Dirichlet character \(\chi_{845}(549,\cdot)\)

• Label: 845.549
• Modulus: $845$
• Conductor: $845$
• Order: $78$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(845\)
Conductor:	\(845\)
Order:	\(78\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 845.bf

\(\chi_{845}(9,\cdot)\) \(\chi_{845}(29,\cdot)\) \(\chi_{845}(74,\cdot)\) \(\chi_{845}(94,\cdot)\) \(\chi_{845}(139,\cdot)\) \(\chi_{845}(159,\cdot)\) \(\chi_{845}(204,\cdot)\) \(\chi_{845}(224,\cdot)\) \(\chi_{845}(269,\cdot)\) \(\chi_{845}(289,\cdot)\) \(\chi_{845}(334,\cdot)\) \(\chi_{845}(354,\cdot)\) \(\chi_{845}(399,\cdot)\) \(\chi_{845}(419,\cdot)\) \(\chi_{845}(464,\cdot)\) \(\chi_{845}(549,\cdot)\) \(\chi_{845}(594,\cdot)\) \(\chi_{845}(614,\cdot)\) \(\chi_{845}(659,\cdot)\) \(\chi_{845}(679,\cdot)\) \(\chi_{845}(724,\cdot)\) \(\chi_{845}(744,\cdot)\) \(\chi_{845}(789,\cdot)\) \(\chi_{845}(809,\cdot)\)

Related number fields

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

Values on generators

\((677,171)\) → \((-1,e\left(\frac{19}{39}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\( \chi_{ 845 }(549, a) \)	\(1\)	\(1\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum