Basic properties
| Modulus: | \(7056\) | |
| Conductor: | \(7056\) | 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 7056.ip
\(\chi_{7056}(347,\cdot)\) \(\chi_{7056}(443,\cdot)\) \(\chi_{7056}(947,\cdot)\) \(\chi_{7056}(1355,\cdot)\) \(\chi_{7056}(1859,\cdot)\) \(\chi_{7056}(1955,\cdot)\) \(\chi_{7056}(2363,\cdot)\) \(\chi_{7056}(2459,\cdot)\) \(\chi_{7056}(2867,\cdot)\) \(\chi_{7056}(2963,\cdot)\) \(\chi_{7056}(3371,\cdot)\) \(\chi_{7056}(3467,\cdot)\) \(\chi_{7056}(3875,\cdot)\) \(\chi_{7056}(3971,\cdot)\) \(\chi_{7056}(4475,\cdot)\) \(\chi_{7056}(4883,\cdot)\) \(\chi_{7056}(5387,\cdot)\) \(\chi_{7056}(5483,\cdot)\) \(\chi_{7056}(5891,\cdot)\) \(\chi_{7056}(5987,\cdot)\) \(\chi_{7056}(6395,\cdot)\) \(\chi_{7056}(6491,\cdot)\) \(\chi_{7056}(6899,\cdot)\) \(\chi_{7056}(6995,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((-1,i,e\left(\frac{5}{6}\right),e\left(\frac{5}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7056 }(347, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{73}{84}\right)\) |