Dirichlet character \(\chi_{8112}(1091,\cdot)\)

• Label: 8112.1091
• Modulus: $8112$
• Conductor: $8112$
• Order: $52$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8112\)
Conductor:	\(8112\)
Order:	\(52\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8112.el

\(\chi_{8112}(155,\cdot)\) \(\chi_{8112}(467,\cdot)\) \(\chi_{8112}(779,\cdot)\) \(\chi_{8112}(1091,\cdot)\) \(\chi_{8112}(1403,\cdot)\) \(\chi_{8112}(1715,\cdot)\) \(\chi_{8112}(2339,\cdot)\) \(\chi_{8112}(2651,\cdot)\) \(\chi_{8112}(2963,\cdot)\) \(\chi_{8112}(3275,\cdot)\) \(\chi_{8112}(3587,\cdot)\) \(\chi_{8112}(3899,\cdot)\) \(\chi_{8112}(4211,\cdot)\) \(\chi_{8112}(4523,\cdot)\) \(\chi_{8112}(4835,\cdot)\) \(\chi_{8112}(5147,\cdot)\) \(\chi_{8112}(5459,\cdot)\) \(\chi_{8112}(5771,\cdot)\) \(\chi_{8112}(6395,\cdot)\) \(\chi_{8112}(6707,\cdot)\) \(\chi_{8112}(7019,\cdot)\) \(\chi_{8112}(7331,\cdot)\) \(\chi_{8112}(7643,\cdot)\) \(\chi_{8112}(7955,\cdot)\)

Related number fields

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

Values on generators

\((5071,6085,2705,3889)\) → \((-1,-i,-1,e\left(\frac{9}{26}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 8112 }(1091, a) \)	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{21}{52}\right)\)