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.cu
\(\chi_{1015}(19,\cdot)\) \(\chi_{1015}(89,\cdot)\) \(\chi_{1015}(124,\cdot)\) \(\chi_{1015}(159,\cdot)\) \(\chi_{1015}(164,\cdot)\) \(\chi_{1015}(229,\cdot)\) \(\chi_{1015}(234,\cdot)\) \(\chi_{1015}(264,\cdot)\) \(\chi_{1015}(269,\cdot)\) \(\chi_{1015}(304,\cdot)\) \(\chi_{1015}(334,\cdot)\) \(\chi_{1015}(369,\cdot)\) \(\chi_{1015}(374,\cdot)\) \(\chi_{1015}(404,\cdot)\) \(\chi_{1015}(409,\cdot)\) \(\chi_{1015}(474,\cdot)\) \(\chi_{1015}(479,\cdot)\) \(\chi_{1015}(514,\cdot)\) \(\chi_{1015}(549,\cdot)\) \(\chi_{1015}(619,\cdot)\) \(\chi_{1015}(649,\cdot)\) \(\chi_{1015}(794,\cdot)\) \(\chi_{1015}(859,\cdot)\) \(\chi_{1015}(1004,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((407,871,176)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{9}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 1015 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{20}{21}\right)\) |