Dirichlet character \(\chi_{139}(67,\cdot)\)

• Label: 139.67
• Modulus: $139$
• Conductor: $139$
• Order: $69$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(139\)
Conductor:	\(139\)
Order:	\(69\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 139.g

\(\chi_{139}(4,\cdot)\) \(\chi_{139}(5,\cdot)\) \(\chi_{139}(7,\cdot)\) \(\chi_{139}(9,\cdot)\) \(\chi_{139}(11,\cdot)\) \(\chi_{139}(13,\cdot)\) \(\chi_{139}(16,\cdot)\) \(\chi_{139}(20,\cdot)\) \(\chi_{139}(24,\cdot)\) \(\chi_{139}(25,\cdot)\) \(\chi_{139}(28,\cdot)\) \(\chi_{139}(29,\cdot)\) \(\chi_{139}(30,\cdot)\) \(\chi_{139}(31,\cdot)\) \(\chi_{139}(35,\cdot)\) \(\chi_{139}(37,\cdot)\) \(\chi_{139}(38,\cdot)\) \(\chi_{139}(41,\cdot)\) \(\chi_{139}(46,\cdot)\) \(\chi_{139}(47,\cdot)\) \(\chi_{139}(49,\cdot)\) \(\chi_{139}(51,\cdot)\) \(\chi_{139}(54,\cdot)\) \(\chi_{139}(66,\cdot)\) \(\chi_{139}(67,\cdot)\) \(\chi_{139}(69,\cdot)\) \(\chi_{139}(71,\cdot)\) \(\chi_{139}(78,\cdot)\) \(\chi_{139}(81,\cdot)\) \(\chi_{139}(83,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{69})$
Fixed field:	Number field defined by a degree 69 polynomial

Values on generators

\(2\) → \(e\left(\frac{8}{69}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 139 }(67, a) \)	\(1\)	\(1\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{56}{69}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum