Dirichlet character \(\chi_{1011}(458,\cdot)\)

• Label: 1011.458
• Modulus: $1011$
• Conductor: $1011$
• Order: $56$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1011\)
Conductor:	\(1011\)
Order:	\(56\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1011.bf

\(\chi_{1011}(47,\cdot)\) \(\chi_{1011}(56,\cdot)\) \(\chi_{1011}(137,\cdot)\) \(\chi_{1011}(200,\cdot)\) \(\chi_{1011}(281,\cdot)\) \(\chi_{1011}(290,\cdot)\) \(\chi_{1011}(344,\cdot)\) \(\chi_{1011}(362,\cdot)\) \(\chi_{1011}(380,\cdot)\) \(\chi_{1011}(458,\cdot)\) \(\chi_{1011}(551,\cdot)\) \(\chi_{1011}(626,\cdot)\) \(\chi_{1011}(635,\cdot)\) \(\chi_{1011}(647,\cdot)\) \(\chi_{1011}(668,\cdot)\) \(\chi_{1011}(680,\cdot)\) \(\chi_{1011}(701,\cdot)\) \(\chi_{1011}(713,\cdot)\) \(\chi_{1011}(722,\cdot)\) \(\chi_{1011}(797,\cdot)\) \(\chi_{1011}(890,\cdot)\) \(\chi_{1011}(968,\cdot)\) \(\chi_{1011}(986,\cdot)\) \(\chi_{1011}(1004,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{56})$
Fixed field:	Number field defined by a degree 56 polynomial

Values on generators

\((338,10)\) → \((-1,e\left(\frac{1}{56}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\( \chi_{ 1011 }(458, a) \)	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)