Dirichlet character \(\chi_{79}(66,\cdot)\)

• Label: 79.66
• Modulus: $79$
• Conductor: $79$
• Order: $78$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(79\)
Conductor:	\(79\)
Order:	\(78\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 79.h

\(\chi_{79}(3,\cdot)\) \(\chi_{79}(6,\cdot)\) \(\chi_{79}(7,\cdot)\) \(\chi_{79}(28,\cdot)\) \(\chi_{79}(29,\cdot)\) \(\chi_{79}(30,\cdot)\) \(\chi_{79}(34,\cdot)\) \(\chi_{79}(35,\cdot)\) \(\chi_{79}(37,\cdot)\) \(\chi_{79}(39,\cdot)\) \(\chi_{79}(43,\cdot)\) \(\chi_{79}(47,\cdot)\) \(\chi_{79}(48,\cdot)\) \(\chi_{79}(53,\cdot)\) \(\chi_{79}(54,\cdot)\) \(\chi_{79}(59,\cdot)\) \(\chi_{79}(60,\cdot)\) \(\chi_{79}(63,\cdot)\) \(\chi_{79}(66,\cdot)\) \(\chi_{79}(68,\cdot)\) \(\chi_{79}(70,\cdot)\) \(\chi_{79}(74,\cdot)\) \(\chi_{79}(75,\cdot)\) \(\chi_{79}(77,\cdot)\)

Related number fields

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

Values on generators

\(3\) → \(e\left(\frac{73}{78}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 79 }(66, a) \)	\(-1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum