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.cw
\(\chi_{1015}(33,\cdot)\) \(\chi_{1015}(38,\cdot)\) \(\chi_{1015}(122,\cdot)\) \(\chi_{1015}(138,\cdot)\) \(\chi_{1015}(178,\cdot)\) \(\chi_{1015}(187,\cdot)\) \(\chi_{1015}(208,\cdot)\) \(\chi_{1015}(283,\cdot)\) \(\chi_{1015}(332,\cdot)\) \(\chi_{1015}(353,\cdot)\) \(\chi_{1015}(383,\cdot)\) \(\chi_{1015}(502,\cdot)\) \(\chi_{1015}(528,\cdot)\) \(\chi_{1015}(593,\cdot)\) \(\chi_{1015}(642,\cdot)\) \(\chi_{1015}(647,\cdot)\) \(\chi_{1015}(738,\cdot)\) \(\chi_{1015}(747,\cdot)\) \(\chi_{1015}(787,\cdot)\) \(\chi_{1015}(817,\cdot)\) \(\chi_{1015}(892,\cdot)\) \(\chi_{1015}(908,\cdot)\) \(\chi_{1015}(962,\cdot)\) \(\chi_{1015}(992,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((407,871,176)\) → \((i,e\left(\frac{1}{6}\right),e\left(\frac{1}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 1015 }(787, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{13}{21}\right)\) |