Basic properties
| Modulus: | \(889\) | |
| Conductor: | \(889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 889.cj
\(\chi_{889}(3,\cdot)\) \(\chi_{889}(101,\cdot)\) \(\chi_{889}(110,\cdot)\) \(\chi_{889}(150,\cdot)\) \(\chi_{889}(166,\cdot)\) \(\chi_{889}(180,\cdot)\) \(\chi_{889}(192,\cdot)\) \(\chi_{889}(236,\cdot)\) \(\chi_{889}(241,\cdot)\) \(\chi_{889}(243,\cdot)\) \(\chi_{889}(299,\cdot)\) \(\chi_{889}(311,\cdot)\) \(\chi_{889}(346,\cdot)\) \(\chi_{889}(388,\cdot)\) \(\chi_{889}(395,\cdot)\) \(\chi_{889}(437,\cdot)\) \(\chi_{889}(439,\cdot)\) \(\chi_{889}(467,\cdot)\) \(\chi_{889}(474,\cdot)\) \(\chi_{889}(493,\cdot)\) \(\chi_{889}(514,\cdot)\) \(\chi_{889}(537,\cdot)\) \(\chi_{889}(551,\cdot)\) \(\chi_{889}(556,\cdot)\) \(\chi_{889}(586,\cdot)\) \(\chi_{889}(593,\cdot)\) \(\chi_{889}(605,\cdot)\) \(\chi_{889}(614,\cdot)\) \(\chi_{889}(647,\cdot)\) \(\chi_{889}(726,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((255,638)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{17}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 889 }(467, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{46}{63}\right)\) |