Dirichlet character \(\chi_{8112}(6995,\cdot)\)

• Label: 8112.6995
• 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.dz

\(\chi_{8112}(131,\cdot)\) \(\chi_{8112}(443,\cdot)\) \(\chi_{8112}(755,\cdot)\) \(\chi_{8112}(1067,\cdot)\) \(\chi_{8112}(1379,\cdot)\) \(\chi_{8112}(2003,\cdot)\) \(\chi_{8112}(2315,\cdot)\) \(\chi_{8112}(2627,\cdot)\) \(\chi_{8112}(2939,\cdot)\) \(\chi_{8112}(3251,\cdot)\) \(\chi_{8112}(3563,\cdot)\) \(\chi_{8112}(3875,\cdot)\) \(\chi_{8112}(4187,\cdot)\) \(\chi_{8112}(4499,\cdot)\) \(\chi_{8112}(4811,\cdot)\) \(\chi_{8112}(5123,\cdot)\) \(\chi_{8112}(5435,\cdot)\) \(\chi_{8112}(6059,\cdot)\) \(\chi_{8112}(6371,\cdot)\) \(\chi_{8112}(6683,\cdot)\) \(\chi_{8112}(6995,\cdot)\) \(\chi_{8112}(7307,\cdot)\) \(\chi_{8112}(7619,\cdot)\) \(\chi_{8112}(7931,\cdot)\)

Related number fields

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

Values on generators

\((5071,6085,2705,3889)\) → \((-1,-i,-1,e\left(\frac{6}{13}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 8112 }(6995, a) \)	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)