Basic properties
| Modulus: | \(3267\) | |
| Conductor: | \(1089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1089}(743,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3267.bp
\(\chi_{3267}(8,\cdot)\) \(\chi_{3267}(17,\cdot)\) \(\chi_{3267}(35,\cdot)\) \(\chi_{3267}(62,\cdot)\) \(\chi_{3267}(116,\cdot)\) \(\chi_{3267}(206,\cdot)\) \(\chi_{3267}(260,\cdot)\) \(\chi_{3267}(305,\cdot)\) \(\chi_{3267}(314,\cdot)\) \(\chi_{3267}(332,\cdot)\) \(\chi_{3267}(359,\cdot)\) \(\chi_{3267}(413,\cdot)\) \(\chi_{3267}(503,\cdot)\) \(\chi_{3267}(530,\cdot)\) \(\chi_{3267}(557,\cdot)\) \(\chi_{3267}(611,\cdot)\) \(\chi_{3267}(629,\cdot)\) \(\chi_{3267}(656,\cdot)\) \(\chi_{3267}(710,\cdot)\) \(\chi_{3267}(800,\cdot)\) \(\chi_{3267}(827,\cdot)\) \(\chi_{3267}(854,\cdot)\) \(\chi_{3267}(899,\cdot)\) \(\chi_{3267}(908,\cdot)\) \(\chi_{3267}(926,\cdot)\) \(\chi_{3267}(953,\cdot)\) \(\chi_{3267}(1007,\cdot)\) \(\chi_{3267}(1097,\cdot)\) \(\chi_{3267}(1124,\cdot)\) \(\chi_{3267}(1151,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((3026,244)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{49}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 3267 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{43}{330}\right)\) | \(e\left(\frac{149}{330}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{217}{330}\right)\) | \(e\left(\frac{241}{330}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{18}{55}\right)\) |