Basic properties
| Modulus: | \(8015\) | |
| Conductor: | \(8015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(228\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.gx
\(\chi_{8015}(17,\cdot)\) \(\chi_{8015}(432,\cdot)\) \(\chi_{8015}(502,\cdot)\) \(\chi_{8015}(703,\cdot)\) \(\chi_{8015}(747,\cdot)\) \(\chi_{8015}(808,\cdot)\) \(\chi_{8015}(852,\cdot)\) \(\chi_{8015}(943,\cdot)\) \(\chi_{8015}(1172,\cdot)\) \(\chi_{8015}(1188,\cdot)\) \(\chi_{8015}(1202,\cdot)\) \(\chi_{8015}(1363,\cdot)\) \(\chi_{8015}(1417,\cdot)\) \(\chi_{8015}(1592,\cdot)\) \(\chi_{8015}(1893,\cdot)\) \(\chi_{8015}(1993,\cdot)\) \(\chi_{8015}(2077,\cdot)\) \(\chi_{8015}(2103,\cdot)\) \(\chi_{8015}(2182,\cdot)\) \(\chi_{8015}(2222,\cdot)\) \(\chi_{8015}(2343,\cdot)\) \(\chi_{8015}(2572,\cdot)\) \(\chi_{8015}(2623,\cdot)\) \(\chi_{8015}(2733,\cdot)\) \(\chi_{8015}(2852,\cdot)\) \(\chi_{8015}(2973,\cdot)\) \(\chi_{8015}(3202,\cdot)\) \(\chi_{8015}(3223,\cdot)\) \(\chi_{8015}(3267,\cdot)\) \(\chi_{8015}(3477,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((i,e\left(\frac{1}{6}\right),e\left(\frac{5}{19}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{228}\right)\) | \(e\left(\frac{149}{228}\right)\) | \(e\left(\frac{25}{114}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{25}{76}\right)\) | \(e\left(\frac{35}{114}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{199}{228}\right)\) | \(e\left(\frac{3}{76}\right)\) | \(e\left(\frac{25}{57}\right)\) |