Dirichlet character \(\chi_{1000}(387,\cdot)\)

• Label: 1000.387
• Modulus: $1000$
• Conductor: $1000$
• Order: $100$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1000\)
Conductor:	\(1000\)
Order:	\(100\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1000.bh

\(\chi_{1000}(3,\cdot)\) \(\chi_{1000}(27,\cdot)\) \(\chi_{1000}(67,\cdot)\) \(\chi_{1000}(83,\cdot)\) \(\chi_{1000}(123,\cdot)\) \(\chi_{1000}(147,\cdot)\) \(\chi_{1000}(163,\cdot)\) \(\chi_{1000}(187,\cdot)\) \(\chi_{1000}(203,\cdot)\) \(\chi_{1000}(227,\cdot)\) \(\chi_{1000}(267,\cdot)\) \(\chi_{1000}(283,\cdot)\) \(\chi_{1000}(323,\cdot)\) \(\chi_{1000}(347,\cdot)\) \(\chi_{1000}(363,\cdot)\) \(\chi_{1000}(387,\cdot)\) \(\chi_{1000}(403,\cdot)\) \(\chi_{1000}(427,\cdot)\) \(\chi_{1000}(467,\cdot)\) \(\chi_{1000}(483,\cdot)\) \(\chi_{1000}(523,\cdot)\) \(\chi_{1000}(547,\cdot)\) \(\chi_{1000}(563,\cdot)\) \(\chi_{1000}(587,\cdot)\) \(\chi_{1000}(603,\cdot)\) \(\chi_{1000}(627,\cdot)\) \(\chi_{1000}(667,\cdot)\) \(\chi_{1000}(683,\cdot)\) \(\chi_{1000}(723,\cdot)\) \(\chi_{1000}(747,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{100})$
Fixed field:	Number field defined by a degree 100 polynomial

Values on generators

\((751,501,377)\) → \((-1,-1,e\left(\frac{9}{100}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\( \chi_{ 1000 }(387, a) \)	\(1\)	\(1\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{89}{100}\right)\)