Basic properties
Modulus: | \(569\) | |
Conductor: | \(569\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(284\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 569.g
\(\chi_{569}(2,\cdot)\) \(\chi_{569}(7,\cdot)\) \(\chi_{569}(8,\cdot)\) \(\chi_{569}(9,\cdot)\) \(\chi_{569}(10,\cdot)\) \(\chi_{569}(13,\cdot)\) \(\chi_{569}(17,\cdot)\) \(\chi_{569}(28,\cdot)\) \(\chi_{569}(32,\cdot)\) \(\chi_{569}(35,\cdot)\) \(\chi_{569}(36,\cdot)\) \(\chi_{569}(40,\cdot)\) \(\chi_{569}(45,\cdot)\) \(\chi_{569}(50,\cdot)\) \(\chi_{569}(52,\cdot)\) \(\chi_{569}(57,\cdot)\) \(\chi_{569}(61,\cdot)\) \(\chi_{569}(65,\cdot)\) \(\chi_{569}(66,\cdot)\) \(\chi_{569}(67,\cdot)\) \(\chi_{569}(68,\cdot)\) \(\chi_{569}(71,\cdot)\) \(\chi_{569}(79,\cdot)\) \(\chi_{569}(82,\cdot)\) \(\chi_{569}(85,\cdot)\) \(\chi_{569}(98,\cdot)\) \(\chi_{569}(112,\cdot)\) \(\chi_{569}(121,\cdot)\) \(\chi_{569}(126,\cdot)\) \(\chi_{569}(127,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{284})$ |
Fixed field: | Number field defined by a degree 284 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{181}{284}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 569 }(186, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{142}\right)\) | \(e\left(\frac{181}{284}\right)\) | \(e\left(\frac{5}{71}\right)\) | \(e\left(\frac{46}{71}\right)\) | \(e\left(\frac{191}{284}\right)\) | \(e\left(\frac{69}{142}\right)\) | \(e\left(\frac{15}{142}\right)\) | \(e\left(\frac{39}{142}\right)\) | \(e\left(\frac{97}{142}\right)\) | \(e\left(\frac{99}{284}\right)\) |