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.em
\(\chi_{2548}(111,\cdot)\) \(\chi_{2548}(167,\cdot)\) \(\chi_{2548}(223,\cdot)\) \(\chi_{2548}(279,\cdot)\) \(\chi_{2548}(475,\cdot)\) \(\chi_{2548}(531,\cdot)\) \(\chi_{2548}(643,\cdot)\) \(\chi_{2548}(839,\cdot)\) \(\chi_{2548}(895,\cdot)\) \(\chi_{2548}(951,\cdot)\) \(\chi_{2548}(1007,\cdot)\) \(\chi_{2548}(1203,\cdot)\) \(\chi_{2548}(1259,\cdot)\) \(\chi_{2548}(1315,\cdot)\) \(\chi_{2548}(1623,\cdot)\) \(\chi_{2548}(1679,\cdot)\) \(\chi_{2548}(1735,\cdot)\) \(\chi_{2548}(1931,\cdot)\) \(\chi_{2548}(1987,\cdot)\) \(\chi_{2548}(2043,\cdot)\) \(\chi_{2548}(2099,\cdot)\) \(\chi_{2548}(2295,\cdot)\) \(\chi_{2548}(2407,\cdot)\) \(\chi_{2548}(2463,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1275,885,197)\) → \((-1,e\left(\frac{11}{14}\right),e\left(\frac{11}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2548 }(111, a) \) | \(-1\) | \(1\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) |