Basic properties
| Modulus: | \(3332\) | |
| Conductor: | \(3332\) | 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 3332.co
\(\chi_{3332}(47,\cdot)\) \(\chi_{3332}(115,\cdot)\) \(\chi_{3332}(327,\cdot)\) \(\chi_{3332}(395,\cdot)\) \(\chi_{3332}(523,\cdot)\) \(\chi_{3332}(591,\cdot)\) \(\chi_{3332}(871,\cdot)\) \(\chi_{3332}(1067,\cdot)\) \(\chi_{3332}(1279,\cdot)\) \(\chi_{3332}(1347,\cdot)\) \(\chi_{3332}(1475,\cdot)\) \(\chi_{3332}(1543,\cdot)\) \(\chi_{3332}(1755,\cdot)\) \(\chi_{3332}(1823,\cdot)\) \(\chi_{3332}(1951,\cdot)\) \(\chi_{3332}(2019,\cdot)\) \(\chi_{3332}(2231,\cdot)\) \(\chi_{3332}(2299,\cdot)\) \(\chi_{3332}(2427,\cdot)\) \(\chi_{3332}(2495,\cdot)\) \(\chi_{3332}(2707,\cdot)\) \(\chi_{3332}(2903,\cdot)\) \(\chi_{3332}(3183,\cdot)\) \(\chi_{3332}(3251,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1667,885,785)\) → \((-1,e\left(\frac{37}{42}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3332 }(1543, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{25}{28}\right)\) |