Dirichlet character χ111(89,⋅)\chi_{111}(89,\cdot)

• Label: 111.89
• Modulus: $111$
• Conductor: $111$
• Order: $36$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$111$
Conductor:	$111$
Order:	$36$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 111.q

$\chi_{111}(2,\cdot)$ $\chi_{111}(5,\cdot)$ $\chi_{111}(17,\cdot)$ $\chi_{111}(20,\cdot)$ $\chi_{111}(32,\cdot)$ $\chi_{111}(35,\cdot)$ $\chi_{111}(50,\cdot)$ $\chi_{111}(56,\cdot)$ $\chi_{111}(59,\cdot)$ $\chi_{111}(89,\cdot)$ $\chi_{111}(92,\cdot)$ $\chi_{111}(98,\cdot)$

Related number fields

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

Values on generators

$(38,76)$ → $(-1,e\left(\frac{13}{36}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{ 111 }(89, a)$	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{4}{9}\right)$

Gauss sum

Jacobi sum

Kloosterman sum