Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(8281\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(546\) | 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 8281.ee
\(\chi_{8281}(12,\cdot)\) \(\chi_{8281}(38,\cdot)\) \(\chi_{8281}(103,\cdot)\) \(\chi_{8281}(194,\cdot)\) \(\chi_{8281}(220,\cdot)\) \(\chi_{8281}(285,\cdot)\) \(\chi_{8281}(311,\cdot)\) \(\chi_{8281}(376,\cdot)\) \(\chi_{8281}(402,\cdot)\) \(\chi_{8281}(467,\cdot)\) \(\chi_{8281}(493,\cdot)\) \(\chi_{8281}(584,\cdot)\) \(\chi_{8281}(649,\cdot)\) \(\chi_{8281}(740,\cdot)\) \(\chi_{8281}(831,\cdot)\) \(\chi_{8281}(857,\cdot)\) \(\chi_{8281}(922,\cdot)\) \(\chi_{8281}(948,\cdot)\) \(\chi_{8281}(1039,\cdot)\) \(\chi_{8281}(1104,\cdot)\) \(\chi_{8281}(1130,\cdot)\) \(\chi_{8281}(1221,\cdot)\) \(\chi_{8281}(1286,\cdot)\) \(\chi_{8281}(1312,\cdot)\) \(\chi_{8281}(1377,\cdot)\) \(\chi_{8281}(1468,\cdot)\) \(\chi_{8281}(1494,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{273})$ |
| Fixed field: | Number field defined by a degree 546 polynomial (not computed) |
Values on generators
\((1522,3382)\) → \((e\left(\frac{11}{42}\right),e\left(\frac{21}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{337}{546}\right)\) | \(e\left(\frac{227}{546}\right)\) | \(e\left(\frac{64}{273}\right)\) | \(e\left(\frac{236}{273}\right)\) | \(e\left(\frac{3}{91}\right)\) | \(e\left(\frac{155}{182}\right)\) | \(e\left(\frac{227}{273}\right)\) | \(e\left(\frac{263}{546}\right)\) | \(e\left(\frac{365}{546}\right)\) | \(e\left(\frac{355}{546}\right)\) |