Dirichlet character χ1386(1369,⋅)\chi_{1386}(1369,\cdot)

• Label: 1386.1369
• Modulus: $1386$
• Conductor: $77$
• Order: $15$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1386$
Conductor:	$77$
Order:	$15$
Real:	no
Primitive:	no, induced from $\chi_{77}(60,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 1386.bx

$\chi_{1386}(37,\cdot)$ $\chi_{1386}(163,\cdot)$ $\chi_{1386}(235,\cdot)$ $\chi_{1386}(289,\cdot)$ $\chi_{1386}(361,\cdot)$ $\chi_{1386}(487,\cdot)$ $\chi_{1386}(1171,\cdot)$ $\chi_{1386}(1369,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	15.15.886528337182930278529.1

Values on generators

$(155,199,1135)$ → $(1,e\left(\frac{2}{3}\right),e\left(\frac{2}{5}\right))$

First values

$a$	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{ 1386 }(1369, a)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$