Dirichlet character \(\chi_{169}(56,\cdot)\)

• Label: 169.56
• Modulus: $169$
• Conductor: $169$
• Order: $78$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(169\)
Conductor:	\(169\)
Order:	\(78\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 169.k

\(\chi_{169}(4,\cdot)\) \(\chi_{169}(10,\cdot)\) \(\chi_{169}(17,\cdot)\) \(\chi_{169}(30,\cdot)\) \(\chi_{169}(36,\cdot)\) \(\chi_{169}(43,\cdot)\) \(\chi_{169}(49,\cdot)\) \(\chi_{169}(56,\cdot)\) \(\chi_{169}(62,\cdot)\) \(\chi_{169}(69,\cdot)\) \(\chi_{169}(75,\cdot)\) \(\chi_{169}(82,\cdot)\) \(\chi_{169}(88,\cdot)\) \(\chi_{169}(95,\cdot)\) \(\chi_{169}(101,\cdot)\) \(\chi_{169}(108,\cdot)\) \(\chi_{169}(114,\cdot)\) \(\chi_{169}(121,\cdot)\) \(\chi_{169}(127,\cdot)\) \(\chi_{169}(134,\cdot)\) \(\chi_{169}(140,\cdot)\) \(\chi_{169}(153,\cdot)\) \(\chi_{169}(160,\cdot)\) \(\chi_{169}(166,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Values on generators

\(2\) → \(e\left(\frac{55}{78}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 169 }(56, a) \)	\(1\)	\(1\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum