Dirichlet character \(\chi_{2000}(1011,\cdot)\)

• Label: 2000.1011
• Modulus: $2000$
• Conductor: $2000$
• Order: $100$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(2000\)
Conductor:	\(2000\)
Order:	\(100\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2000.bw

\(\chi_{2000}(11,\cdot)\) \(\chi_{2000}(91,\cdot)\) \(\chi_{2000}(131,\cdot)\) \(\chi_{2000}(171,\cdot)\) \(\chi_{2000}(211,\cdot)\) \(\chi_{2000}(291,\cdot)\) \(\chi_{2000}(331,\cdot)\) \(\chi_{2000}(371,\cdot)\) \(\chi_{2000}(411,\cdot)\) \(\chi_{2000}(491,\cdot)\) \(\chi_{2000}(531,\cdot)\) \(\chi_{2000}(571,\cdot)\) \(\chi_{2000}(611,\cdot)\) \(\chi_{2000}(691,\cdot)\) \(\chi_{2000}(731,\cdot)\) \(\chi_{2000}(771,\cdot)\) \(\chi_{2000}(811,\cdot)\) \(\chi_{2000}(891,\cdot)\) \(\chi_{2000}(931,\cdot)\) \(\chi_{2000}(971,\cdot)\) \(\chi_{2000}(1011,\cdot)\) \(\chi_{2000}(1091,\cdot)\) \(\chi_{2000}(1131,\cdot)\) \(\chi_{2000}(1171,\cdot)\) \(\chi_{2000}(1211,\cdot)\) \(\chi_{2000}(1291,\cdot)\) \(\chi_{2000}(1331,\cdot)\) \(\chi_{2000}(1371,\cdot)\) \(\chi_{2000}(1411,\cdot)\) \(\chi_{2000}(1491,\cdot)\) ...

Related number fields

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

Values on generators

\((751,501,1377)\) → \((-1,-i,e\left(\frac{19}{25}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\( \chi_{ 2000 }(1011, a) \)	\(-1\)	\(1\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{21}{100}\right)\)