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 \(\chi_{784}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fr
\(\chi_{3920}(131,\cdot)\) \(\chi_{3920}(171,\cdot)\) \(\chi_{3920}(451,\cdot)\) \(\chi_{3920}(691,\cdot)\) \(\chi_{3920}(731,\cdot)\) \(\chi_{3920}(971,\cdot)\) \(\chi_{3920}(1251,\cdot)\) \(\chi_{3920}(1291,\cdot)\) \(\chi_{3920}(1531,\cdot)\) \(\chi_{3920}(1571,\cdot)\) \(\chi_{3920}(1811,\cdot)\) \(\chi_{3920}(1851,\cdot)\) \(\chi_{3920}(2091,\cdot)\) \(\chi_{3920}(2131,\cdot)\) \(\chi_{3920}(2411,\cdot)\) \(\chi_{3920}(2651,\cdot)\) \(\chi_{3920}(2691,\cdot)\) \(\chi_{3920}(2931,\cdot)\) \(\chi_{3920}(3211,\cdot)\) \(\chi_{3920}(3251,\cdot)\) \(\chi_{3920}(3491,\cdot)\) \(\chi_{3920}(3531,\cdot)\) \(\chi_{3920}(3771,\cdot)\) \(\chi_{3920}(3811,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((-1,i,1,e\left(\frac{13}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 3920 }(2411, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) |