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 \(\chi_{1960}(507,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fw
\(\chi_{3920}(87,\cdot)\) \(\chi_{3920}(103,\cdot)\) \(\chi_{3920}(327,\cdot)\) \(\chi_{3920}(647,\cdot)\) \(\chi_{3920}(663,\cdot)\) \(\chi_{3920}(887,\cdot)\) \(\chi_{3920}(983,\cdot)\) \(\chi_{3920}(1223,\cdot)\) \(\chi_{3920}(1447,\cdot)\) \(\chi_{3920}(1543,\cdot)\) \(\chi_{3920}(1767,\cdot)\) \(\chi_{3920}(2007,\cdot)\) \(\chi_{3920}(2103,\cdot)\) \(\chi_{3920}(2327,\cdot)\) \(\chi_{3920}(2343,\cdot)\) \(\chi_{3920}(2663,\cdot)\) \(\chi_{3920}(2887,\cdot)\) \(\chi_{3920}(2903,\cdot)\) \(\chi_{3920}(3127,\cdot)\) \(\chi_{3920}(3223,\cdot)\) \(\chi_{3920}(3447,\cdot)\) \(\chi_{3920}(3463,\cdot)\) \(\chi_{3920}(3687,\cdot)\) \(\chi_{3920}(3783,\cdot)\)
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
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 3920 }(3447, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{3}\right)\) |