Dirichlet character \(\chi_{59}(17,\cdot)\)

• Label: 59.17
• Modulus: $59$
• Conductor: $59$
• Order: $29$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(59\)
Conductor:	\(59\)
Order:	\(29\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 59.c

\(\chi_{59}(3,\cdot)\) \(\chi_{59}(4,\cdot)\) \(\chi_{59}(5,\cdot)\) \(\chi_{59}(7,\cdot)\) \(\chi_{59}(9,\cdot)\) \(\chi_{59}(12,\cdot)\) \(\chi_{59}(15,\cdot)\) \(\chi_{59}(16,\cdot)\) \(\chi_{59}(17,\cdot)\) \(\chi_{59}(19,\cdot)\) \(\chi_{59}(20,\cdot)\) \(\chi_{59}(21,\cdot)\) \(\chi_{59}(22,\cdot)\) \(\chi_{59}(25,\cdot)\) \(\chi_{59}(26,\cdot)\) \(\chi_{59}(27,\cdot)\) \(\chi_{59}(28,\cdot)\) \(\chi_{59}(29,\cdot)\) \(\chi_{59}(35,\cdot)\) \(\chi_{59}(36,\cdot)\) \(\chi_{59}(41,\cdot)\) \(\chi_{59}(45,\cdot)\) \(\chi_{59}(46,\cdot)\) \(\chi_{59}(48,\cdot)\) \(\chi_{59}(49,\cdot)\) \(\chi_{59}(51,\cdot)\) \(\chi_{59}(53,\cdot)\) \(\chi_{59}(57,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{29})$
Fixed field:	Number field defined by a degree 29 polynomial

Values on generators

\(2\) → \(e\left(\frac{20}{29}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 59 }(17, a) \)	\(1\)	\(1\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum