Dirichlet character \(\chi_{1060}(19,\cdot)\)

• Label: 1060.19
• Modulus: $1060$
• Conductor: $1060$
• Order: $52$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 1060.bk

\(\chi_{1060}(19,\cdot)\) \(\chi_{1060}(39,\cdot)\) \(\chi_{1060}(79,\cdot)\) \(\chi_{1060}(139,\cdot)\) \(\chi_{1060}(179,\cdot)\) \(\chi_{1060}(239,\cdot)\) \(\chi_{1060}(279,\cdot)\) \(\chi_{1060}(299,\cdot)\) \(\chi_{1060}(339,\cdot)\) \(\chi_{1060}(359,\cdot)\) \(\chi_{1060}(379,\cdot)\) \(\chi_{1060}(419,\cdot)\) \(\chi_{1060}(459,\cdot)\) \(\chi_{1060}(479,\cdot)\) \(\chi_{1060}(499,\cdot)\) \(\chi_{1060}(639,\cdot)\) \(\chi_{1060}(739,\cdot)\) \(\chi_{1060}(879,\cdot)\) \(\chi_{1060}(899,\cdot)\) \(\chi_{1060}(919,\cdot)\) \(\chi_{1060}(959,\cdot)\) \(\chi_{1060}(999,\cdot)\) \(\chi_{1060}(1019,\cdot)\) \(\chi_{1060}(1039,\cdot)\)

Related number fields

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

Values on generators

\((531,637,161)\) → \((-1,-1,e\left(\frac{37}{52}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\( \chi_{ 1060 }(19, a) \)	\(1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(-i\)	\(e\left(\frac{15}{52}\right)\)