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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3332.cm
\(\chi_{3332}(123,\cdot)\) \(\chi_{3332}(191,\cdot)\) \(\chi_{3332}(319,\cdot)\) \(\chi_{3332}(387,\cdot)\) \(\chi_{3332}(599,\cdot)\) \(\chi_{3332}(795,\cdot)\) \(\chi_{3332}(1075,\cdot)\) \(\chi_{3332}(1143,\cdot)\) \(\chi_{3332}(1271,\cdot)\) \(\chi_{3332}(1339,\cdot)\) \(\chi_{3332}(1551,\cdot)\) \(\chi_{3332}(1619,\cdot)\) \(\chi_{3332}(1747,\cdot)\) \(\chi_{3332}(1815,\cdot)\) \(\chi_{3332}(2095,\cdot)\) \(\chi_{3332}(2291,\cdot)\) \(\chi_{3332}(2503,\cdot)\) \(\chi_{3332}(2571,\cdot)\) \(\chi_{3332}(2699,\cdot)\) \(\chi_{3332}(2767,\cdot)\) \(\chi_{3332}(2979,\cdot)\) \(\chi_{3332}(3047,\cdot)\) \(\chi_{3332}(3175,\cdot)\) \(\chi_{3332}(3243,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1667,885,785)\) → \((-1,e\left(\frac{8}{21}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3332 }(123, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{25}{28}\right)\) |