Basic properties
| Modulus: | \(2557\) | |
| Conductor: | \(2557\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(639\) | 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 2557.o
\(\chi_{2557}(3,\cdot)\) \(\chi_{2557}(9,\cdot)\) \(\chi_{2557}(10,\cdot)\) \(\chi_{2557}(11,\cdot)\) \(\chi_{2557}(13,\cdot)\) \(\chi_{2557}(16,\cdot)\) \(\chi_{2557}(19,\cdot)\) \(\chi_{2557}(28,\cdot)\) \(\chi_{2557}(48,\cdot)\) \(\chi_{2557}(49,\cdot)\) \(\chi_{2557}(71,\cdot)\) \(\chi_{2557}(81,\cdot)\) \(\chi_{2557}(84,\cdot)\) \(\chi_{2557}(85,\cdot)\) \(\chi_{2557}(90,\cdot)\) \(\chi_{2557}(92,\cdot)\) \(\chi_{2557}(99,\cdot)\) \(\chi_{2557}(100,\cdot)\) \(\chi_{2557}(110,\cdot)\) \(\chi_{2557}(116,\cdot)\) \(\chi_{2557}(117,\cdot)\) \(\chi_{2557}(121,\cdot)\) \(\chi_{2557}(130,\cdot)\) \(\chi_{2557}(136,\cdot)\) \(\chi_{2557}(143,\cdot)\) \(\chi_{2557}(147,\cdot)\) \(\chi_{2557}(148,\cdot)\) \(\chi_{2557}(158,\cdot)\) \(\chi_{2557}(161,\cdot)\) \(\chi_{2557}(169,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{639})$ |
| Fixed field: | Number field defined by a degree 639 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{554}{639}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2557 }(1066, a) \) | \(1\) | \(1\) | \(e\left(\frac{554}{639}\right)\) | \(e\left(\frac{263}{639}\right)\) | \(e\left(\frac{469}{639}\right)\) | \(e\left(\frac{389}{639}\right)\) | \(e\left(\frac{178}{639}\right)\) | \(e\left(\frac{238}{639}\right)\) | \(e\left(\frac{128}{213}\right)\) | \(e\left(\frac{526}{639}\right)\) | \(e\left(\frac{304}{639}\right)\) | \(e\left(\frac{538}{639}\right)\) |