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.hc
\(\chi_{8015}(54,\cdot)\) \(\chi_{8015}(199,\cdot)\) \(\chi_{8015}(374,\cdot)\) \(\chi_{8015}(404,\cdot)\) \(\chi_{8015}(479,\cdot)\) \(\chi_{8015}(544,\cdot)\) \(\chi_{8015}(689,\cdot)\) \(\chi_{8015}(719,\cdot)\) \(\chi_{8015}(864,\cdot)\) \(\chi_{8015}(894,\cdot)\) \(\chi_{8015}(929,\cdot)\) \(\chi_{8015}(1004,\cdot)\) \(\chi_{8015}(1039,\cdot)\) \(\chi_{8015}(1179,\cdot)\) \(\chi_{8015}(1489,\cdot)\) \(\chi_{8015}(1494,\cdot)\) \(\chi_{8015}(1704,\cdot)\) \(\chi_{8015}(1739,\cdot)\) \(\chi_{8015}(2154,\cdot)\) \(\chi_{8015}(2189,\cdot)\) \(\chi_{8015}(2399,\cdot)\) \(\chi_{8015}(2404,\cdot)\) \(\chi_{8015}(2714,\cdot)\) \(\chi_{8015}(2854,\cdot)\) \(\chi_{8015}(2889,\cdot)\) \(\chi_{8015}(2964,\cdot)\) \(\chi_{8015}(2999,\cdot)\) \(\chi_{8015}(3029,\cdot)\) \(\chi_{8015}(3174,\cdot)\) \(\chi_{8015}(3204,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{63}{76}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(54, a) \) | \(1\) | \(1\) | \(e\left(\frac{131}{228}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{17}{114}\right)\) | \(e\left(\frac{25}{76}\right)\) | \(e\left(\frac{55}{76}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{71}{114}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{75}{76}\right)\) | \(e\left(\frac{17}{57}\right)\) |