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.gp
\(\chi_{8015}(248,\cdot)\) \(\chi_{8015}(402,\cdot)\) \(\chi_{8015}(472,\cdot)\) \(\chi_{8015}(642,\cdot)\) \(\chi_{8015}(682,\cdot)\) \(\chi_{8015}(712,\cdot)\) \(\chi_{8015}(768,\cdot)\) \(\chi_{8015}(838,\cdot)\) \(\chi_{8015}(1048,\cdot)\) \(\chi_{8015}(1298,\cdot)\) \(\chi_{8015}(1312,\cdot)\) \(\chi_{8015}(1328,\cdot)\) \(\chi_{8015}(1377,\cdot)\) \(\chi_{8015}(1503,\cdot)\) \(\chi_{8015}(1762,\cdot)\) \(\chi_{8015}(1783,\cdot)\) \(\chi_{8015}(1907,\cdot)\) \(\chi_{8015}(1958,\cdot)\) \(\chi_{8015}(2028,\cdot)\) \(\chi_{8015}(2098,\cdot)\) \(\chi_{8015}(2112,\cdot)\) \(\chi_{8015}(2152,\cdot)\) \(\chi_{8015}(2567,\cdot)\) \(\chi_{8015}(2602,\cdot)\) \(\chi_{8015}(2663,\cdot)\) \(\chi_{8015}(2677,\cdot)\) \(\chi_{8015}(2712,\cdot)\) \(\chi_{8015}(2768,\cdot)\) \(\chi_{8015}(2803,\cdot)\) \(\chi_{8015}(3148,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-i,e\left(\frac{1}{6}\right),e\left(\frac{23}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(248, a) \) | \(1\) | \(1\) | \(e\left(\frac{127}{228}\right)\) | \(e\left(\frac{79}{228}\right)\) | \(e\left(\frac{13}{114}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{51}{76}\right)\) | \(e\left(\frac{79}{114}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{35}{76}\right)\) | \(e\left(\frac{73}{76}\right)\) | \(e\left(\frac{13}{57}\right)\) |