Dirichlet character \(\chi_{2001}(133,\cdot)\)

• Label: 2001.133
• Modulus: $2001$
• Conductor: $667$
• Order: $44$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(2001\)
Conductor:	\(667\)
Order:	\(44\)
Real:	no
Primitive:	no, induced from \(\chi_{667}(133,\cdot)\)
Minimal:	yes
Parity:	odd

Galois orbit 2001.bi

\(\chi_{2001}(133,\cdot)\) \(\chi_{2001}(220,\cdot)\) \(\chi_{2001}(307,\cdot)\) \(\chi_{2001}(331,\cdot)\) \(\chi_{2001}(394,\cdot)\) \(\chi_{2001}(418,\cdot)\) \(\chi_{2001}(568,\cdot)\) \(\chi_{2001}(679,\cdot)\) \(\chi_{2001}(742,\cdot)\) \(\chi_{2001}(853,\cdot)\) \(\chi_{2001}(1090,\cdot)\) \(\chi_{2001}(1177,\cdot)\) \(\chi_{2001}(1375,\cdot)\) \(\chi_{2001}(1438,\cdot)\) \(\chi_{2001}(1462,\cdot)\) \(\chi_{2001}(1549,\cdot)\) \(\chi_{2001}(1612,\cdot)\) \(\chi_{2001}(1636,\cdot)\) \(\chi_{2001}(1810,\cdot)\) \(\chi_{2001}(1984,\cdot)\)

Related number fields

Field of values:	\(\Q(\zeta_{44})\)
Fixed field:	Number field defined by a degree 44 polynomial

Values on generators

\((668,1132,553)\) → \((1,e\left(\frac{6}{11}\right),-i)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\( \chi_{ 2001 }(133, a) \)	\(-1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)