Dirichlet character \(\chi_{1060}(243,\cdot)\)

• Label: 1060.243
• Modulus: $1060$
• Conductor: $1060$
• Order: $52$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1060\)
Conductor:	\(1060\)
Order:	\(52\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1060.bc

\(\chi_{1060}(3,\cdot)\) \(\chi_{1060}(27,\cdot)\) \(\chi_{1060}(67,\cdot)\) \(\chi_{1060}(87,\cdot)\) \(\chi_{1060}(127,\cdot)\) \(\chi_{1060}(167,\cdot)\) \(\chi_{1060}(243,\cdot)\) \(\chi_{1060}(287,\cdot)\) \(\chi_{1060}(363,\cdot)\) \(\chi_{1060}(403,\cdot)\) \(\chi_{1060}(443,\cdot)\) \(\chi_{1060}(463,\cdot)\) \(\chi_{1060}(503,\cdot)\) \(\chi_{1060}(527,\cdot)\) \(\chi_{1060}(603,\cdot)\) \(\chi_{1060}(687,\cdot)\) \(\chi_{1060}(707,\cdot)\) \(\chi_{1060}(747,\cdot)\) \(\chi_{1060}(783,\cdot)\) \(\chi_{1060}(807,\cdot)\) \(\chi_{1060}(843,\cdot)\) \(\chi_{1060}(883,\cdot)\) \(\chi_{1060}(903,\cdot)\) \(\chi_{1060}(987,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Values on generators

\((531,637,161)\) → \((-1,-i,e\left(\frac{33}{52}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\( \chi_{ 1060 }(243, a) \)	\(-1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(-1\)	\(e\left(\frac{8}{13}\right)\)