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 \(\chi_{2527}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5054.cj
\(\chi_{5054}(17,\cdot)\) \(\chi_{5054}(47,\cdot)\) \(\chi_{5054}(61,\cdot)\) \(\chi_{5054}(73,\cdot)\) \(\chi_{5054}(157,\cdot)\) \(\chi_{5054}(215,\cdot)\) \(\chi_{5054}(283,\cdot)\) \(\chi_{5054}(313,\cdot)\) \(\chi_{5054}(327,\cdot)\) \(\chi_{5054}(339,\cdot)\) \(\chi_{5054}(481,\cdot)\) \(\chi_{5054}(549,\cdot)\) \(\chi_{5054}(579,\cdot)\) \(\chi_{5054}(593,\cdot)\) \(\chi_{5054}(605,\cdot)\) \(\chi_{5054}(689,\cdot)\) \(\chi_{5054}(747,\cdot)\) \(\chi_{5054}(815,\cdot)\) \(\chi_{5054}(845,\cdot)\) \(\chi_{5054}(859,\cdot)\) \(\chi_{5054}(871,\cdot)\) \(\chi_{5054}(955,\cdot)\) \(\chi_{5054}(1013,\cdot)\) \(\chi_{5054}(1081,\cdot)\) \(\chi_{5054}(1125,\cdot)\) \(\chi_{5054}(1221,\cdot)\) \(\chi_{5054}(1279,\cdot)\) \(\chi_{5054}(1347,\cdot)\) \(\chi_{5054}(1377,\cdot)\) \(\chi_{5054}(1391,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{13}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 5054 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{137}{342}\right)\) | \(e\left(\frac{275}{342}\right)\) | \(e\left(\frac{137}{171}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{175}{342}\right)\) | \(e\left(\frac{35}{171}\right)\) | \(e\left(\frac{5}{342}\right)\) | \(e\left(\frac{131}{171}\right)\) | \(e\left(\frac{104}{171}\right)\) | \(e\left(\frac{23}{114}\right)\) |