Basic properties
| Modulus: | \(1127\) | |
| Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(231\) | 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.bc
\(\chi_{1127}(2,\cdot)\) \(\chi_{1127}(4,\cdot)\) \(\chi_{1127}(9,\cdot)\) \(\chi_{1127}(16,\cdot)\) \(\chi_{1127}(25,\cdot)\) \(\chi_{1127}(32,\cdot)\) \(\chi_{1127}(39,\cdot)\) \(\chi_{1127}(58,\cdot)\) \(\chi_{1127}(72,\cdot)\) \(\chi_{1127}(81,\cdot)\) \(\chi_{1127}(95,\cdot)\) \(\chi_{1127}(100,\cdot)\) \(\chi_{1127}(121,\cdot)\) \(\chi_{1127}(123,\cdot)\) \(\chi_{1127}(142,\cdot)\) \(\chi_{1127}(144,\cdot)\) \(\chi_{1127}(151,\cdot)\) \(\chi_{1127}(156,\cdot)\) \(\chi_{1127}(163,\cdot)\) \(\chi_{1127}(170,\cdot)\) \(\chi_{1127}(179,\cdot)\) \(\chi_{1127}(186,\cdot)\) \(\chi_{1127}(193,\cdot)\) \(\chi_{1127}(200,\cdot)\) \(\chi_{1127}(219,\cdot)\) \(\chi_{1127}(233,\cdot)\) \(\chi_{1127}(242,\cdot)\) \(\chi_{1127}(256,\cdot)\) \(\chi_{1127}(261,\cdot)\) \(\chi_{1127}(282,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 231 polynomial (not computed) |
Values on generators
\((346,442)\) → \((e\left(\frac{5}{21}\right),e\left(\frac{2}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1127 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{128}{231}\right)\) | \(e\left(\frac{34}{231}\right)\) | \(e\left(\frac{25}{231}\right)\) | \(e\left(\frac{20}{231}\right)\) | \(e\left(\frac{54}{77}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{68}{231}\right)\) | \(e\left(\frac{148}{231}\right)\) | \(e\left(\frac{37}{231}\right)\) | \(e\left(\frac{59}{231}\right)\) |