Dirichlet character \(\chi_{8112}(1685,\cdot)\)

• Label: 8112.1685
• 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.dv

\(\chi_{8112}(317,\cdot)\) \(\chi_{8112}(941,\cdot)\) \(\chi_{8112}(1061,\cdot)\) \(\chi_{8112}(1565,\cdot)\) \(\chi_{8112}(1685,\cdot)\) \(\chi_{8112}(2189,\cdot)\) \(\chi_{8112}(2309,\cdot)\) \(\chi_{8112}(2813,\cdot)\) \(\chi_{8112}(2933,\cdot)\) \(\chi_{8112}(3437,\cdot)\) \(\chi_{8112}(3557,\cdot)\) \(\chi_{8112}(4061,\cdot)\) \(\chi_{8112}(4181,\cdot)\) \(\chi_{8112}(4685,\cdot)\) \(\chi_{8112}(4805,\cdot)\) \(\chi_{8112}(5429,\cdot)\) \(\chi_{8112}(5933,\cdot)\) \(\chi_{8112}(6053,\cdot)\) \(\chi_{8112}(6557,\cdot)\) \(\chi_{8112}(6677,\cdot)\) \(\chi_{8112}(7181,\cdot)\) \(\chi_{8112}(7301,\cdot)\) \(\chi_{8112}(7805,\cdot)\) \(\chi_{8112}(7925,\cdot)\)

Related number fields

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

Values on generators

\((5071,6085,2705,3889)\) → \((1,i,-1,e\left(\frac{29}{52}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 8112 }(1685, a) \)	\(1\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)