi_{1312}(347,\cdot)$ $\chi_{1312}(363,\cdot)$ $\chi_{1312}(499,\cdot)$ $\chi_{1312}(539,\cdot)$ $\chi_{1312}(555,\cdot)$ $\chi_{1312}(563,\cdot)$ $\chi_{1312}(643,\cdot)$ $\chi_{1312}(915,\cdot)$ $\chi_{1312}(995,\cdot)$ $\chi_{1312}(1051,\cdot)$ $\chi_{1312}(1059,\cdot)$ $\chi_{1312}(1083,\cdot)$ $\chi_{1312}(1131,\cdot)$ $\chi_{1312}(1163,\cdot)$ $\chi_{1312}(1283,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{40})$
Fixed field:	Number field defined by a degree 40 polynomial

Values on generators

$(575,165,129)$ → $(-1,e\left(\frac{1}{8}\right),e\left(\frac{17}{40}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 1312 }(1051, a)$	$1$	$1$	$i$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{13}{40}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{40}\right)$