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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.ga
\(\chi_{3920}(53,\cdot)\) \(\chi_{3920}(317,\cdot)\) \(\chi_{3920}(613,\cdot)\) \(\chi_{3920}(877,\cdot)\) \(\chi_{3920}(933,\cdot)\) \(\chi_{3920}(1117,\cdot)\) \(\chi_{3920}(1173,\cdot)\) \(\chi_{3920}(1437,\cdot)\) \(\chi_{3920}(1493,\cdot)\) \(\chi_{3920}(1677,\cdot)\) \(\chi_{3920}(1997,\cdot)\) \(\chi_{3920}(2053,\cdot)\) \(\chi_{3920}(2237,\cdot)\) \(\chi_{3920}(2293,\cdot)\) \(\chi_{3920}(2557,\cdot)\) \(\chi_{3920}(2613,\cdot)\) \(\chi_{3920}(2797,\cdot)\) \(\chi_{3920}(2853,\cdot)\) \(\chi_{3920}(3173,\cdot)\) \(\chi_{3920}(3357,\cdot)\) \(\chi_{3920}(3413,\cdot)\) \(\chi_{3920}(3677,\cdot)\) \(\chi_{3920}(3733,\cdot)\) \(\chi_{3920}(3917,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((1,-i,i,e\left(\frac{1}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 3920 }(2557, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{3}\right)\) |