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.ft
\(\chi_{3920}(59,\cdot)\) \(\chi_{3920}(299,\cdot)\) \(\chi_{3920}(339,\cdot)\) \(\chi_{3920}(579,\cdot)\) \(\chi_{3920}(859,\cdot)\) \(\chi_{3920}(899,\cdot)\) \(\chi_{3920}(1139,\cdot)\) \(\chi_{3920}(1179,\cdot)\) \(\chi_{3920}(1419,\cdot)\) \(\chi_{3920}(1459,\cdot)\) \(\chi_{3920}(1699,\cdot)\) \(\chi_{3920}(1739,\cdot)\) \(\chi_{3920}(2019,\cdot)\) \(\chi_{3920}(2259,\cdot)\) \(\chi_{3920}(2299,\cdot)\) \(\chi_{3920}(2539,\cdot)\) \(\chi_{3920}(2819,\cdot)\) \(\chi_{3920}(2859,\cdot)\) \(\chi_{3920}(3099,\cdot)\) \(\chi_{3920}(3139,\cdot)\) \(\chi_{3920}(3379,\cdot)\) \(\chi_{3920}(3419,\cdot)\) \(\chi_{3920}(3659,\cdot)\) \(\chi_{3920}(3699,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((-1,-i,-1,e\left(\frac{23}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 3920 }(579, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{1}{3}\right)\) |