Basic properties
| Modulus: | \(2557\) | |
| Conductor: | \(2557\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(284\) | 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.m
\(\chi_{2557}(14,\cdot)\) \(\chi_{2557}(18,\cdot)\) \(\chi_{2557}(26,\cdot)\) \(\chi_{2557}(50,\cdot)\) \(\chi_{2557}(55,\cdot)\) \(\chi_{2557}(79,\cdot)\) \(\chi_{2557}(93,\cdot)\) \(\chi_{2557}(95,\cdot)\) \(\chi_{2557}(96,\cdot)\) \(\chi_{2557}(142,\cdot)\) \(\chi_{2557}(145,\cdot)\) \(\chi_{2557}(170,\cdot)\) \(\chi_{2557}(185,\cdot)\) \(\chi_{2557}(187,\cdot)\) \(\chi_{2557}(233,\cdot)\) \(\chi_{2557}(293,\cdot)\) \(\chi_{2557}(295,\cdot)\) \(\chi_{2557}(301,\cdot)\) \(\chi_{2557}(317,\cdot)\) \(\chi_{2557}(323,\cdot)\) \(\chi_{2557}(329,\cdot)\) \(\chi_{2557}(358,\cdot)\) \(\chi_{2557}(387,\cdot)\) \(\chi_{2557}(420,\cdot)\) \(\chi_{2557}(423,\cdot)\) \(\chi_{2557}(428,\cdot)\) \(\chi_{2557}(431,\cdot)\) \(\chi_{2557}(436,\cdot)\) \(\chi_{2557}(462,\cdot)\) \(\chi_{2557}(493,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{284})$ |
| Fixed field: | Number field defined by a degree 284 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{227}{284}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2557 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{227}{284}\right)\) | \(e\left(\frac{23}{71}\right)\) | \(e\left(\frac{85}{142}\right)\) | \(e\left(\frac{37}{284}\right)\) | \(e\left(\frac{35}{284}\right)\) | \(e\left(\frac{23}{142}\right)\) | \(e\left(\frac{113}{284}\right)\) | \(e\left(\frac{46}{71}\right)\) | \(e\left(\frac{66}{71}\right)\) | \(e\left(\frac{43}{71}\right)\) |