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.cv
\(\chi_{1015}(23,\cdot)\) \(\chi_{1015}(53,\cdot)\) \(\chi_{1015}(107,\cdot)\) \(\chi_{1015}(123,\cdot)\) \(\chi_{1015}(198,\cdot)\) \(\chi_{1015}(228,\cdot)\) \(\chi_{1015}(268,\cdot)\) \(\chi_{1015}(277,\cdot)\) \(\chi_{1015}(368,\cdot)\) \(\chi_{1015}(373,\cdot)\) \(\chi_{1015}(422,\cdot)\) \(\chi_{1015}(487,\cdot)\) \(\chi_{1015}(513,\cdot)\) \(\chi_{1015}(632,\cdot)\) \(\chi_{1015}(662,\cdot)\) \(\chi_{1015}(683,\cdot)\) \(\chi_{1015}(732,\cdot)\) \(\chi_{1015}(807,\cdot)\) \(\chi_{1015}(828,\cdot)\) \(\chi_{1015}(837,\cdot)\) \(\chi_{1015}(877,\cdot)\) \(\chi_{1015}(893,\cdot)\) \(\chi_{1015}(977,\cdot)\) \(\chi_{1015}(982,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((407,871,176)\) → \((-i,e\left(\frac{1}{3}\right),e\left(\frac{5}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 1015 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{11}{21}\right)\) |