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.im
\(\chi_{7056}(115,\cdot)\) \(\chi_{7056}(355,\cdot)\) \(\chi_{7056}(859,\cdot)\) \(\chi_{7056}(1123,\cdot)\) \(\chi_{7056}(1363,\cdot)\) \(\chi_{7056}(1627,\cdot)\) \(\chi_{7056}(1867,\cdot)\) \(\chi_{7056}(2131,\cdot)\) \(\chi_{7056}(2635,\cdot)\) \(\chi_{7056}(2875,\cdot)\) \(\chi_{7056}(3139,\cdot)\) \(\chi_{7056}(3379,\cdot)\) \(\chi_{7056}(3643,\cdot)\) \(\chi_{7056}(3883,\cdot)\) \(\chi_{7056}(4387,\cdot)\) \(\chi_{7056}(4651,\cdot)\) \(\chi_{7056}(4891,\cdot)\) \(\chi_{7056}(5155,\cdot)\) \(\chi_{7056}(5395,\cdot)\) \(\chi_{7056}(5659,\cdot)\) \(\chi_{7056}(6163,\cdot)\) \(\chi_{7056}(6403,\cdot)\) \(\chi_{7056}(6667,\cdot)\) \(\chi_{7056}(6907,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((-1,-i,e\left(\frac{2}{3}\right),e\left(\frac{25}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7056 }(115, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(1\) | \(e\left(\frac{67}{84}\right)\) |