Basic properties
Modulus: | \(3920\) | |
Conductor: | \(980\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{980}(787,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fn
\(\chi_{3920}(47,\cdot)\) \(\chi_{3920}(143,\cdot)\) \(\chi_{3920}(367,\cdot)\) \(\chi_{3920}(383,\cdot)\) \(\chi_{3920}(703,\cdot)\) \(\chi_{3920}(927,\cdot)\) \(\chi_{3920}(943,\cdot)\) \(\chi_{3920}(1167,\cdot)\) \(\chi_{3920}(1263,\cdot)\) \(\chi_{3920}(1487,\cdot)\) \(\chi_{3920}(1503,\cdot)\) \(\chi_{3920}(1727,\cdot)\) \(\chi_{3920}(1823,\cdot)\) \(\chi_{3920}(2047,\cdot)\) \(\chi_{3920}(2063,\cdot)\) \(\chi_{3920}(2287,\cdot)\) \(\chi_{3920}(2607,\cdot)\) \(\chi_{3920}(2623,\cdot)\) \(\chi_{3920}(2847,\cdot)\) \(\chi_{3920}(2943,\cdot)\) \(\chi_{3920}(3183,\cdot)\) \(\chi_{3920}(3407,\cdot)\) \(\chi_{3920}(3503,\cdot)\) \(\chi_{3920}(3727,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((-1,1,i,e\left(\frac{1}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 3920 }(3727, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{2}{3}\right)\) |