Dirichlet character \(\chi_{109}(48,\cdot)\)

• Label: 109.48
• Modulus: $109$
• Conductor: $109$
• Order: $27$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(109\)
Conductor:	\(109\)
Order:	\(27\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 109.i

\(\chi_{109}(3,\cdot)\) \(\chi_{109}(5,\cdot)\) \(\chi_{109}(7,\cdot)\) \(\chi_{109}(9,\cdot)\) \(\chi_{109}(15,\cdot)\) \(\chi_{109}(21,\cdot)\) \(\chi_{109}(22,\cdot)\) \(\chi_{109}(25,\cdot)\) \(\chi_{109}(26,\cdot)\) \(\chi_{109}(35,\cdot)\) \(\chi_{109}(48,\cdot)\) \(\chi_{109}(49,\cdot)\) \(\chi_{109}(73,\cdot)\) \(\chi_{109}(78,\cdot)\) \(\chi_{109}(80,\cdot)\) \(\chi_{109}(81,\cdot)\) \(\chi_{109}(89,\cdot)\) \(\chi_{109}(97,\cdot)\)

Related number fields

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

Values on generators

\(6\) → \(e\left(\frac{16}{27}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 109 }(48, a) \)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum