Basic properties
| Modulus: | \(569\) | |
| Conductor: | \(569\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(568\) | 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 569.h
\(\chi_{569}(3,\cdot)\) \(\chi_{569}(6,\cdot)\) \(\chi_{569}(11,\cdot)\) \(\chi_{569}(12,\cdot)\) \(\chi_{569}(15,\cdot)\) \(\chi_{569}(19,\cdot)\) \(\chi_{569}(21,\cdot)\) \(\chi_{569}(22,\cdot)\) \(\chi_{569}(23,\cdot)\) \(\chi_{569}(24,\cdot)\) \(\chi_{569}(27,\cdot)\) \(\chi_{569}(29,\cdot)\) \(\chi_{569}(30,\cdot)\) \(\chi_{569}(31,\cdot)\) \(\chi_{569}(37,\cdot)\) \(\chi_{569}(38,\cdot)\) \(\chi_{569}(39,\cdot)\) \(\chi_{569}(42,\cdot)\) \(\chi_{569}(44,\cdot)\) \(\chi_{569}(46,\cdot)\) \(\chi_{569}(47,\cdot)\) \(\chi_{569}(48,\cdot)\) \(\chi_{569}(51,\cdot)\) \(\chi_{569}(53,\cdot)\) \(\chi_{569}(54,\cdot)\) \(\chi_{569}(55,\cdot)\) \(\chi_{569}(58,\cdot)\) \(\chi_{569}(59,\cdot)\) \(\chi_{569}(60,\cdot)\) \(\chi_{569}(62,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{568})$ |
| Fixed field: | Number field defined by a degree 568 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{361}{568}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 569 }(62, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{284}\right)\) | \(e\left(\frac{361}{568}\right)\) | \(e\left(\frac{39}{142}\right)\) | \(e\left(\frac{9}{71}\right)\) | \(e\left(\frac{439}{568}\right)\) | \(e\left(\frac{27}{284}\right)\) | \(e\left(\frac{117}{284}\right)\) | \(e\left(\frac{77}{284}\right)\) | \(e\left(\frac{75}{284}\right)\) | \(e\left(\frac{119}{568}\right)\) |