Basic properties
| Modulus: | \(2557\) | |
| Conductor: | \(2557\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1278\) | 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.q
\(\chi_{2557}(4,\cdot)\) \(\chi_{2557}(7,\cdot)\) \(\chi_{2557}(23,\cdot)\) \(\chi_{2557}(25,\cdot)\) \(\chi_{2557}(29,\cdot)\) \(\chi_{2557}(34,\cdot)\) \(\chi_{2557}(36,\cdot)\) \(\chi_{2557}(37,\cdot)\) \(\chi_{2557}(40,\cdot)\) \(\chi_{2557}(44,\cdot)\) \(\chi_{2557}(52,\cdot)\) \(\chi_{2557}(59,\cdot)\) \(\chi_{2557}(63,\cdot)\) \(\chi_{2557}(70,\cdot)\) \(\chi_{2557}(73,\cdot)\) \(\chi_{2557}(76,\cdot)\) \(\chi_{2557}(77,\cdot)\) \(\chi_{2557}(86,\cdot)\) \(\chi_{2557}(91,\cdot)\) \(\chi_{2557}(94,\cdot)\) \(\chi_{2557}(108,\cdot)\) \(\chi_{2557}(120,\cdot)\) \(\chi_{2557}(127,\cdot)\) \(\chi_{2557}(132,\cdot)\) \(\chi_{2557}(133,\cdot)\) \(\chi_{2557}(156,\cdot)\) \(\chi_{2557}(159,\cdot)\) \(\chi_{2557}(173,\cdot)\) \(\chi_{2557}(186,\cdot)\) \(\chi_{2557}(189,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{639})$ |
| Fixed field: | Number field defined by a degree 1278 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{1278}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2557 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{1278}\right)\) | \(e\left(\frac{551}{639}\right)\) | \(e\left(\frac{1}{639}\right)\) | \(e\left(\frac{1093}{1278}\right)\) | \(e\left(\frac{1103}{1278}\right)\) | \(e\left(\frac{382}{639}\right)\) | \(e\left(\frac{1}{426}\right)\) | \(e\left(\frac{463}{639}\right)\) | \(e\left(\frac{547}{639}\right)\) | \(e\left(\frac{493}{639}\right)\) |