Basic properties
| Modulus: | \(2548\) | |
| Conductor: | \(637\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{637}(109,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2548.ej
\(\chi_{2548}(109,\cdot)\) \(\chi_{2548}(317,\cdot)\) \(\chi_{2548}(333,\cdot)\) \(\chi_{2548}(473,\cdot)\) \(\chi_{2548}(541,\cdot)\) \(\chi_{2548}(681,\cdot)\) \(\chi_{2548}(697,\cdot)\) \(\chi_{2548}(837,\cdot)\) \(\chi_{2548}(905,\cdot)\) \(\chi_{2548}(1045,\cdot)\) \(\chi_{2548}(1061,\cdot)\) \(\chi_{2548}(1201,\cdot)\) \(\chi_{2548}(1269,\cdot)\) \(\chi_{2548}(1409,\cdot)\) \(\chi_{2548}(1425,\cdot)\) \(\chi_{2548}(1565,\cdot)\) \(\chi_{2548}(1633,\cdot)\) \(\chi_{2548}(1773,\cdot)\) \(\chi_{2548}(1789,\cdot)\) \(\chi_{2548}(1997,\cdot)\) \(\chi_{2548}(2153,\cdot)\) \(\chi_{2548}(2293,\cdot)\) \(\chi_{2548}(2361,\cdot)\) \(\chi_{2548}(2501,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1275,885,197)\) → \((1,e\left(\frac{20}{21}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2548 }(109, a) \) | \(-1\) | \(1\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{6}{7}\right)\) |