Basic properties
| Modulus: | \(1289\) | |
| Conductor: | \(1289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1288\) | 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 1289.p
\(\chi_{1289}(6,\cdot)\) \(\chi_{1289}(11,\cdot)\) \(\chi_{1289}(12,\cdot)\) \(\chi_{1289}(13,\cdot)\) \(\chi_{1289}(15,\cdot)\) \(\chi_{1289}(21,\cdot)\) \(\chi_{1289}(22,\cdot)\) \(\chi_{1289}(24,\cdot)\) \(\chi_{1289}(26,\cdot)\) \(\chi_{1289}(34,\cdot)\) \(\chi_{1289}(37,\cdot)\) \(\chi_{1289}(42,\cdot)\) \(\chi_{1289}(44,\cdot)\) \(\chi_{1289}(47,\cdot)\) \(\chi_{1289}(48,\cdot)\) \(\chi_{1289}(52,\cdot)\) \(\chi_{1289}(54,\cdot)\) \(\chi_{1289}(55,\cdot)\) \(\chi_{1289}(57,\cdot)\) \(\chi_{1289}(59,\cdot)\) \(\chi_{1289}(60,\cdot)\) \(\chi_{1289}(61,\cdot)\) \(\chi_{1289}(65,\cdot)\) \(\chi_{1289}(68,\cdot)\) \(\chi_{1289}(71,\cdot)\) \(\chi_{1289}(74,\cdot)\) \(\chi_{1289}(75,\cdot)\) \(\chi_{1289}(77,\cdot)\) \(\chi_{1289}(84,\cdot)\) \(\chi_{1289}(85,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1288})$ |
| Fixed field: | Number field defined by a degree 1288 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{645}{1288}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1289 }(1283, a) \) | \(-1\) | \(1\) | \(e\left(\frac{127}{161}\right)\) | \(e\left(\frac{131}{184}\right)\) | \(e\left(\frac{93}{161}\right)\) | \(e\left(\frac{395}{644}\right)\) | \(e\left(\frac{645}{1288}\right)\) | \(e\left(\frac{1}{322}\right)\) | \(e\left(\frac{59}{161}\right)\) | \(e\left(\frac{39}{92}\right)\) | \(e\left(\frac{37}{92}\right)\) | \(e\left(\frac{1075}{1288}\right)\) |