Dirichlet character \(\chi_{3267}(89,\cdot)\)

• Label: 3267.89
• Modulus: $3267$
• Conductor: $1089$
• Order: $66$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	\(3267\)
Conductor:	\(1089\)
Order:	\(66\)
Real:	no
Primitive:	no, induced from \(\chi_{1089}(452,\cdot)\)
Minimal:	no
Parity:	odd

Galois orbit 3267.bb

\(\chi_{3267}(89,\cdot)\) \(\chi_{3267}(287,\cdot)\) \(\chi_{3267}(386,\cdot)\) \(\chi_{3267}(584,\cdot)\) \(\chi_{3267}(683,\cdot)\) \(\chi_{3267}(881,\cdot)\) \(\chi_{3267}(980,\cdot)\) \(\chi_{3267}(1178,\cdot)\) \(\chi_{3267}(1277,\cdot)\) \(\chi_{3267}(1475,\cdot)\) \(\chi_{3267}(1772,\cdot)\) \(\chi_{3267}(1871,\cdot)\) \(\chi_{3267}(2069,\cdot)\) \(\chi_{3267}(2168,\cdot)\) \(\chi_{3267}(2366,\cdot)\) \(\chi_{3267}(2465,\cdot)\) \(\chi_{3267}(2762,\cdot)\) \(\chi_{3267}(2960,\cdot)\) \(\chi_{3267}(3059,\cdot)\) \(\chi_{3267}(3257,\cdot)\)

Related number fields

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

Values on generators

\((3026,244)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{6}{11}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 3267 }(89, a) \)	\(-1\)	\(1\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)