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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1015.da
\(\chi_{1015}(2,\cdot)\) \(\chi_{1015}(18,\cdot)\) \(\chi_{1015}(32,\cdot)\) \(\chi_{1015}(72,\cdot)\) \(\chi_{1015}(137,\cdot)\) \(\chi_{1015}(163,\cdot)\) \(\chi_{1015}(177,\cdot)\) \(\chi_{1015}(282,\cdot)\) \(\chi_{1015}(298,\cdot)\) \(\chi_{1015}(403,\cdot)\) \(\chi_{1015}(417,\cdot)\) \(\chi_{1015}(443,\cdot)\) \(\chi_{1015}(508,\cdot)\) \(\chi_{1015}(548,\cdot)\) \(\chi_{1015}(562,\cdot)\) \(\chi_{1015}(578,\cdot)\) \(\chi_{1015}(648,\cdot)\) \(\chi_{1015}(653,\cdot)\) \(\chi_{1015}(723,\cdot)\) \(\chi_{1015}(793,\cdot)\) \(\chi_{1015}(802,\cdot)\) \(\chi_{1015}(872,\cdot)\) \(\chi_{1015}(942,\cdot)\) \(\chi_{1015}(947,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((407,871,176)\) → \((i,e\left(\frac{2}{3}\right),e\left(\frac{5}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 1015 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{1}{21}\right)\) |