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 \(\chi_{245}(193,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3920.fz
\(\chi_{3920}(193,\cdot)\) \(\chi_{3920}(417,\cdot)\) \(\chi_{3920}(513,\cdot)\) \(\chi_{3920}(737,\cdot)\) \(\chi_{3920}(977,\cdot)\) \(\chi_{3920}(1073,\cdot)\) \(\chi_{3920}(1297,\cdot)\) \(\chi_{3920}(1313,\cdot)\) \(\chi_{3920}(1633,\cdot)\) \(\chi_{3920}(1857,\cdot)\) \(\chi_{3920}(1873,\cdot)\) \(\chi_{3920}(2097,\cdot)\) \(\chi_{3920}(2193,\cdot)\) \(\chi_{3920}(2417,\cdot)\) \(\chi_{3920}(2433,\cdot)\) \(\chi_{3920}(2657,\cdot)\) \(\chi_{3920}(2753,\cdot)\) \(\chi_{3920}(2977,\cdot)\) \(\chi_{3920}(2993,\cdot)\) \(\chi_{3920}(3217,\cdot)\) \(\chi_{3920}(3537,\cdot)\) \(\chi_{3920}(3553,\cdot)\) \(\chi_{3920}(3777,\cdot)\) \(\chi_{3920}(3873,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,3137,3041)\) → \((1,1,-i,e\left(\frac{11}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 3920 }(193, a) \) | \(-1\) | \(1\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{2}{3}\right)\) |