Dirichlet character χ3216(2353,⋅)\chi_{3216}(2353,\cdot)

• Label: 3216.2353
• Modulus: $3216$
• Conductor: $67$
• Order: $22$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$3216$
Conductor:	$67$
Order:	$22$
Real:	no
Primitive:	no, induced from $\chi_{67}(8,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 3216.cl

$\chi_{3216}(673,\cdot)$ $\chi_{3216}(913,\cdot)$ $\chi_{3216}(1057,\cdot)$ $\chi_{3216}(1249,\cdot)$ $\chi_{3216}(1345,\cdot)$ $\chi_{3216}(1393,\cdot)$ $\chi_{3216}(1921,\cdot)$ $\chi_{3216}(2305,\cdot)$ $\chi_{3216}(2353,\cdot)$ $\chi_{3216}(3073,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{11})$
Fixed field:	Number field defined by a degree 22 polynomial

Values on generators

$(2815,805,1073,337)$ → $(1,1,1,e\left(\frac{1}{22}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{ 3216 }(2353, a)$	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{4}{11}\right)$	$1$	$e\left(\frac{3}{22}\right)$