Dirichlet character \(\chi_{1024}(139,\cdot)\)

• Label: 1024.139
• Modulus: $1024$
• Conductor: $1024$
• Order: $256$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1024\)
Conductor:	\(1024\)
Order:	\(256\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1024.r

\(\chi_{1024}(3,\cdot)\) \(\chi_{1024}(11,\cdot)\) \(\chi_{1024}(19,\cdot)\) \(\chi_{1024}(27,\cdot)\) \(\chi_{1024}(35,\cdot)\) \(\chi_{1024}(43,\cdot)\) \(\chi_{1024}(51,\cdot)\) \(\chi_{1024}(59,\cdot)\) \(\chi_{1024}(67,\cdot)\) \(\chi_{1024}(75,\cdot)\) \(\chi_{1024}(83,\cdot)\) \(\chi_{1024}(91,\cdot)\) \(\chi_{1024}(99,\cdot)\) \(\chi_{1024}(107,\cdot)\) \(\chi_{1024}(115,\cdot)\) \(\chi_{1024}(123,\cdot)\) \(\chi_{1024}(131,\cdot)\) \(\chi_{1024}(139,\cdot)\) \(\chi_{1024}(147,\cdot)\) \(\chi_{1024}(155,\cdot)\) \(\chi_{1024}(163,\cdot)\) \(\chi_{1024}(171,\cdot)\) \(\chi_{1024}(179,\cdot)\) \(\chi_{1024}(187,\cdot)\) \(\chi_{1024}(195,\cdot)\) \(\chi_{1024}(203,\cdot)\) \(\chi_{1024}(211,\cdot)\) \(\chi_{1024}(219,\cdot)\) \(\chi_{1024}(227,\cdot)\) \(\chi_{1024}(235,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{256})$
Fixed field:	Number field defined by a degree 256 polynomial (not computed)

Values on generators

\((1023,5)\) → \((-1,e\left(\frac{117}{256}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 1024 }(139, a) \)	\(-1\)	\(1\)	\(e\left(\frac{255}{256}\right)\)	\(e\left(\frac{117}{256}\right)\)	\(e\left(\frac{105}{128}\right)\)	\(e\left(\frac{127}{128}\right)\)	\(e\left(\frac{217}{256}\right)\)	\(e\left(\frac{59}{256}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{131}{256}\right)\)	\(e\left(\frac{209}{256}\right)\)