Basic properties
| Modulus: | \(5929\) | |
| Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(165\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{847}(214,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5929.bt
\(\chi_{5929}(214,\cdot)\) \(\chi_{5929}(312,\cdot)\) \(\chi_{5929}(324,\cdot)\) \(\chi_{5929}(361,\cdot)\) \(\chi_{5929}(410,\cdot)\) \(\chi_{5929}(422,\cdot)\) \(\chi_{5929}(471,\cdot)\) \(\chi_{5929}(520,\cdot)\) \(\chi_{5929}(851,\cdot)\) \(\chi_{5929}(863,\cdot)\) \(\chi_{5929}(900,\cdot)\) \(\chi_{5929}(949,\cdot)\) \(\chi_{5929}(961,\cdot)\) \(\chi_{5929}(1010,\cdot)\) \(\chi_{5929}(1059,\cdot)\) \(\chi_{5929}(1292,\cdot)\) \(\chi_{5929}(1390,\cdot)\) \(\chi_{5929}(1402,\cdot)\) \(\chi_{5929}(1439,\cdot)\) \(\chi_{5929}(1488,\cdot)\) \(\chi_{5929}(1500,\cdot)\) \(\chi_{5929}(1549,\cdot)\) \(\chi_{5929}(1598,\cdot)\) \(\chi_{5929}(1831,\cdot)\) \(\chi_{5929}(1929,\cdot)\) \(\chi_{5929}(1941,\cdot)\) \(\chi_{5929}(1978,\cdot)\) \(\chi_{5929}(2027,\cdot)\) \(\chi_{5929}(2039,\cdot)\) \(\chi_{5929}(2088,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((1816,2059)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{32}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 5929 }(214, a) \) | \(1\) | \(1\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{137}{165}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{42}{55}\right)\) |