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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fq
\(\chi_{3920}(109,\cdot)\) \(\chi_{3920}(149,\cdot)\) \(\chi_{3920}(389,\cdot)\) \(\chi_{3920}(429,\cdot)\) \(\chi_{3920}(669,\cdot)\) \(\chi_{3920}(709,\cdot)\) \(\chi_{3920}(989,\cdot)\) \(\chi_{3920}(1229,\cdot)\) \(\chi_{3920}(1269,\cdot)\) \(\chi_{3920}(1509,\cdot)\) \(\chi_{3920}(1789,\cdot)\) \(\chi_{3920}(1829,\cdot)\) \(\chi_{3920}(2069,\cdot)\) \(\chi_{3920}(2109,\cdot)\) \(\chi_{3920}(2349,\cdot)\) \(\chi_{3920}(2389,\cdot)\) \(\chi_{3920}(2629,\cdot)\) \(\chi_{3920}(2669,\cdot)\) \(\chi_{3920}(2949,\cdot)\) \(\chi_{3920}(3189,\cdot)\) \(\chi_{3920}(3229,\cdot)\) \(\chi_{3920}(3469,\cdot)\) \(\chi_{3920}(3749,\cdot)\) \(\chi_{3920}(3789,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((1,-i,-1,e\left(\frac{2}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 3920 }(669, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) |