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.id
\(\chi_{7056}(461,\cdot)\) \(\chi_{7056}(797,\cdot)\) \(\chi_{7056}(965,\cdot)\) \(\chi_{7056}(1301,\cdot)\) \(\chi_{7056}(1805,\cdot)\) \(\chi_{7056}(1973,\cdot)\) \(\chi_{7056}(2309,\cdot)\) \(\chi_{7056}(2477,\cdot)\) \(\chi_{7056}(2813,\cdot)\) \(\chi_{7056}(2981,\cdot)\) \(\chi_{7056}(3317,\cdot)\) \(\chi_{7056}(3485,\cdot)\) \(\chi_{7056}(3989,\cdot)\) \(\chi_{7056}(4325,\cdot)\) \(\chi_{7056}(4493,\cdot)\) \(\chi_{7056}(4829,\cdot)\) \(\chi_{7056}(5333,\cdot)\) \(\chi_{7056}(5501,\cdot)\) \(\chi_{7056}(5837,\cdot)\) \(\chi_{7056}(6005,\cdot)\) \(\chi_{7056}(6341,\cdot)\) \(\chi_{7056}(6509,\cdot)\) \(\chi_{7056}(6845,\cdot)\) \(\chi_{7056}(7013,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((1,-i,e\left(\frac{1}{6}\right),e\left(\frac{13}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7056 }(461, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(-i\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{28}\right)\) |