Dirichlet character χ3380(1627,⋅)\chi_{3380}(1627,\cdot)

• Label: 3380.1627
• Modulus: $3380$
• Conductor: $3380$
• Order: $156$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3380$
Conductor:	$3380$
Order:	$156$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 3380.cz

$\chi_{3380}(63,\cdot)$ $\chi_{3380}(67,\cdot)$ $\chi_{3380}(163,\cdot)$ $\chi_{3380}(227,\cdot)$ $\chi_{3380}(323,\cdot)$ $\chi_{3380}(327,\cdot)$ $\chi_{3380}(423,\cdot)$ $\chi_{3380}(487,\cdot)$ $\chi_{3380}(583,\cdot)$ $\chi_{3380}(683,\cdot)$ $\chi_{3380}(747,\cdot)$ $\chi_{3380}(843,\cdot)$ $\chi_{3380}(847,\cdot)$ $\chi_{3380}(943,\cdot)$ $\chi_{3380}(1007,\cdot)$ $\chi_{3380}(1107,\cdot)$ $\chi_{3380}(1203,\cdot)$ $\chi_{3380}(1267,\cdot)$ $\chi_{3380}(1363,\cdot)$ $\chi_{3380}(1367,\cdot)$ $\chi_{3380}(1463,\cdot)$ $\chi_{3380}(1527,\cdot)$ $\chi_{3380}(1623,\cdot)$ $\chi_{3380}(1627,\cdot)$ $\chi_{3380}(1723,\cdot)$ $\chi_{3380}(1787,\cdot)$ $\chi_{3380}(1883,\cdot)$ $\chi_{3380}(1887,\cdot)$ $\chi_{3380}(1983,\cdot)$ $\chi_{3380}(2143,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{156})$
Fixed field:	Number field defined by a degree 156 polynomial (not computed)

Values on generators

$(1691,677,1861)$ → $(-1,i,e\left(\frac{121}{156}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 3380 }(1627, a)$	$-1$	$1$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{41}{78}\right)$