Dirichlet character \(\chi_{1449}(842,\cdot)\)

• Label: 1449.842
• Modulus: $1449$
• Conductor: $1449$
• Order: $66$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1449\)
Conductor:	\(1449\)
Order:	\(66\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1449.db

\(\chi_{1449}(11,\cdot)\) \(\chi_{1449}(74,\cdot)\) \(\chi_{1449}(86,\cdot)\) \(\chi_{1449}(149,\cdot)\) \(\chi_{1449}(212,\cdot)\) \(\chi_{1449}(263,\cdot)\) \(\chi_{1449}(389,\cdot)\) \(\chi_{1449}(401,\cdot)\) \(\chi_{1449}(452,\cdot)\) \(\chi_{1449}(527,\cdot)\) \(\chi_{1449}(590,\cdot)\) \(\chi_{1449}(641,\cdot)\) \(\chi_{1449}(704,\cdot)\) \(\chi_{1449}(779,\cdot)\) \(\chi_{1449}(842,\cdot)\) \(\chi_{1449}(893,\cdot)\) \(\chi_{1449}(1019,\cdot)\) \(\chi_{1449}(1031,\cdot)\) \(\chi_{1449}(1157,\cdot)\) \(\chi_{1449}(1397,\cdot)\)

Related number fields

Field of values:	\(\Q(\zeta_{33})\)
Fixed field:	Number field defined by a degree 66 polynomial

Values on generators

\((1289,829,442)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{1}{3}\right),e\left(\frac{21}{22}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 1449 }(842, a) \)	\(1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)