Basic properties
| Modulus: | \(1015\) | |
| Conductor: | \(1015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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 1015.cq
\(\chi_{1015}(3,\cdot)\) \(\chi_{1015}(47,\cdot)\) \(\chi_{1015}(108,\cdot)\) \(\chi_{1015}(192,\cdot)\) \(\chi_{1015}(243,\cdot)\) \(\chi_{1015}(327,\cdot)\) \(\chi_{1015}(388,\cdot)\) \(\chi_{1015}(432,\cdot)\) \(\chi_{1015}(472,\cdot)\) \(\chi_{1015}(537,\cdot)\) \(\chi_{1015}(577,\cdot)\) \(\chi_{1015}(607,\cdot)\) \(\chi_{1015}(628,\cdot)\) \(\chi_{1015}(677,\cdot)\) \(\chi_{1015}(682,\cdot)\) \(\chi_{1015}(698,\cdot)\) \(\chi_{1015}(752,\cdot)\) \(\chi_{1015}(768,\cdot)\) \(\chi_{1015}(773,\cdot)\) \(\chi_{1015}(822,\cdot)\) \(\chi_{1015}(843,\cdot)\) \(\chi_{1015}(873,\cdot)\) \(\chi_{1015}(913,\cdot)\) \(\chi_{1015}(978,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((407,871,176)\) → \((-i,e\left(\frac{1}{6}\right),e\left(\frac{5}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 1015 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{1}{21}\right)\) |