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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7056.ja
\(\chi_{7056}(59,\cdot)\) \(\chi_{7056}(299,\cdot)\) \(\chi_{7056}(563,\cdot)\) \(\chi_{7056}(1067,\cdot)\) \(\chi_{7056}(1307,\cdot)\) \(\chi_{7056}(1571,\cdot)\) \(\chi_{7056}(1811,\cdot)\) \(\chi_{7056}(2075,\cdot)\) \(\chi_{7056}(2315,\cdot)\) \(\chi_{7056}(2819,\cdot)\) \(\chi_{7056}(3083,\cdot)\) \(\chi_{7056}(3323,\cdot)\) \(\chi_{7056}(3587,\cdot)\) \(\chi_{7056}(3827,\cdot)\) \(\chi_{7056}(4091,\cdot)\) \(\chi_{7056}(4595,\cdot)\) \(\chi_{7056}(4835,\cdot)\) \(\chi_{7056}(5099,\cdot)\) \(\chi_{7056}(5339,\cdot)\) \(\chi_{7056}(5603,\cdot)\) \(\chi_{7056}(5843,\cdot)\) \(\chi_{7056}(6347,\cdot)\) \(\chi_{7056}(6611,\cdot)\) \(\chi_{7056}(6851,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((-1,i,e\left(\frac{5}{6}\right),e\left(\frac{13}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7056 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{84}\right)\) |