Basic properties
| Modulus: | \(2563\) | |
| Conductor: | \(2563\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(580\) | 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 2563.bd
\(\chi_{2563}(9,\cdot)\) \(\chi_{2563}(14,\cdot)\) \(\chi_{2563}(15,\cdot)\) \(\chi_{2563}(25,\cdot)\) \(\chi_{2563}(26,\cdot)\) \(\chi_{2563}(31,\cdot)\) \(\chi_{2563}(36,\cdot)\) \(\chi_{2563}(60,\cdot)\) \(\chi_{2563}(104,\cdot)\) \(\chi_{2563}(113,\cdot)\) \(\chi_{2563}(124,\cdot)\) \(\chi_{2563}(181,\cdot)\) \(\chi_{2563}(202,\cdot)\) \(\chi_{2563}(203,\cdot)\) \(\chi_{2563}(207,\cdot)\) \(\chi_{2563}(218,\cdot)\) \(\chi_{2563}(224,\cdot)\) \(\chi_{2563}(240,\cdot)\) \(\chi_{2563}(246,\cdot)\) \(\chi_{2563}(247,\cdot)\) \(\chi_{2563}(251,\cdot)\) \(\chi_{2563}(258,\cdot)\) \(\chi_{2563}(269,\cdot)\) \(\chi_{2563}(289,\cdot)\) \(\chi_{2563}(295,\cdot)\) \(\chi_{2563}(333,\cdot)\) \(\chi_{2563}(334,\cdot)\) \(\chi_{2563}(345,\cdot)\) \(\chi_{2563}(346,\cdot)\) \(\chi_{2563}(356,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{580})$ |
| Fixed field: | Number field defined by a degree 580 polynomial (not computed) |
Values on generators
\((1399,2333)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{1}{116}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2563 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{145}\right)\) | \(e\left(\frac{469}{580}\right)\) | \(e\left(\frac{64}{145}\right)\) | \(e\left(\frac{477}{580}\right)\) | \(e\left(\frac{17}{580}\right)\) | \(e\left(\frac{33}{290}\right)\) | \(e\left(\frac{96}{145}\right)\) | \(e\left(\frac{179}{290}\right)\) | \(e\left(\frac{5}{116}\right)\) | \(i\) |