Basic properties
| Modulus: | \(257\) | |
| Conductor: | \(257\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(256\) | 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 257.i
\(\chi_{257}(3,\cdot)\) \(\chi_{257}(5,\cdot)\) \(\chi_{257}(6,\cdot)\) \(\chi_{257}(7,\cdot)\) \(\chi_{257}(10,\cdot)\) \(\chi_{257}(12,\cdot)\) \(\chi_{257}(14,\cdot)\) \(\chi_{257}(19,\cdot)\) \(\chi_{257}(20,\cdot)\) \(\chi_{257}(24,\cdot)\) \(\chi_{257}(27,\cdot)\) \(\chi_{257}(28,\cdot)\) \(\chi_{257}(33,\cdot)\) \(\chi_{257}(37,\cdot)\) \(\chi_{257}(38,\cdot)\) \(\chi_{257}(39,\cdot)\) \(\chi_{257}(40,\cdot)\) \(\chi_{257}(41,\cdot)\) \(\chi_{257}(43,\cdot)\) \(\chi_{257}(45,\cdot)\) \(\chi_{257}(47,\cdot)\) \(\chi_{257}(48,\cdot)\) \(\chi_{257}(51,\cdot)\) \(\chi_{257}(53,\cdot)\) \(\chi_{257}(54,\cdot)\) \(\chi_{257}(55,\cdot)\) \(\chi_{257}(56,\cdot)\) \(\chi_{257}(63,\cdot)\) \(\chi_{257}(65,\cdot)\) \(\chi_{257}(66,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{256})$ |
| Fixed field: | Number field defined by a degree 256 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{129}{256}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 257 }(254, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{129}{256}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{183}{256}\right)\) | \(e\left(\frac{177}{256}\right)\) | \(e\left(\frac{213}{256}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{1}{128}\right)\) | \(e\left(\frac{231}{256}\right)\) | \(e\left(\frac{49}{64}\right)\) |