Basic properties
| Modulus: | \(587\) | |
| Conductor: | \(587\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(293\) | 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 587.c
\(\chi_{587}(3,\cdot)\) \(\chi_{587}(4,\cdot)\) \(\chi_{587}(7,\cdot)\) \(\chi_{587}(9,\cdot)\) \(\chi_{587}(10,\cdot)\) \(\chi_{587}(12,\cdot)\) \(\chi_{587}(16,\cdot)\) \(\chi_{587}(17,\cdot)\) \(\chi_{587}(21,\cdot)\) \(\chi_{587}(22,\cdot)\) \(\chi_{587}(25,\cdot)\) \(\chi_{587}(26,\cdot)\) \(\chi_{587}(27,\cdot)\) \(\chi_{587}(28,\cdot)\) \(\chi_{587}(29,\cdot)\) \(\chi_{587}(30,\cdot)\) \(\chi_{587}(31,\cdot)\) \(\chi_{587}(36,\cdot)\) \(\chi_{587}(38,\cdot)\) \(\chi_{587}(40,\cdot)\) \(\chi_{587}(43,\cdot)\) \(\chi_{587}(46,\cdot)\) \(\chi_{587}(47,\cdot)\) \(\chi_{587}(48,\cdot)\) \(\chi_{587}(49,\cdot)\) \(\chi_{587}(51,\cdot)\) \(\chi_{587}(53,\cdot)\) \(\chi_{587}(55,\cdot)\) \(\chi_{587}(59,\cdot)\) \(\chi_{587}(63,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{293})$ |
| Fixed field: | Number field defined by a degree 293 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{106}{293}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 587 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{106}{293}\right)\) | \(e\left(\frac{272}{293}\right)\) | \(e\left(\frac{212}{293}\right)\) | \(e\left(\frac{48}{293}\right)\) | \(e\left(\frac{85}{293}\right)\) | \(e\left(\frac{51}{293}\right)\) | \(e\left(\frac{25}{293}\right)\) | \(e\left(\frac{251}{293}\right)\) | \(e\left(\frac{154}{293}\right)\) | \(e\left(\frac{8}{293}\right)\) |