Basic properties
Modulus: | \(3920\) | |
Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{784}(397,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fo
\(\chi_{3920}(61,\cdot)\) \(\chi_{3920}(101,\cdot)\) \(\chi_{3920}(341,\cdot)\) \(\chi_{3920}(381,\cdot)\) \(\chi_{3920}(621,\cdot)\) \(\chi_{3920}(661,\cdot)\) \(\chi_{3920}(941,\cdot)\) \(\chi_{3920}(1181,\cdot)\) \(\chi_{3920}(1221,\cdot)\) \(\chi_{3920}(1461,\cdot)\) \(\chi_{3920}(1741,\cdot)\) \(\chi_{3920}(1781,\cdot)\) \(\chi_{3920}(2021,\cdot)\) \(\chi_{3920}(2061,\cdot)\) \(\chi_{3920}(2301,\cdot)\) \(\chi_{3920}(2341,\cdot)\) \(\chi_{3920}(2581,\cdot)\) \(\chi_{3920}(2621,\cdot)\) \(\chi_{3920}(2901,\cdot)\) \(\chi_{3920}(3141,\cdot)\) \(\chi_{3920}(3181,\cdot)\) \(\chi_{3920}(3421,\cdot)\) \(\chi_{3920}(3701,\cdot)\) \(\chi_{3920}(3741,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((1,-i,1,e\left(\frac{29}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 3920 }(1181, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) |