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.eb
\(\chi_{8281}(10,\cdot)\) \(\chi_{8281}(82,\cdot)\) \(\chi_{8281}(101,\cdot)\) \(\chi_{8281}(173,\cdot)\) \(\chi_{8281}(283,\cdot)\) \(\chi_{8281}(355,\cdot)\) \(\chi_{8281}(446,\cdot)\) \(\chi_{8281}(465,\cdot)\) \(\chi_{8281}(537,\cdot)\) \(\chi_{8281}(556,\cdot)\) \(\chi_{8281}(628,\cdot)\) \(\chi_{8281}(647,\cdot)\) \(\chi_{8281}(719,\cdot)\) \(\chi_{8281}(738,\cdot)\) \(\chi_{8281}(810,\cdot)\) \(\chi_{8281}(829,\cdot)\) \(\chi_{8281}(920,\cdot)\) \(\chi_{8281}(1083,\cdot)\) \(\chi_{8281}(1102,\cdot)\) \(\chi_{8281}(1174,\cdot)\) \(\chi_{8281}(1193,\cdot)\) \(\chi_{8281}(1265,\cdot)\) \(\chi_{8281}(1284,\cdot)\) \(\chi_{8281}(1356,\cdot)\) \(\chi_{8281}(1447,\cdot)\) \(\chi_{8281}(1466,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{273})$ |
| Fixed field: | Number field defined by a degree 546 polynomial (not computed) |
Values on generators
\((1522,3382)\) → \((e\left(\frac{13}{42}\right),e\left(\frac{5}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{546}\right)\) | \(e\left(\frac{47}{182}\right)\) | \(e\left(\frac{61}{273}\right)\) | \(e\left(\frac{151}{273}\right)\) | \(e\left(\frac{101}{273}\right)\) | \(e\left(\frac{61}{182}\right)\) | \(e\left(\frac{47}{91}\right)\) | \(e\left(\frac{121}{182}\right)\) | \(e\left(\frac{179}{182}\right)\) | \(e\left(\frac{263}{546}\right)\) |