Basic properties
| Modulus: | \(3920\) | |
| Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{784}(387,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fv
\(\chi_{3920}(11,\cdot)\) \(\chi_{3920}(51,\cdot)\) \(\chi_{3920}(291,\cdot)\) \(\chi_{3920}(331,\cdot)\) \(\chi_{3920}(571,\cdot)\) \(\chi_{3920}(611,\cdot)\) \(\chi_{3920}(891,\cdot)\) \(\chi_{3920}(1131,\cdot)\) \(\chi_{3920}(1171,\cdot)\) \(\chi_{3920}(1411,\cdot)\) \(\chi_{3920}(1691,\cdot)\) \(\chi_{3920}(1731,\cdot)\) \(\chi_{3920}(1971,\cdot)\) \(\chi_{3920}(2011,\cdot)\) \(\chi_{3920}(2251,\cdot)\) \(\chi_{3920}(2291,\cdot)\) \(\chi_{3920}(2531,\cdot)\) \(\chi_{3920}(2571,\cdot)\) \(\chi_{3920}(2851,\cdot)\) \(\chi_{3920}(3091,\cdot)\) \(\chi_{3920}(3131,\cdot)\) \(\chi_{3920}(3371,\cdot)\) \(\chi_{3920}(3651,\cdot)\) \(\chi_{3920}(3691,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((-1,-i,1,e\left(\frac{4}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 3920 }(1171, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) |