Dirichlet character χ109(40,⋅)\chi_{109}(40,\cdot)

• Label: 109.40
• Modulus: $109$
• Conductor: $109$
• Order: $108$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$109$
Conductor:	$109$
Order:	$108$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 109.l

$\chi_{109}(6,\cdot)$ $\chi_{109}(10,\cdot)$ $\chi_{109}(11,\cdot)$ $\chi_{109}(13,\cdot)$ $\chi_{109}(14,\cdot)$ $\chi_{109}(18,\cdot)$ $\chi_{109}(24,\cdot)$ $\chi_{109}(30,\cdot)$ $\chi_{109}(37,\cdot)$ $\chi_{109}(39,\cdot)$ $\chi_{109}(40,\cdot)$ $\chi_{109}(42,\cdot)$ $\chi_{109}(44,\cdot)$ $\chi_{109}(47,\cdot)$ $\chi_{109}(50,\cdot)$ $\chi_{109}(51,\cdot)$ $\chi_{109}(52,\cdot)$ $\chi_{109}(53,\cdot)$ $\chi_{109}(56,\cdot)$ $\chi_{109}(57,\cdot)$ $\chi_{109}(58,\cdot)$ $\chi_{109}(59,\cdot)$ $\chi_{109}(62,\cdot)$ $\chi_{109}(65,\cdot)$ $\chi_{109}(67,\cdot)$ $\chi_{109}(69,\cdot)$ $\chi_{109}(70,\cdot)$ $\chi_{109}(72,\cdot)$ $\chi_{109}(79,\cdot)$ $\chi_{109}(85,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{108})$
Fixed field:	Number field defined by a degree 108 polynomial (not computed)

Values on generators

$6$ → $e\left(\frac{31}{108}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 109 }(40, a)$	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{89}{108}\right)$

Gauss sum

Jacobi sum

Kloosterman sum