Dirichlet character χ3549(1760,⋅)\chi_{3549}(1760,\cdot)

• Label: 3549.1760
• Modulus: $3549$
• Conductor: $273$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3549$
Conductor:	$273$
Order:	$12$
Real:	no
Primitive:	no, induced from $\chi_{273}(122,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 3549.cb

$\chi_{3549}(437,\cdot)$ $\chi_{3549}(1760,\cdot)$ $\chi_{3549}(1958,\cdot)$ $\chi_{3549}(3281,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.0.2183725770062310261333.1

Values on generators

$(1184,1522,3382)$ → $(-1,e\left(\frac{1}{6}\right),-i)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{ 3549 }(1760, a)$	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$