Basic properties
| Modulus: | \(3920\) | |
| Conductor: | \(1960\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1960}(997,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fm
\(\chi_{3920}(73,\cdot)\) \(\chi_{3920}(297,\cdot)\) \(\chi_{3920}(537,\cdot)\) \(\chi_{3920}(633,\cdot)\) \(\chi_{3920}(857,\cdot)\) \(\chi_{3920}(873,\cdot)\) \(\chi_{3920}(1193,\cdot)\) \(\chi_{3920}(1417,\cdot)\) \(\chi_{3920}(1433,\cdot)\) \(\chi_{3920}(1657,\cdot)\) \(\chi_{3920}(1753,\cdot)\) \(\chi_{3920}(1977,\cdot)\) \(\chi_{3920}(1993,\cdot)\) \(\chi_{3920}(2217,\cdot)\) \(\chi_{3920}(2313,\cdot)\) \(\chi_{3920}(2537,\cdot)\) \(\chi_{3920}(2553,\cdot)\) \(\chi_{3920}(2777,\cdot)\) \(\chi_{3920}(3097,\cdot)\) \(\chi_{3920}(3113,\cdot)\) \(\chi_{3920}(3337,\cdot)\) \(\chi_{3920}(3433,\cdot)\) \(\chi_{3920}(3673,\cdot)\) \(\chi_{3920}(3897,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((1,-1,i,e\left(\frac{25}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 3920 }(1977, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{6}\right)\) |