Basic properties
| Modulus: | \(2888\) | |
| Conductor: | \(1444\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1444}(615,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2888.bk
\(\chi_{2888}(7,\cdot)\) \(\chi_{2888}(87,\cdot)\) \(\chi_{2888}(159,\cdot)\) \(\chi_{2888}(239,\cdot)\) \(\chi_{2888}(311,\cdot)\) \(\chi_{2888}(391,\cdot)\) \(\chi_{2888}(463,\cdot)\) \(\chi_{2888}(543,\cdot)\) \(\chi_{2888}(615,\cdot)\) \(\chi_{2888}(695,\cdot)\) \(\chi_{2888}(767,\cdot)\) \(\chi_{2888}(847,\cdot)\) \(\chi_{2888}(919,\cdot)\) \(\chi_{2888}(999,\cdot)\) \(\chi_{2888}(1071,\cdot)\) \(\chi_{2888}(1223,\cdot)\) \(\chi_{2888}(1303,\cdot)\) \(\chi_{2888}(1455,\cdot)\) \(\chi_{2888}(1527,\cdot)\) \(\chi_{2888}(1607,\cdot)\) \(\chi_{2888}(1679,\cdot)\) \(\chi_{2888}(1759,\cdot)\) \(\chi_{2888}(1831,\cdot)\) \(\chi_{2888}(1911,\cdot)\) \(\chi_{2888}(1983,\cdot)\) \(\chi_{2888}(2063,\cdot)\) \(\chi_{2888}(2135,\cdot)\) \(\chi_{2888}(2215,\cdot)\) \(\chi_{2888}(2287,\cdot)\) \(\chi_{2888}(2367,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2167,1445,2529)\) → \((-1,1,e\left(\frac{16}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2888 }(615, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{114}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{73}{114}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{55}{114}\right)\) |