Dirichlet character \(\chi_{158}(83,\cdot)\)

• Label: 158.83
• Modulus: $158$
• Conductor: $79$
• Order: $39$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(158\)
Conductor:	\(79\)
Order:	\(39\)
Real:	no
Primitive:	no, induced from \(\chi_{79}(4,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 158.g

\(\chi_{158}(5,\cdot)\) \(\chi_{158}(9,\cdot)\) \(\chi_{158}(11,\cdot)\) \(\chi_{158}(13,\cdot)\) \(\chi_{158}(19,\cdot)\) \(\chi_{158}(25,\cdot)\) \(\chi_{158}(31,\cdot)\) \(\chi_{158}(45,\cdot)\) \(\chi_{158}(49,\cdot)\) \(\chi_{158}(51,\cdot)\) \(\chi_{158}(73,\cdot)\) \(\chi_{158}(81,\cdot)\) \(\chi_{158}(83,\cdot)\) \(\chi_{158}(95,\cdot)\) \(\chi_{158}(99,\cdot)\) \(\chi_{158}(105,\cdot)\) \(\chi_{158}(111,\cdot)\) \(\chi_{158}(115,\cdot)\) \(\chi_{158}(119,\cdot)\) \(\chi_{158}(121,\cdot)\) \(\chi_{158}(123,\cdot)\) \(\chi_{158}(129,\cdot)\) \(\chi_{158}(151,\cdot)\) \(\chi_{158}(155,\cdot)\)

Related number fields

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

Values on generators

\(3\) → \(e\left(\frac{4}{39}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 158 }(83, a) \)	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum