Basic properties
| Modulus: | \(2548\) | |
| Conductor: | \(2548\) | 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 2548.ei
\(\chi_{2548}(59,\cdot)\) \(\chi_{2548}(271,\cdot)\) \(\chi_{2548}(327,\cdot)\) \(\chi_{2548}(591,\cdot)\) \(\chi_{2548}(635,\cdot)\) \(\chi_{2548}(691,\cdot)\) \(\chi_{2548}(787,\cdot)\) \(\chi_{2548}(955,\cdot)\) \(\chi_{2548}(1055,\cdot)\) \(\chi_{2548}(1151,\cdot)\) \(\chi_{2548}(1319,\cdot)\) \(\chi_{2548}(1363,\cdot)\) \(\chi_{2548}(1419,\cdot)\) \(\chi_{2548}(1515,\cdot)\) \(\chi_{2548}(1683,\cdot)\) \(\chi_{2548}(1727,\cdot)\) \(\chi_{2548}(1879,\cdot)\) \(\chi_{2548}(2047,\cdot)\) \(\chi_{2548}(2091,\cdot)\) \(\chi_{2548}(2147,\cdot)\) \(\chi_{2548}(2243,\cdot)\) \(\chi_{2548}(2411,\cdot)\) \(\chi_{2548}(2455,\cdot)\) \(\chi_{2548}(2511,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1275,885,197)\) → \((-1,e\left(\frac{13}{42}\right),e\left(\frac{11}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2548 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{3}{7}\right)\) |