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.dx
\(\chi_{8281}(17,\cdot)\) \(\chi_{8281}(75,\cdot)\) \(\chi_{8281}(108,\cdot)\) \(\chi_{8281}(199,\cdot)\) \(\chi_{8281}(257,\cdot)\) \(\chi_{8281}(290,\cdot)\) \(\chi_{8281}(348,\cdot)\) \(\chi_{8281}(381,\cdot)\) \(\chi_{8281}(439,\cdot)\) \(\chi_{8281}(563,\cdot)\) \(\chi_{8281}(621,\cdot)\) \(\chi_{8281}(712,\cdot)\) \(\chi_{8281}(745,\cdot)\) \(\chi_{8281}(836,\cdot)\) \(\chi_{8281}(894,\cdot)\) \(\chi_{8281}(927,\cdot)\) \(\chi_{8281}(985,\cdot)\) \(\chi_{8281}(1018,\cdot)\) \(\chi_{8281}(1076,\cdot)\) \(\chi_{8281}(1167,\cdot)\) \(\chi_{8281}(1200,\cdot)\) \(\chi_{8281}(1258,\cdot)\) \(\chi_{8281}(1291,\cdot)\) \(\chi_{8281}(1349,\cdot)\) \(\chi_{8281}(1382,\cdot)\) \(\chi_{8281}(1473,\cdot)\) \(\chi_{8281}(1531,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{273})$ |
| Fixed field: | Number field defined by a degree 546 polynomial (not computed) |
Values on generators
\((1522,3382)\) → \((e\left(\frac{25}{42}\right),e\left(\frac{73}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{75}{182}\right)\) | \(e\left(\frac{353}{546}\right)\) | \(e\left(\frac{75}{91}\right)\) | \(e\left(\frac{187}{273}\right)\) | \(e\left(\frac{16}{273}\right)\) | \(e\left(\frac{43}{182}\right)\) | \(e\left(\frac{80}{273}\right)\) | \(e\left(\frac{53}{546}\right)\) | \(e\left(\frac{113}{546}\right)\) | \(e\left(\frac{257}{546}\right)\) |