Dirichlet character \(\chi_{109}(59,\cdot)\)

• Label: 109.59
• 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

\(6\) → \(e\left(\frac{47}{108}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 109 }(59, a) \)	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{13}{108}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum