Dirichlet character \(\chi_{676}(55,\cdot)\)

• Label: 676.55
• Modulus: $676$
• Conductor: $676$
• Order: $78$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(676\)
Conductor:	\(676\)
Order:	\(78\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 676.t

\(\chi_{676}(3,\cdot)\) \(\chi_{676}(35,\cdot)\) \(\chi_{676}(55,\cdot)\) \(\chi_{676}(87,\cdot)\) \(\chi_{676}(107,\cdot)\) \(\chi_{676}(139,\cdot)\) \(\chi_{676}(159,\cdot)\) \(\chi_{676}(211,\cdot)\) \(\chi_{676}(243,\cdot)\) \(\chi_{676}(263,\cdot)\) \(\chi_{676}(295,\cdot)\) \(\chi_{676}(347,\cdot)\) \(\chi_{676}(367,\cdot)\) \(\chi_{676}(399,\cdot)\) \(\chi_{676}(419,\cdot)\) \(\chi_{676}(451,\cdot)\) \(\chi_{676}(471,\cdot)\) \(\chi_{676}(503,\cdot)\) \(\chi_{676}(523,\cdot)\) \(\chi_{676}(555,\cdot)\) \(\chi_{676}(575,\cdot)\) \(\chi_{676}(607,\cdot)\) \(\chi_{676}(627,\cdot)\) \(\chi_{676}(659,\cdot)\)

Related number fields

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

Values on generators

\((339,509)\) → \((-1,e\left(\frac{28}{39}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 676 }(55, a) \)	\(-1\)	\(1\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum