Basic properties
| Modulus: | \(1127\) | |
| Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(462\) | 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 1127.bd
\(\chi_{1127}(11,\cdot)\) \(\chi_{1127}(37,\cdot)\) \(\chi_{1127}(44,\cdot)\) \(\chi_{1127}(51,\cdot)\) \(\chi_{1127}(53,\cdot)\) \(\chi_{1127}(60,\cdot)\) \(\chi_{1127}(65,\cdot)\) \(\chi_{1127}(74,\cdot)\) \(\chi_{1127}(86,\cdot)\) \(\chi_{1127}(88,\cdot)\) \(\chi_{1127}(102,\cdot)\) \(\chi_{1127}(107,\cdot)\) \(\chi_{1127}(109,\cdot)\) \(\chi_{1127}(130,\cdot)\) \(\chi_{1127}(135,\cdot)\) \(\chi_{1127}(149,\cdot)\) \(\chi_{1127}(158,\cdot)\) \(\chi_{1127}(172,\cdot)\) \(\chi_{1127}(191,\cdot)\) \(\chi_{1127}(198,\cdot)\) \(\chi_{1127}(205,\cdot)\) \(\chi_{1127}(212,\cdot)\) \(\chi_{1127}(221,\cdot)\) \(\chi_{1127}(228,\cdot)\) \(\chi_{1127}(235,\cdot)\) \(\chi_{1127}(240,\cdot)\) \(\chi_{1127}(247,\cdot)\) \(\chi_{1127}(249,\cdot)\) \(\chi_{1127}(268,\cdot)\) \(\chi_{1127}(270,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((346,442)\) → \((e\left(\frac{2}{21}\right),e\left(\frac{21}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1127 }(865, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{231}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{178}{231}\right)\) | \(e\left(\frac{331}{462}\right)\) | \(e\left(\frac{58}{77}\right)\) | \(e\left(\frac{12}{77}\right)\) | \(e\left(\frac{170}{231}\right)\) | \(e\left(\frac{47}{462}\right)\) | \(e\left(\frac{185}{462}\right)\) | \(e\left(\frac{32}{231}\right)\) |