Basic properties
| Modulus: | \(2557\) | |
| Conductor: | \(2557\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2556\) | 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 2557.r
\(\chi_{2557}(2,\cdot)\) \(\chi_{2557}(5,\cdot)\) \(\chi_{2557}(6,\cdot)\) \(\chi_{2557}(15,\cdot)\) \(\chi_{2557}(17,\cdot)\) \(\chi_{2557}(24,\cdot)\) \(\chi_{2557}(31,\cdot)\) \(\chi_{2557}(32,\cdot)\) \(\chi_{2557}(41,\cdot)\) \(\chi_{2557}(42,\cdot)\) \(\chi_{2557}(43,\cdot)\) \(\chi_{2557}(47,\cdot)\) \(\chi_{2557}(51,\cdot)\) \(\chi_{2557}(54,\cdot)\) \(\chi_{2557}(56,\cdot)\) \(\chi_{2557}(60,\cdot)\) \(\chi_{2557}(66,\cdot)\) \(\chi_{2557}(67,\cdot)\) \(\chi_{2557}(72,\cdot)\) \(\chi_{2557}(78,\cdot)\) \(\chi_{2557}(80,\cdot)\) \(\chi_{2557}(83,\cdot)\) \(\chi_{2557}(88,\cdot)\) \(\chi_{2557}(89,\cdot)\) \(\chi_{2557}(98,\cdot)\) \(\chi_{2557}(103,\cdot)\) \(\chi_{2557}(104,\cdot)\) \(\chi_{2557}(105,\cdot)\) \(\chi_{2557}(106,\cdot)\) \(\chi_{2557}(107,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{2556})$ |
| Fixed field: | Number field defined by a degree 2556 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1001}{2556}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2557 }(89, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1001}{2556}\right)\) | \(e\left(\frac{47}{639}\right)\) | \(e\left(\frac{1001}{1278}\right)\) | \(e\left(\frac{1403}{2556}\right)\) | \(e\left(\frac{1189}{2556}\right)\) | \(e\left(\frac{899}{1278}\right)\) | \(e\left(\frac{149}{852}\right)\) | \(e\left(\frac{94}{639}\right)\) | \(e\left(\frac{601}{639}\right)\) | \(e\left(\frac{412}{639}\right)\) |