Basic properties
| Modulus: | \(3920\) | |
| Conductor: | \(3920\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fh
\(\chi_{3920}(123,\cdot)\) \(\chi_{3920}(387,\cdot)\) \(\chi_{3920}(443,\cdot)\) \(\chi_{3920}(627,\cdot)\) \(\chi_{3920}(683,\cdot)\) \(\chi_{3920}(947,\cdot)\) \(\chi_{3920}(1003,\cdot)\) \(\chi_{3920}(1187,\cdot)\) \(\chi_{3920}(1507,\cdot)\) \(\chi_{3920}(1563,\cdot)\) \(\chi_{3920}(1747,\cdot)\) \(\chi_{3920}(1803,\cdot)\) \(\chi_{3920}(2067,\cdot)\) \(\chi_{3920}(2123,\cdot)\) \(\chi_{3920}(2307,\cdot)\) \(\chi_{3920}(2363,\cdot)\) \(\chi_{3920}(2683,\cdot)\) \(\chi_{3920}(2867,\cdot)\) \(\chi_{3920}(2923,\cdot)\) \(\chi_{3920}(3187,\cdot)\) \(\chi_{3920}(3243,\cdot)\) \(\chi_{3920}(3427,\cdot)\) \(\chi_{3920}(3483,\cdot)\) \(\chi_{3920}(3747,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((-1,i,-i,e\left(\frac{8}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 3920 }(123, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{1}{6}\right)\) |