Dirichlet character \(\chi_{8007}(1787,\cdot)\)

• Label: 8007.1787
• Modulus: $8007$
• Conductor: $8007$
• Order: $312$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8007\)
Conductor:	\(8007\)
Order:	\(312\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8007.fe

\(\chi_{8007}(26,\cdot)\) \(\chi_{8007}(77,\cdot)\) \(\chi_{8007}(104,\cdot)\) \(\chi_{8007}(308,\cdot)\) \(\chi_{8007}(338,\cdot)\) \(\chi_{8007}(416,\cdot)\) \(\chi_{8007}(791,\cdot)\) \(\chi_{8007}(995,\cdot)\) \(\chi_{8007}(1022,\cdot)\) \(\chi_{8007}(1073,\cdot)\) \(\chi_{8007}(1154,\cdot)\) \(\chi_{8007}(1232,\cdot)\) \(\chi_{8007}(1277,\cdot)\) \(\chi_{8007}(1352,\cdot)\) \(\chi_{8007}(1613,\cdot)\) \(\chi_{8007}(1658,\cdot)\) \(\chi_{8007}(1664,\cdot)\) \(\chi_{8007}(1709,\cdot)\) \(\chi_{8007}(1742,\cdot)\) \(\chi_{8007}(1787,\cdot)\) \(\chi_{8007}(1793,\cdot)\) \(\chi_{8007}(1811,\cdot)\) \(\chi_{8007}(1889,\cdot)\) \(\chi_{8007}(1946,\cdot)\) \(\chi_{8007}(2021,\cdot)\) \(\chi_{8007}(2270,\cdot)\) \(\chi_{8007}(2321,\cdot)\) \(\chi_{8007}(2429,\cdot)\) \(\chi_{8007}(2450,\cdot)\) \(\chi_{8007}(2474,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{312})$
Fixed field:	Number field defined by a degree 312 polynomial (not computed)

Values on generators

\((5339,1414,7855)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{53}{156}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\( \chi_{ 8007 }(1787, a) \)	\(1\)	\(1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{67}{312}\right)\)	\(e\left(\frac{59}{104}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{271}{312}\right)\)	\(e\left(\frac{43}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{104}\right)\)	\(e\left(\frac{8}{13}\right)\)