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.fq
\(\chi_{3920}(109,\cdot)\) \(\chi_{3920}(149,\cdot)\) \(\chi_{3920}(389,\cdot)\) \(\chi_{3920}(429,\cdot)\) \(\chi_{3920}(669,\cdot)\) \(\chi_{3920}(709,\cdot)\) \(\chi_{3920}(989,\cdot)\) \(\chi_{3920}(1229,\cdot)\) \(\chi_{3920}(1269,\cdot)\) \(\chi_{3920}(1509,\cdot)\) \(\chi_{3920}(1789,\cdot)\) \(\chi_{3920}(1829,\cdot)\) \(\chi_{3920}(2069,\cdot)\) \(\chi_{3920}(2109,\cdot)\) \(\chi_{3920}(2349,\cdot)\) \(\chi_{3920}(2389,\cdot)\) \(\chi_{3920}(2629,\cdot)\) \(\chi_{3920}(2669,\cdot)\) \(\chi_{3920}(2949,\cdot)\) \(\chi_{3920}(3189,\cdot)\) \(\chi_{3920}(3229,\cdot)\) \(\chi_{3920}(3469,\cdot)\) \(\chi_{3920}(3749,\cdot)\) \(\chi_{3920}(3789,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((1,-i,-1,e\left(\frac{8}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 3920 }(1789, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) |