Basic properties
Modulus: | \(569\) | |
Conductor: | \(569\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(71\) | 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 569.e
\(\chi_{569}(5,\cdot)\) \(\chi_{569}(16,\cdot)\) \(\chi_{569}(18,\cdot)\) \(\chi_{569}(25,\cdot)\) \(\chi_{569}(33,\cdot)\) \(\chi_{569}(56,\cdot)\) \(\chi_{569}(63,\cdot)\) \(\chi_{569}(69,\cdot)\) \(\chi_{569}(80,\cdot)\) \(\chi_{569}(90,\cdot)\) \(\chi_{569}(101,\cdot)\) \(\chi_{569}(104,\cdot)\) \(\chi_{569}(107,\cdot)\) \(\chi_{569}(111,\cdot)\) \(\chi_{569}(113,\cdot)\) \(\chi_{569}(114,\cdot)\) \(\chi_{569}(117,\cdot)\) \(\chi_{569}(125,\cdot)\) \(\chi_{569}(134,\cdot)\) \(\chi_{569}(136,\cdot)\) \(\chi_{569}(141,\cdot)\) \(\chi_{569}(142,\cdot)\) \(\chi_{569}(153,\cdot)\) \(\chi_{569}(164,\cdot)\) \(\chi_{569}(165,\cdot)\) \(\chi_{569}(172,\cdot)\) \(\chi_{569}(196,\cdot)\) \(\chi_{569}(209,\cdot)\) \(\chi_{569}(219,\cdot)\) \(\chi_{569}(249,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{71})$ |
Fixed field: | Number field defined by a degree 71 polynomial |
Values on generators
\(3\) → \(e\left(\frac{19}{71}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 569 }(111, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{71}\right)\) | \(e\left(\frac{19}{71}\right)\) | \(e\left(\frac{68}{71}\right)\) | \(e\left(\frac{15}{71}\right)\) | \(e\left(\frac{53}{71}\right)\) | \(e\left(\frac{29}{71}\right)\) | \(e\left(\frac{31}{71}\right)\) | \(e\left(\frac{38}{71}\right)\) | \(e\left(\frac{49}{71}\right)\) | \(e\left(\frac{10}{71}\right)\) |