Basic properties
| Modulus: | \(8027\) | |
| Conductor: | \(8027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1276\) | 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 8027.bp
\(\chi_{8027}(6,\cdot)\) \(\chi_{8027}(8,\cdot)\) \(\chi_{8027}(35,\cdot)\) \(\chi_{8027}(39,\cdot)\) \(\chi_{8027}(52,\cdot)\) \(\chi_{8027}(58,\cdot)\) \(\chi_{8027}(98,\cdot)\) \(\chi_{8027}(101,\cdot)\) \(\chi_{8027}(127,\cdot)\) \(\chi_{8027}(131,\cdot)\) \(\chi_{8027}(133,\cdot)\) \(\chi_{8027}(146,\cdot)\) \(\chi_{8027}(163,\cdot)\) \(\chi_{8027}(167,\cdot)\) \(\chi_{8027}(170,\cdot)\) \(\chi_{8027}(179,\cdot)\) \(\chi_{8027}(186,\cdot)\) \(\chi_{8027}(187,\cdot)\) \(\chi_{8027}(216,\cdot)\) \(\chi_{8027}(246,\cdot)\) \(\chi_{8027}(248,\cdot)\) \(\chi_{8027}(284,\cdot)\) \(\chi_{8027}(288,\cdot)\) \(\chi_{8027}(302,\cdot)\) \(\chi_{8027}(311,\cdot)\) \(\chi_{8027}(328,\cdot)\) \(\chi_{8027}(338,\cdot)\) \(\chi_{8027}(357,\cdot)\) \(\chi_{8027}(370,\cdot)\) \(\chi_{8027}(377,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1276})$ |
| Fixed field: | Number field defined by a degree 1276 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((e\left(\frac{3}{11}\right),e\left(\frac{1}{116}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8027 }(8, a) \) | \(-1\) | \(1\) | \(e\left(\frac{707}{1276}\right)\) | \(e\left(\frac{375}{638}\right)\) | \(e\left(\frac{69}{638}\right)\) | \(e\left(\frac{625}{638}\right)\) | \(e\left(\frac{181}{1276}\right)\) | \(e\left(\frac{969}{1276}\right)\) | \(e\left(\frac{845}{1276}\right)\) | \(e\left(\frac{56}{319}\right)\) | \(e\left(\frac{681}{1276}\right)\) | \(e\left(\frac{811}{1276}\right)\) |