Basic properties
| Modulus: | \(1412\) | |
| Conductor: | \(1412\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | 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 1412.s
\(\chi_{1412}(11,\cdot)\) \(\chi_{1412}(83,\cdot)\) \(\chi_{1412}(91,\cdot)\) \(\chi_{1412}(111,\cdot)\) \(\chi_{1412}(159,\cdot)\) \(\chi_{1412}(351,\cdot)\) \(\chi_{1412}(355,\cdot)\) \(\chi_{1412}(547,\cdot)\) \(\chi_{1412}(595,\cdot)\) \(\chi_{1412}(615,\cdot)\) \(\chi_{1412}(623,\cdot)\) \(\chi_{1412}(695,\cdot)\) \(\chi_{1412}(723,\cdot)\) \(\chi_{1412}(727,\cdot)\) \(\chi_{1412}(735,\cdot)\) \(\chi_{1412}(767,\cdot)\) \(\chi_{1412}(779,\cdot)\) \(\chi_{1412}(787,\cdot)\) \(\chi_{1412}(815,\cdot)\) \(\chi_{1412}(883,\cdot)\) \(\chi_{1412}(931,\cdot)\) \(\chi_{1412}(975,\cdot)\) \(\chi_{1412}(991,\cdot)\) \(\chi_{1412}(1015,\cdot)\) \(\chi_{1412}(1027,\cdot)\) \(\chi_{1412}(1051,\cdot)\) \(\chi_{1412}(1067,\cdot)\) \(\chi_{1412}(1091,\cdot)\) \(\chi_{1412}(1103,\cdot)\) \(\chi_{1412}(1127,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((707,709)\) → \((-1,e\left(\frac{73}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1412 }(1027, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{88}\right)\) | \(e\left(\frac{29}{88}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{49}{88}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) |