Basic properties
Modulus: | \(3920\) | |
Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{245}(208,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fx
\(\chi_{3920}(17,\cdot)\) \(\chi_{3920}(33,\cdot)\) \(\chi_{3920}(257,\cdot)\) \(\chi_{3920}(353,\cdot)\) \(\chi_{3920}(577,\cdot)\) \(\chi_{3920}(593,\cdot)\) \(\chi_{3920}(817,\cdot)\) \(\chi_{3920}(1137,\cdot)\) \(\chi_{3920}(1153,\cdot)\) \(\chi_{3920}(1377,\cdot)\) \(\chi_{3920}(1473,\cdot)\) \(\chi_{3920}(1713,\cdot)\) \(\chi_{3920}(1937,\cdot)\) \(\chi_{3920}(2033,\cdot)\) \(\chi_{3920}(2257,\cdot)\) \(\chi_{3920}(2497,\cdot)\) \(\chi_{3920}(2593,\cdot)\) \(\chi_{3920}(2817,\cdot)\) \(\chi_{3920}(2833,\cdot)\) \(\chi_{3920}(3153,\cdot)\) \(\chi_{3920}(3377,\cdot)\) \(\chi_{3920}(3393,\cdot)\) \(\chi_{3920}(3617,\cdot)\) \(\chi_{3920}(3713,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((1,1,-i,e\left(\frac{11}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 3920 }(3393, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{5}{6}\right)\) |