Dirichlet character χ109(106,⋅)\chi_{109}(106,\cdot)

• Label: 109.106
• Modulus: $109$
• Conductor: $109$
• Order: $54$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$109$
Conductor:	$109$
Order:	$54$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 109.k

$\chi_{109}(12,\cdot)$ $\chi_{109}(20,\cdot)$ $\chi_{109}(28,\cdot)$ $\chi_{109}(29,\cdot)$ $\chi_{109}(31,\cdot)$ $\chi_{109}(36,\cdot)$ $\chi_{109}(60,\cdot)$ $\chi_{109}(61,\cdot)$ $\chi_{109}(74,\cdot)$ $\chi_{109}(83,\cdot)$ $\chi_{109}(84,\cdot)$ $\chi_{109}(87,\cdot)$ $\chi_{109}(88,\cdot)$ $\chi_{109}(94,\cdot)$ $\chi_{109}(100,\cdot)$ $\chi_{109}(102,\cdot)$ $\chi_{109}(104,\cdot)$ $\chi_{109}(106,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{27})$
Fixed field:	Number field defined by a degree 54 polynomial

Values on generators

$6$ → $e\left(\frac{53}{54}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 109 }(106, a)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{25}{54}\right)$

Gauss sum

Jacobi sum

Kloosterman sum