Dirichlet character χ1312(1125,⋅)\chi_{1312}(1125,\cdot)

• Label: 1312.1125
• 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.dd

$\chi_{1312}(37,\cdot)$ $\chi_{1312}(133,\cdot)$ $\chi_{1312}(141,\cdot)$ $\chi_{1312}(221,\cdot)$ $\chi_{1312}(365,\cdot)$ $\chi_{1312}(461,\cdot)$ $\chi_{1312}(469,\cdot)$ $\chi_{1312}(549,\cdot)$ $\chi_{1312}(693,\cdot)$ $\chi_{1312}(789,\cdot)$ $\chi_{1312}(797,\cdot)$ $\chi_{1312}(877,\cdot)$ $\chi_{1312}(1021,\cdot)$ $\chi_{1312}(1117,\cdot)$ $\chi_{1312}(1125,\cdot)$ $\chi_{1312}(1205,\cdot)$

Related number fields

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

Values on generators

$(575,165,129)$ → $(1,e\left(\frac{1}{8}\right),e\left(\frac{2}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 1312 }(1125, a)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{17}{20}\right)$	$-i$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{9}{40}\right)$