Basic properties
Modulus: | \(3920\) | |
Conductor: | \(3920\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fi
\(\chi_{3920}(37,\cdot)\) \(\chi_{3920}(93,\cdot)\) \(\chi_{3920}(277,\cdot)\) \(\chi_{3920}(333,\cdot)\) \(\chi_{3920}(597,\cdot)\) \(\chi_{3920}(653,\cdot)\) \(\chi_{3920}(837,\cdot)\) \(\chi_{3920}(893,\cdot)\) \(\chi_{3920}(1213,\cdot)\) \(\chi_{3920}(1397,\cdot)\) \(\chi_{3920}(1453,\cdot)\) \(\chi_{3920}(1717,\cdot)\) \(\chi_{3920}(1773,\cdot)\) \(\chi_{3920}(1957,\cdot)\) \(\chi_{3920}(2013,\cdot)\) \(\chi_{3920}(2277,\cdot)\) \(\chi_{3920}(2573,\cdot)\) \(\chi_{3920}(2837,\cdot)\) \(\chi_{3920}(2893,\cdot)\) \(\chi_{3920}(3077,\cdot)\) \(\chi_{3920}(3133,\cdot)\) \(\chi_{3920}(3397,\cdot)\) \(\chi_{3920}(3453,\cdot)\) \(\chi_{3920}(3637,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((1,-i,-i,e\left(\frac{11}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 3920 }(3133, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) |