Dirichlet character χ1312(179,⋅)\chi_{1312}(179,\cdot)

• Label: 1312.179
• 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.di

$\chi_{1312}(67,\cdot)$ $\chi_{1312}(99,\cdot)$ $\chi_{1312}(147,\cdot)$ $\chi_{1312}(171,\cdot)$ $\chi_{1312}(179,\cdot)$ $\chi_{1312}(235,\cdot)$ $\chi_{1312}(315,\cdot)$ $\chi_{1312}(587,\cdot)$ $\chi_{1312}(667,\cdot)$ $\chi_{1312}(675,\cdot)$ $\chi_{1312}(691,\cdot)$ $\chi_{1312}(731,\cdot)$ $\chi_{1312}(867,\cdot)$ $\chi_{1312}(883,\cdot)$ $\chi_{1312}(955,\cdot)$ $\chi_{1312}(1259,\cdot)$

Related number fields

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

Values on generators

$(575,165,129)$ → $(-1,e\left(\frac{7}{8}\right),e\left(\frac{37}{40}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 1312 }(179, a)$	$1$	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{40}\right)$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{40}\right)$