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.ir
\(\chi_{7056}(173,\cdot)\) \(\chi_{7056}(437,\cdot)\) \(\chi_{7056}(677,\cdot)\) \(\chi_{7056}(941,\cdot)\) \(\chi_{7056}(1181,\cdot)\) \(\chi_{7056}(1445,\cdot)\) \(\chi_{7056}(1949,\cdot)\) \(\chi_{7056}(2189,\cdot)\) \(\chi_{7056}(2453,\cdot)\) \(\chi_{7056}(2693,\cdot)\) \(\chi_{7056}(2957,\cdot)\) \(\chi_{7056}(3197,\cdot)\) \(\chi_{7056}(3701,\cdot)\) \(\chi_{7056}(3965,\cdot)\) \(\chi_{7056}(4205,\cdot)\) \(\chi_{7056}(4469,\cdot)\) \(\chi_{7056}(4709,\cdot)\) \(\chi_{7056}(4973,\cdot)\) \(\chi_{7056}(5477,\cdot)\) \(\chi_{7056}(5717,\cdot)\) \(\chi_{7056}(5981,\cdot)\) \(\chi_{7056}(6221,\cdot)\) \(\chi_{7056}(6485,\cdot)\) \(\chi_{7056}(6725,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((1,-i,e\left(\frac{1}{6}\right),e\left(\frac{17}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7056 }(173, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{59}{84}\right)\) |