Dirichlet character \(\chi_{1013}(93,\cdot)\)

• Label: 1013.93
• Modulus: $1013$
• Conductor: $1013$
• Order: $506$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1013\)
Conductor:	\(1013\)
Order:	\(506\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1013.k

\(\chi_{1013}(9,\cdot)\) \(\chi_{1013}(13,\cdot)\) \(\chi_{1013}(15,\cdot)\) \(\chi_{1013}(21,\cdot)\) \(\chi_{1013}(24,\cdot)\) \(\chi_{1013}(25,\cdot)\) \(\chi_{1013}(35,\cdot)\) \(\chi_{1013}(40,\cdot)\) \(\chi_{1013}(43,\cdot)\) \(\chi_{1013}(49,\cdot)\) \(\chi_{1013}(51,\cdot)\) \(\chi_{1013}(53,\cdot)\) \(\chi_{1013}(54,\cdot)\) \(\chi_{1013}(56,\cdot)\) \(\chi_{1013}(66,\cdot)\) \(\chi_{1013}(71,\cdot)\) \(\chi_{1013}(73,\cdot)\) \(\chi_{1013}(74,\cdot)\) \(\chi_{1013}(76,\cdot)\) \(\chi_{1013}(78,\cdot)\) \(\chi_{1013}(79,\cdot)\) \(\chi_{1013}(85,\cdot)\) \(\chi_{1013}(87,\cdot)\) \(\chi_{1013}(93,\cdot)\) \(\chi_{1013}(110,\cdot)\) \(\chi_{1013}(119,\cdot)\) \(\chi_{1013}(123,\cdot)\) \(\chi_{1013}(126,\cdot)\) \(\chi_{1013}(130,\cdot)\) \(\chi_{1013}(136,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{253})$
Fixed field:	Number field defined by a degree 506 polynomial (not computed)

Values on generators

\(3\) → \(e\left(\frac{263}{506}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 1013 }(93, a) \)	\(1\)	\(1\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{263}{506}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{233}{506}\right)\)	\(e\left(\frac{49}{253}\right)\)	\(e\left(\frac{367}{506}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{10}{253}\right)\)	\(e\left(\frac{34}{253}\right)\)	\(e\left(\frac{17}{23}\right)\)