Basic properties
| Modulus: | \(5054\) | |
| Conductor: | \(2527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2527}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5054.cf
\(\chi_{5054}(33,\cdot)\) \(\chi_{5054}(117,\cdot)\) \(\chi_{5054}(129,\cdot)\) \(\chi_{5054}(143,\cdot)\) \(\chi_{5054}(173,\cdot)\) \(\chi_{5054}(241,\cdot)\) \(\chi_{5054}(383,\cdot)\) \(\chi_{5054}(395,\cdot)\) \(\chi_{5054}(409,\cdot)\) \(\chi_{5054}(439,\cdot)\) \(\chi_{5054}(507,\cdot)\) \(\chi_{5054}(565,\cdot)\) \(\chi_{5054}(649,\cdot)\) \(\chi_{5054}(661,\cdot)\) \(\chi_{5054}(675,\cdot)\) \(\chi_{5054}(705,\cdot)\) \(\chi_{5054}(773,\cdot)\) \(\chi_{5054}(831,\cdot)\) \(\chi_{5054}(915,\cdot)\) \(\chi_{5054}(927,\cdot)\) \(\chi_{5054}(941,\cdot)\) \(\chi_{5054}(971,\cdot)\) \(\chi_{5054}(1039,\cdot)\) \(\chi_{5054}(1097,\cdot)\) \(\chi_{5054}(1181,\cdot)\) \(\chi_{5054}(1193,\cdot)\) \(\chi_{5054}(1207,\cdot)\) \(\chi_{5054}(1237,\cdot)\) \(\chi_{5054}(1305,\cdot)\) \(\chi_{5054}(1363,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{241}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 5054 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{134}{171}\right)\) | \(e\left(\frac{223}{342}\right)\) | \(e\left(\frac{97}{171}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{58}{171}\right)\) | \(e\left(\frac{149}{342}\right)\) | \(e\left(\frac{31}{342}\right)\) | \(e\left(\frac{94}{171}\right)\) | \(e\left(\frac{52}{171}\right)\) | \(e\left(\frac{20}{57}\right)\) |