Dirichlet character \(\chi_{507}(113,\cdot)\)

• Label: 507.113
• 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.u

\(\chi_{507}(29,\cdot)\) \(\chi_{507}(35,\cdot)\) \(\chi_{507}(68,\cdot)\) \(\chi_{507}(74,\cdot)\) \(\chi_{507}(107,\cdot)\) \(\chi_{507}(113,\cdot)\) \(\chi_{507}(152,\cdot)\) \(\chi_{507}(185,\cdot)\) \(\chi_{507}(224,\cdot)\) \(\chi_{507}(230,\cdot)\) \(\chi_{507}(263,\cdot)\) \(\chi_{507}(269,\cdot)\) \(\chi_{507}(302,\cdot)\) \(\chi_{507}(308,\cdot)\) \(\chi_{507}(341,\cdot)\) \(\chi_{507}(347,\cdot)\) \(\chi_{507}(380,\cdot)\) \(\chi_{507}(386,\cdot)\) \(\chi_{507}(419,\cdot)\) \(\chi_{507}(425,\cdot)\) \(\chi_{507}(458,\cdot)\) \(\chi_{507}(464,\cdot)\) \(\chi_{507}(497,\cdot)\) \(\chi_{507}(503,\cdot)\)

Related number fields

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

Values on generators

\((170,340)\) → \((-1,e\left(\frac{8}{39}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 507 }(113, a) \)	\(-1\)	\(1\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum