Dirichlet character \(\chi_{4000}(411,\cdot)\)

• Label: 4000.411
• Modulus: $4000$
• Conductor: $4000$
• Order: $200$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(4000\)
Conductor:	\(4000\)
Order:	\(200\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 4000.db

\(\chi_{4000}(11,\cdot)\) \(\chi_{4000}(91,\cdot)\) \(\chi_{4000}(131,\cdot)\) \(\chi_{4000}(171,\cdot)\) \(\chi_{4000}(211,\cdot)\) \(\chi_{4000}(291,\cdot)\) \(\chi_{4000}(331,\cdot)\) \(\chi_{4000}(371,\cdot)\) \(\chi_{4000}(411,\cdot)\) \(\chi_{4000}(491,\cdot)\) \(\chi_{4000}(531,\cdot)\) \(\chi_{4000}(571,\cdot)\) \(\chi_{4000}(611,\cdot)\) \(\chi_{4000}(691,\cdot)\) \(\chi_{4000}(731,\cdot)\) \(\chi_{4000}(771,\cdot)\) \(\chi_{4000}(811,\cdot)\) \(\chi_{4000}(891,\cdot)\) \(\chi_{4000}(931,\cdot)\) \(\chi_{4000}(971,\cdot)\) \(\chi_{4000}(1011,\cdot)\) \(\chi_{4000}(1091,\cdot)\) \(\chi_{4000}(1131,\cdot)\) \(\chi_{4000}(1171,\cdot)\) \(\chi_{4000}(1211,\cdot)\) \(\chi_{4000}(1291,\cdot)\) \(\chi_{4000}(1331,\cdot)\) \(\chi_{4000}(1371,\cdot)\) \(\chi_{4000}(1411,\cdot)\) \(\chi_{4000}(1491,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{200})$
Fixed field:	Number field defined by a degree 200 polynomial (not computed)

Values on generators

\((2751,2501,1377)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{4}{25}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\( \chi_{ 4000 }(411, a) \)	\(-1\)	\(1\)	\(e\left(\frac{199}{200}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{57}{200}\right)\)	\(e\left(\frac{23}{200}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{51}{200}\right)\)	\(e\left(\frac{69}{200}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{197}{200}\right)\)