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 \(\chi_{1089}(745,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3267.bq
\(\chi_{3267}(19,\cdot)\) \(\chi_{3267}(46,\cdot)\) \(\chi_{3267}(73,\cdot)\) \(\chi_{3267}(127,\cdot)\) \(\chi_{3267}(145,\cdot)\) \(\chi_{3267}(172,\cdot)\) \(\chi_{3267}(226,\cdot)\) \(\chi_{3267}(316,\cdot)\) \(\chi_{3267}(343,\cdot)\) \(\chi_{3267}(370,\cdot)\) \(\chi_{3267}(415,\cdot)\) \(\chi_{3267}(424,\cdot)\) \(\chi_{3267}(442,\cdot)\) \(\chi_{3267}(469,\cdot)\) \(\chi_{3267}(523,\cdot)\) \(\chi_{3267}(613,\cdot)\) \(\chi_{3267}(640,\cdot)\) \(\chi_{3267}(667,\cdot)\) \(\chi_{3267}(712,\cdot)\) \(\chi_{3267}(721,\cdot)\) \(\chi_{3267}(739,\cdot)\) \(\chi_{3267}(910,\cdot)\) \(\chi_{3267}(937,\cdot)\) \(\chi_{3267}(964,\cdot)\) \(\chi_{3267}(1009,\cdot)\) \(\chi_{3267}(1018,\cdot)\) \(\chi_{3267}(1036,\cdot)\) \(\chi_{3267}(1063,\cdot)\) \(\chi_{3267}(1117,\cdot)\) \(\chi_{3267}(1234,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((3026,244)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{83}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 3267 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{139}{330}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{313}{330}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{179}{330}\right)\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{107}{110}\right)\) |