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 \(\chi_{784}(123,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fv
\(\chi_{3920}(11,\cdot)\) \(\chi_{3920}(51,\cdot)\) \(\chi_{3920}(291,\cdot)\) \(\chi_{3920}(331,\cdot)\) \(\chi_{3920}(571,\cdot)\) \(\chi_{3920}(611,\cdot)\) \(\chi_{3920}(891,\cdot)\) \(\chi_{3920}(1131,\cdot)\) \(\chi_{3920}(1171,\cdot)\) \(\chi_{3920}(1411,\cdot)\) \(\chi_{3920}(1691,\cdot)\) \(\chi_{3920}(1731,\cdot)\) \(\chi_{3920}(1971,\cdot)\) \(\chi_{3920}(2011,\cdot)\) \(\chi_{3920}(2251,\cdot)\) \(\chi_{3920}(2291,\cdot)\) \(\chi_{3920}(2531,\cdot)\) \(\chi_{3920}(2571,\cdot)\) \(\chi_{3920}(2851,\cdot)\) \(\chi_{3920}(3091,\cdot)\) \(\chi_{3920}(3131,\cdot)\) \(\chi_{3920}(3371,\cdot)\) \(\chi_{3920}(3651,\cdot)\) \(\chi_{3920}(3691,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((-1,i,1,e\left(\frac{8}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 3920 }(1691, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{6}\right)\) |