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.bf
\(\chi_{1127}(3,\cdot)\) \(\chi_{1127}(12,\cdot)\) \(\chi_{1127}(26,\cdot)\) \(\chi_{1127}(52,\cdot)\) \(\chi_{1127}(54,\cdot)\) \(\chi_{1127}(59,\cdot)\) \(\chi_{1127}(73,\cdot)\) \(\chi_{1127}(75,\cdot)\) \(\chi_{1127}(82,\cdot)\) \(\chi_{1127}(87,\cdot)\) \(\chi_{1127}(94,\cdot)\) \(\chi_{1127}(96,\cdot)\) \(\chi_{1127}(101,\cdot)\) \(\chi_{1127}(108,\cdot)\) \(\chi_{1127}(110,\cdot)\) \(\chi_{1127}(124,\cdot)\) \(\chi_{1127}(131,\cdot)\) \(\chi_{1127}(150,\cdot)\) \(\chi_{1127}(164,\cdot)\) \(\chi_{1127}(173,\cdot)\) \(\chi_{1127}(187,\cdot)\) \(\chi_{1127}(192,\cdot)\) \(\chi_{1127}(213,\cdot)\) \(\chi_{1127}(220,\cdot)\) \(\chi_{1127}(234,\cdot)\) \(\chi_{1127}(236,\cdot)\) \(\chi_{1127}(243,\cdot)\) \(\chi_{1127}(248,\cdot)\) \(\chi_{1127}(255,\cdot)\) \(\chi_{1127}(257,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((346,442)\) → \((e\left(\frac{1}{42}\right),e\left(\frac{9}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1127 }(52, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{231}\right)\) | \(e\left(\frac{53}{462}\right)\) | \(e\left(\frac{118}{231}\right)\) | \(e\left(\frac{235}{462}\right)\) | \(e\left(\frac{57}{154}\right)\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{53}{231}\right)\) | \(e\left(\frac{353}{462}\right)\) | \(e\left(\frac{73}{231}\right)\) | \(e\left(\frac{289}{462}\right)\) |