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.db
\(\chi_{1015}(68,\cdot)\) \(\chi_{1015}(73,\cdot)\) \(\chi_{1015}(143,\cdot)\) \(\chi_{1015}(213,\cdot)\) \(\chi_{1015}(222,\cdot)\) \(\chi_{1015}(292,\cdot)\) \(\chi_{1015}(362,\cdot)\) \(\chi_{1015}(367,\cdot)\) \(\chi_{1015}(437,\cdot)\) \(\chi_{1015}(453,\cdot)\) \(\chi_{1015}(467,\cdot)\) \(\chi_{1015}(507,\cdot)\) \(\chi_{1015}(572,\cdot)\) \(\chi_{1015}(598,\cdot)\) \(\chi_{1015}(612,\cdot)\) \(\chi_{1015}(717,\cdot)\) \(\chi_{1015}(733,\cdot)\) \(\chi_{1015}(838,\cdot)\) \(\chi_{1015}(852,\cdot)\) \(\chi_{1015}(878,\cdot)\) \(\chi_{1015}(943,\cdot)\) \(\chi_{1015}(983,\cdot)\) \(\chi_{1015}(997,\cdot)\) \(\chi_{1015}(1013,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((407,871,176)\) → \((i,e\left(\frac{5}{6}\right),e\left(\frac{1}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 1015 }(292, a) \) | \(-1\) | \(1\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) |