Dirichlet character \(\chi_{8007}(431,\cdot)\)

• Label: 8007.431
• Modulus: $8007$
• Conductor: $8007$
• Order: $624$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8007\)
Conductor:	\(8007\)
Order:	\(624\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8007.fi

\(\chi_{8007}(44,\cdot)\) \(\chi_{8007}(122,\cdot)\) \(\chi_{8007}(146,\cdot)\) \(\chi_{8007}(167,\cdot)\) \(\chi_{8007}(182,\cdot)\) \(\chi_{8007}(233,\cdot)\) \(\chi_{8007}(284,\cdot)\) \(\chi_{8007}(317,\cdot)\) \(\chi_{8007}(347,\cdot)\) \(\chi_{8007}(350,\cdot)\) \(\chi_{8007}(362,\cdot)\) \(\chi_{8007}(371,\cdot)\) \(\chi_{8007}(419,\cdot)\) \(\chi_{8007}(431,\cdot)\) \(\chi_{8007}(452,\cdot)\) \(\chi_{8007}(515,\cdot)\) \(\chi_{8007}(539,\cdot)\) \(\chi_{8007}(581,\cdot)\) \(\chi_{8007}(617,\cdot)\) \(\chi_{8007}(653,\cdot)\) \(\chi_{8007}(704,\cdot)\) \(\chi_{8007}(755,\cdot)\) \(\chi_{8007}(776,\cdot)\) \(\chi_{8007}(788,\cdot)\) \(\chi_{8007}(821,\cdot)\) \(\chi_{8007}(827,\cdot)\) \(\chi_{8007}(836,\cdot)\) \(\chi_{8007}(890,\cdot)\) \(\chi_{8007}(923,\cdot)\) \(\chi_{8007}(1010,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{624})$
Fixed field:	Number field defined by a degree 624 polynomial (not computed)

Values on generators

\((5339,1414,7855)\) → \((-1,e\left(\frac{15}{16}\right),e\left(\frac{17}{78}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\( \chi_{ 8007 }(431, a) \)	\(1\)	\(1\)	\(e\left(\frac{37}{104}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{253}{624}\right)\)	\(e\left(\frac{73}{208}\right)\)	\(e\left(\frac{7}{104}\right)\)	\(e\left(\frac{475}{624}\right)\)	\(e\left(\frac{103}{624}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{147}{208}\right)\)	\(e\left(\frac{11}{26}\right)\)