Dirichlet character χ666(17,⋅)\chi_{666}(17,\cdot)

• Label: 666.17
• Modulus: $666$
• Conductor: $111$
• Order: $36$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$666$
Conductor:	$111$
Order:	$36$
Real:	no
Primitive:	no, induced from $\chi_{111}(17,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 666.bs

$\chi_{666}(17,\cdot)$ $\chi_{666}(35,\cdot)$ $\chi_{666}(89,\cdot)$ $\chi_{666}(143,\cdot)$ $\chi_{666}(161,\cdot)$ $\chi_{666}(431,\cdot)$ $\chi_{666}(449,\cdot)$ $\chi_{666}(503,\cdot)$ $\chi_{666}(557,\cdot)$ $\chi_{666}(575,\cdot)$ $\chi_{666}(611,\cdot)$ $\chi_{666}(647,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	$\Q(\zeta_{111})^+$

Values on generators

$(371,631)$ → $(-1,e\left(\frac{7}{36}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{ 666 }(17, a)$	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{12}\right)$	$-i$

Gauss sum

Jacobi sum

Kloosterman sum