Dirichlet character \(\chi_{7581}(2678,\cdot)\)

• Label: 7581.2678
• Modulus: $7581$
• Conductor: $7581$
• Order: $114$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(7581\)
Conductor:	\(7581\)
Order:	\(114\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 7581.dp

\(\chi_{7581}(170,\cdot)\) \(\chi_{7581}(284,\cdot)\) \(\chi_{7581}(569,\cdot)\) \(\chi_{7581}(683,\cdot)\) \(\chi_{7581}(968,\cdot)\) \(\chi_{7581}(1367,\cdot)\) \(\chi_{7581}(1481,\cdot)\) \(\chi_{7581}(1766,\cdot)\) \(\chi_{7581}(1880,\cdot)\) \(\chi_{7581}(2279,\cdot)\) \(\chi_{7581}(2564,\cdot)\) \(\chi_{7581}(2678,\cdot)\) \(\chi_{7581}(2963,\cdot)\) \(\chi_{7581}(3077,\cdot)\) \(\chi_{7581}(3362,\cdot)\) \(\chi_{7581}(3476,\cdot)\) \(\chi_{7581}(3761,\cdot)\) \(\chi_{7581}(3875,\cdot)\) \(\chi_{7581}(4160,\cdot)\) \(\chi_{7581}(4274,\cdot)\) \(\chi_{7581}(4559,\cdot)\) \(\chi_{7581}(4673,\cdot)\) \(\chi_{7581}(4958,\cdot)\) \(\chi_{7581}(5072,\cdot)\) \(\chi_{7581}(5357,\cdot)\) \(\chi_{7581}(5471,\cdot)\) \(\chi_{7581}(5756,\cdot)\) \(\chi_{7581}(5870,\cdot)\) \(\chi_{7581}(6155,\cdot)\) \(\chi_{7581}(6269,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{57})$
Fixed field:	Number field defined by a degree 114 polynomial (not computed)

Values on generators

\((2528,6499,1807)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{1}{38}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(20\)
\( \chi_{ 7581 }(2678, a) \)	\(1\)	\(1\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{25}{38}\right)\)