Basic properties
| Modulus: | \(5776\) | |
| Conductor: | \(2888\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2888}(1547,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5776.by
\(\chi_{5776}(103,\cdot)\) \(\chi_{5776}(183,\cdot)\) \(\chi_{5776}(407,\cdot)\) \(\chi_{5776}(487,\cdot)\) \(\chi_{5776}(711,\cdot)\) \(\chi_{5776}(1095,\cdot)\) \(\chi_{5776}(1319,\cdot)\) \(\chi_{5776}(1399,\cdot)\) \(\chi_{5776}(1623,\cdot)\) \(\chi_{5776}(1703,\cdot)\) \(\chi_{5776}(1927,\cdot)\) \(\chi_{5776}(2007,\cdot)\) \(\chi_{5776}(2231,\cdot)\) \(\chi_{5776}(2311,\cdot)\) \(\chi_{5776}(2535,\cdot)\) \(\chi_{5776}(2615,\cdot)\) \(\chi_{5776}(2839,\cdot)\) \(\chi_{5776}(2919,\cdot)\) \(\chi_{5776}(3143,\cdot)\) \(\chi_{5776}(3223,\cdot)\) \(\chi_{5776}(3447,\cdot)\) \(\chi_{5776}(3527,\cdot)\) \(\chi_{5776}(3751,\cdot)\) \(\chi_{5776}(3831,\cdot)\) \(\chi_{5776}(4055,\cdot)\) \(\chi_{5776}(4135,\cdot)\) \(\chi_{5776}(4359,\cdot)\) \(\chi_{5776}(4439,\cdot)\) \(\chi_{5776}(4663,\cdot)\) \(\chi_{5776}(4743,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((5055,1445,2529)\) → \((-1,-1,e\left(\frac{7}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 5776 }(103, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{53}{114}\right)\) |