Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(637\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{637}(89,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8281.cz
\(\chi_{8281}(89,\cdot)\) \(\chi_{8281}(150,\cdot)\) \(\chi_{8281}(418,\cdot)\) \(\chi_{8281}(1272,\cdot)\) \(\chi_{8281}(1333,\cdot)\) \(\chi_{8281}(1601,\cdot)\) \(\chi_{8281}(2047,\cdot)\) \(\chi_{8281}(2455,\cdot)\) \(\chi_{8281}(2516,\cdot)\) \(\chi_{8281}(2784,\cdot)\) \(\chi_{8281}(3230,\cdot)\) \(\chi_{8281}(3638,\cdot)\) \(\chi_{8281}(3699,\cdot)\) \(\chi_{8281}(3967,\cdot)\) \(\chi_{8281}(4413,\cdot)\) \(\chi_{8281}(5150,\cdot)\) \(\chi_{8281}(5596,\cdot)\) \(\chi_{8281}(6004,\cdot)\) \(\chi_{8281}(6065,\cdot)\) \(\chi_{8281}(6333,\cdot)\) \(\chi_{8281}(6779,\cdot)\) \(\chi_{8281}(7187,\cdot)\) \(\chi_{8281}(7248,\cdot)\) \(\chi_{8281}(7962,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1522,3382)\) → \((e\left(\frac{23}{42}\right),e\left(\frac{7}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{11}{21}\right)\) |