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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.gs
\(\chi_{8015}(37,\cdot)\) \(\chi_{8015}(158,\cdot)\) \(\chi_{8015}(193,\cdot)\) \(\chi_{8015}(382,\cdot)\) \(\chi_{8015}(998,\cdot)\) \(\chi_{8015}(1087,\cdot)\) \(\chi_{8015}(1383,\cdot)\) \(\chi_{8015}(1523,\cdot)\) \(\chi_{8015}(1733,\cdot)\) \(\chi_{8015}(1747,\cdot)\) \(\chi_{8015}(1787,\cdot)\) \(\chi_{8015}(1852,\cdot)\) \(\chi_{8015}(1857,\cdot)\) \(\chi_{8015}(1887,\cdot)\) \(\chi_{8015}(1913,\cdot)\) \(\chi_{8015}(1943,\cdot)\) \(\chi_{8015}(1983,\cdot)\) \(\chi_{8015}(2193,\cdot)\) \(\chi_{8015}(2473,\cdot)\) \(\chi_{8015}(2522,\cdot)\) \(\chi_{8015}(2538,\cdot)\) \(\chi_{8015}(2648,\cdot)\) \(\chi_{8015}(2692,\cdot)\) \(\chi_{8015}(2762,\cdot)\) \(\chi_{8015}(2907,\cdot)\) \(\chi_{8015}(2928,\cdot)\) \(\chi_{8015}(2972,\cdot)\) \(\chi_{8015}(3103,\cdot)\) \(\chi_{8015}(3173,\cdot)\) \(\chi_{8015}(3243,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((i,e\left(\frac{1}{3}\right),e\left(\frac{55}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{228}\right)\) | \(e\left(\frac{179}{228}\right)\) | \(e\left(\frac{41}{114}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{41}{76}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{11}{76}\right)\) | \(e\left(\frac{49}{76}\right)\) | \(e\left(\frac{41}{57}\right)\) |