Basic properties
| Modulus: | \(1229\) | |
| Conductor: | \(1229\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1228\) | 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 1229.f
\(\chi_{1229}(2,\cdot)\) \(\chi_{1229}(3,\cdot)\) \(\chi_{1229}(8,\cdot)\) \(\chi_{1229}(10,\cdot)\) \(\chi_{1229}(11,\cdot)\) \(\chi_{1229}(12,\cdot)\) \(\chi_{1229}(13,\cdot)\) \(\chi_{1229}(14,\cdot)\) \(\chi_{1229}(15,\cdot)\) \(\chi_{1229}(17,\cdot)\) \(\chi_{1229}(18,\cdot)\) \(\chi_{1229}(19,\cdot)\) \(\chi_{1229}(21,\cdot)\) \(\chi_{1229}(23,\cdot)\) \(\chi_{1229}(27,\cdot)\) \(\chi_{1229}(29,\cdot)\) \(\chi_{1229}(32,\cdot)\) \(\chi_{1229}(37,\cdot)\) \(\chi_{1229}(40,\cdot)\) \(\chi_{1229}(44,\cdot)\) \(\chi_{1229}(48,\cdot)\) \(\chi_{1229}(50,\cdot)\) \(\chi_{1229}(52,\cdot)\) \(\chi_{1229}(55,\cdot)\) \(\chi_{1229}(56,\cdot)\) \(\chi_{1229}(60,\cdot)\) \(\chi_{1229}(62,\cdot)\) \(\chi_{1229}(65,\cdot)\) \(\chi_{1229}(66,\cdot)\) \(\chi_{1229}(68,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1228})$ |
| Fixed field: | Number field defined by a degree 1228 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{1228}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1229 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{1228}\right)\) | \(e\left(\frac{603}{1228}\right)\) | \(e\left(\frac{1}{614}\right)\) | \(e\left(\frac{91}{614}\right)\) | \(e\left(\frac{151}{307}\right)\) | \(e\left(\frac{63}{614}\right)\) | \(e\left(\frac{3}{1228}\right)\) | \(e\left(\frac{603}{614}\right)\) | \(e\left(\frac{183}{1228}\right)\) | \(e\left(\frac{473}{1228}\right)\) |