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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2563.bc
\(\chi_{2563}(7,\cdot)\) \(\chi_{2563}(13,\cdot)\) \(\chi_{2563}(18,\cdot)\) \(\chi_{2563}(28,\cdot)\) \(\chi_{2563}(30,\cdot)\) \(\chi_{2563}(50,\cdot)\) \(\chi_{2563}(52,\cdot)\) \(\chi_{2563}(62,\cdot)\) \(\chi_{2563}(72,\cdot)\) \(\chi_{2563}(101,\cdot)\) \(\chi_{2563}(112,\cdot)\) \(\chi_{2563}(123,\cdot)\) \(\chi_{2563}(129,\cdot)\) \(\chi_{2563}(161,\cdot)\) \(\chi_{2563}(167,\cdot)\) \(\chi_{2563}(171,\cdot)\) \(\chi_{2563}(173,\cdot)\) \(\chi_{2563}(178,\cdot)\) \(\chi_{2563}(183,\cdot)\) \(\chi_{2563}(200,\cdot)\) \(\chi_{2563}(205,\cdot)\) \(\chi_{2563}(215,\cdot)\) \(\chi_{2563}(226,\cdot)\) \(\chi_{2563}(248,\cdot)\) \(\chi_{2563}(259,\cdot)\) \(\chi_{2563}(261,\cdot)\) \(\chi_{2563}(266,\cdot)\) \(\chi_{2563}(283,\cdot)\) \(\chi_{2563}(288,\cdot)\) \(\chi_{2563}(293,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{580})$ |
| Fixed field: | Number field defined by a degree 580 polynomial (not computed) |
Values on generators
\((1399,2333)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{111}{116}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2563 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{173}{290}\right)\) | \(e\left(\frac{323}{580}\right)\) | \(e\left(\frac{28}{145}\right)\) | \(e\left(\frac{399}{580}\right)\) | \(e\left(\frac{89}{580}\right)\) | \(e\left(\frac{48}{145}\right)\) | \(e\left(\frac{229}{290}\right)\) | \(e\left(\frac{33}{290}\right)\) | \(e\left(\frac{33}{116}\right)\) | \(-i\) |