Basic properties
| Modulus: | \(3332\) | |
| Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{833}(89,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3332.cp
\(\chi_{3332}(89,\cdot)\) \(\chi_{3332}(157,\cdot)\) \(\chi_{3332}(285,\cdot)\) \(\chi_{3332}(353,\cdot)\) \(\chi_{3332}(565,\cdot)\) \(\chi_{3332}(633,\cdot)\) \(\chi_{3332}(761,\cdot)\) \(\chi_{3332}(829,\cdot)\) \(\chi_{3332}(1041,\cdot)\) \(\chi_{3332}(1237,\cdot)\) \(\chi_{3332}(1517,\cdot)\) \(\chi_{3332}(1585,\cdot)\) \(\chi_{3332}(1713,\cdot)\) \(\chi_{3332}(1781,\cdot)\) \(\chi_{3332}(1993,\cdot)\) \(\chi_{3332}(2061,\cdot)\) \(\chi_{3332}(2189,\cdot)\) \(\chi_{3332}(2257,\cdot)\) \(\chi_{3332}(2537,\cdot)\) \(\chi_{3332}(2733,\cdot)\) \(\chi_{3332}(2945,\cdot)\) \(\chi_{3332}(3013,\cdot)\) \(\chi_{3332}(3141,\cdot)\) \(\chi_{3332}(3209,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1667,885,785)\) → \((1,e\left(\frac{23}{42}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3332 }(89, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{25}{28}\right)\) |