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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1127.be
\(\chi_{1127}(5,\cdot)\) \(\chi_{1127}(10,\cdot)\) \(\chi_{1127}(17,\cdot)\) \(\chi_{1127}(33,\cdot)\) \(\chi_{1127}(38,\cdot)\) \(\chi_{1127}(40,\cdot)\) \(\chi_{1127}(61,\cdot)\) \(\chi_{1127}(66,\cdot)\) \(\chi_{1127}(89,\cdot)\) \(\chi_{1127}(103,\cdot)\) \(\chi_{1127}(122,\cdot)\) \(\chi_{1127}(136,\cdot)\) \(\chi_{1127}(143,\cdot)\) \(\chi_{1127}(145,\cdot)\) \(\chi_{1127}(152,\cdot)\) \(\chi_{1127}(157,\cdot)\) \(\chi_{1127}(159,\cdot)\) \(\chi_{1127}(171,\cdot)\) \(\chi_{1127}(180,\cdot)\) \(\chi_{1127}(194,\cdot)\) \(\chi_{1127}(199,\cdot)\) \(\chi_{1127}(201,\cdot)\) \(\chi_{1127}(222,\cdot)\) \(\chi_{1127}(241,\cdot)\) \(\chi_{1127}(250,\cdot)\) \(\chi_{1127}(283,\cdot)\) \(\chi_{1127}(290,\cdot)\) \(\chi_{1127}(297,\cdot)\) \(\chi_{1127}(304,\cdot)\) \(\chi_{1127}(306,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((346,442)\) → \((e\left(\frac{23}{42}\right),e\left(\frac{7}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1127 }(40, a) \) | \(1\) | \(1\) | \(e\left(\frac{202}{231}\right)\) | \(e\left(\frac{295}{462}\right)\) | \(e\left(\frac{173}{231}\right)\) | \(e\left(\frac{46}{231}\right)\) | \(e\left(\frac{79}{154}\right)\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{64}{231}\right)\) | \(e\left(\frac{17}{231}\right)\) | \(e\left(\frac{355}{462}\right)\) | \(e\left(\frac{179}{462}\right)\) |