Dirichlet character \(\chi_{8007}(7700,\cdot)\)

• Label: 8007.7700
• Modulus: $8007$
• Conductor: $8007$
• Order: $52$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8007\)
Conductor:	\(8007\)
Order:	\(52\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8007.dh

\(\chi_{8007}(1070,\cdot)\) \(\chi_{8007}(1478,\cdot)\) \(\chi_{8007}(1529,\cdot)\) \(\chi_{8007}(1682,\cdot)\) \(\chi_{8007}(1886,\cdot)\) \(\chi_{8007}(2039,\cdot)\) \(\chi_{8007}(2243,\cdot)\) \(\chi_{8007}(2396,\cdot)\) \(\chi_{8007}(2447,\cdot)\) \(\chi_{8007}(2855,\cdot)\) \(\chi_{8007}(4028,\cdot)\) \(\chi_{8007}(4232,\cdot)\) \(\chi_{8007}(4742,\cdot)\) \(\chi_{8007}(4844,\cdot)\) \(\chi_{8007}(4946,\cdot)\) \(\chi_{8007}(5660,\cdot)\) \(\chi_{8007}(5711,\cdot)\) \(\chi_{8007}(6221,\cdot)\) \(\chi_{8007}(6272,\cdot)\) \(\chi_{8007}(6986,\cdot)\) \(\chi_{8007}(7088,\cdot)\) \(\chi_{8007}(7190,\cdot)\) \(\chi_{8007}(7700,\cdot)\) \(\chi_{8007}(7904,\cdot)\)

Related number fields

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

Values on generators

\((5339,1414,7855)\) → \((-1,-1,e\left(\frac{49}{52}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\( \chi_{ 8007 }(7700, a) \)	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(-1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)