Basic properties
| Modulus: | \(1421\) | |
| Conductor: | \(1421\) | 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 1421.du
\(\chi_{1421}(11,\cdot)\) \(\chi_{1421}(39,\cdot)\) \(\chi_{1421}(130,\cdot)\) \(\chi_{1421}(142,\cdot)\) \(\chi_{1421}(317,\cdot)\) \(\chi_{1421}(438,\cdot)\) \(\chi_{1421}(478,\cdot)\) \(\chi_{1421}(583,\cdot)\) \(\chi_{1421}(611,\cdot)\) \(\chi_{1421}(646,\cdot)\) \(\chi_{1421}(891,\cdot)\) \(\chi_{1421}(907,\cdot)\) \(\chi_{1421}(914,\cdot)\) \(\chi_{1421}(947,\cdot)\) \(\chi_{1421}(984,\cdot)\) \(\chi_{1421}(996,\cdot)\) \(\chi_{1421}(1152,\cdot)\) \(\chi_{1421}(1178,\cdot)\) \(\chi_{1421}(1236,\cdot)\) \(\chi_{1421}(1262,\cdot)\) \(\chi_{1421}(1278,\cdot)\) \(\chi_{1421}(1374,\cdot)\) \(\chi_{1421}(1411,\cdot)\) \(\chi_{1421}(1418,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1277,785)\) → \((e\left(\frac{20}{21}\right),e\left(\frac{25}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1421 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{61}{84}\right)\) |