Dirichlet character \(\chi_{845}(829,\cdot)\)

• Label: 845.829
• 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.bh

\(\chi_{845}(4,\cdot)\) \(\chi_{845}(49,\cdot)\) \(\chi_{845}(69,\cdot)\) \(\chi_{845}(114,\cdot)\) \(\chi_{845}(134,\cdot)\) \(\chi_{845}(179,\cdot)\) \(\chi_{845}(199,\cdot)\) \(\chi_{845}(244,\cdot)\) \(\chi_{845}(264,\cdot)\) \(\chi_{845}(309,\cdot)\) \(\chi_{845}(329,\cdot)\) \(\chi_{845}(374,\cdot)\) \(\chi_{845}(394,\cdot)\) \(\chi_{845}(439,\cdot)\) \(\chi_{845}(459,\cdot)\) \(\chi_{845}(504,\cdot)\) \(\chi_{845}(524,\cdot)\) \(\chi_{845}(569,\cdot)\) \(\chi_{845}(589,\cdot)\) \(\chi_{845}(634,\cdot)\) \(\chi_{845}(719,\cdot)\) \(\chi_{845}(764,\cdot)\) \(\chi_{845}(784,\cdot)\) \(\chi_{845}(829,\cdot)\)

Related number fields

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

Values on generators

\((677,171)\) → \((-1,e\left(\frac{41}{78}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\( \chi_{ 845 }(829, a) \)	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum