Basic properties
| Modulus: | \(6664\) | |
| Conductor: | \(3332\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3332}(1755,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6664.fc
\(\chi_{6664}(47,\cdot)\) \(\chi_{6664}(327,\cdot)\) \(\chi_{6664}(591,\cdot)\) \(\chi_{6664}(871,\cdot)\) \(\chi_{6664}(1279,\cdot)\) \(\chi_{6664}(1543,\cdot)\) \(\chi_{6664}(1823,\cdot)\) \(\chi_{6664}(1951,\cdot)\) \(\chi_{6664}(2231,\cdot)\) \(\chi_{6664}(2495,\cdot)\) \(\chi_{6664}(2903,\cdot)\) \(\chi_{6664}(3183,\cdot)\) \(\chi_{6664}(3447,\cdot)\) \(\chi_{6664}(3727,\cdot)\) \(\chi_{6664}(3855,\cdot)\) \(\chi_{6664}(4399,\cdot)\) \(\chi_{6664}(4679,\cdot)\) \(\chi_{6664}(4807,\cdot)\) \(\chi_{6664}(5087,\cdot)\) \(\chi_{6664}(5351,\cdot)\) \(\chi_{6664}(5631,\cdot)\) \(\chi_{6664}(5759,\cdot)\) \(\chi_{6664}(6039,\cdot)\) \(\chi_{6664}(6583,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4999,3333,4217,785)\) → \((-1,1,e\left(\frac{23}{42}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 6664 }(5087, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{11}{28}\right)\) |