Dirichlet character \(\chi_{507}(368,\cdot)\)

• Label: 507.368
• Modulus: $507$
• Conductor: $507$
• Order: $78$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(507\)
Conductor:	\(507\)
Order:	\(78\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 507.v

\(\chi_{507}(17,\cdot)\) \(\chi_{507}(56,\cdot)\) \(\chi_{507}(62,\cdot)\) \(\chi_{507}(95,\cdot)\) \(\chi_{507}(101,\cdot)\) \(\chi_{507}(134,\cdot)\) \(\chi_{507}(140,\cdot)\) \(\chi_{507}(173,\cdot)\) \(\chi_{507}(179,\cdot)\) \(\chi_{507}(212,\cdot)\) \(\chi_{507}(218,\cdot)\) \(\chi_{507}(251,\cdot)\) \(\chi_{507}(257,\cdot)\) \(\chi_{507}(290,\cdot)\) \(\chi_{507}(296,\cdot)\) \(\chi_{507}(329,\cdot)\) \(\chi_{507}(335,\cdot)\) \(\chi_{507}(368,\cdot)\) \(\chi_{507}(374,\cdot)\) \(\chi_{507}(407,\cdot)\) \(\chi_{507}(413,\cdot)\) \(\chi_{507}(446,\cdot)\) \(\chi_{507}(452,\cdot)\) \(\chi_{507}(491,\cdot)\)

Related number fields

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

Values on generators

\((170,340)\) → \((-1,e\left(\frac{67}{78}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 507 }(368, a) \)	\(-1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum