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 \(\chi_{1960}(947,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fy
\(\chi_{3920}(23,\cdot)\) \(\chi_{3920}(247,\cdot)\) \(\chi_{3920}(487,\cdot)\) \(\chi_{3920}(583,\cdot)\) \(\chi_{3920}(807,\cdot)\) \(\chi_{3920}(823,\cdot)\) \(\chi_{3920}(1143,\cdot)\) \(\chi_{3920}(1367,\cdot)\) \(\chi_{3920}(1383,\cdot)\) \(\chi_{3920}(1607,\cdot)\) \(\chi_{3920}(1703,\cdot)\) \(\chi_{3920}(1927,\cdot)\) \(\chi_{3920}(1943,\cdot)\) \(\chi_{3920}(2167,\cdot)\) \(\chi_{3920}(2263,\cdot)\) \(\chi_{3920}(2487,\cdot)\) \(\chi_{3920}(2503,\cdot)\) \(\chi_{3920}(2727,\cdot)\) \(\chi_{3920}(3047,\cdot)\) \(\chi_{3920}(3063,\cdot)\) \(\chi_{3920}(3287,\cdot)\) \(\chi_{3920}(3383,\cdot)\) \(\chi_{3920}(3623,\cdot)\) \(\chi_{3920}(3847,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((-1,-1,i,e\left(\frac{10}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 3920 }(1927, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) |