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 \(\chi_{2527}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5054.cd
\(\chi_{5054}(53,\cdot)\) \(\chi_{5054}(67,\cdot)\) \(\chi_{5054}(79,\cdot)\) \(\chi_{5054}(135,\cdot)\) \(\chi_{5054}(165,\cdot)\) \(\chi_{5054}(261,\cdot)\) \(\chi_{5054}(319,\cdot)\) \(\chi_{5054}(345,\cdot)\) \(\chi_{5054}(401,\cdot)\) \(\chi_{5054}(431,\cdot)\) \(\chi_{5054}(527,\cdot)\) \(\chi_{5054}(585,\cdot)\) \(\chi_{5054}(599,\cdot)\) \(\chi_{5054}(611,\cdot)\) \(\chi_{5054}(667,\cdot)\) \(\chi_{5054}(697,\cdot)\) \(\chi_{5054}(793,\cdot)\) \(\chi_{5054}(851,\cdot)\) \(\chi_{5054}(865,\cdot)\) \(\chi_{5054}(877,\cdot)\) \(\chi_{5054}(933,\cdot)\) \(\chi_{5054}(963,\cdot)\) \(\chi_{5054}(1059,\cdot)\) \(\chi_{5054}(1117,\cdot)\) \(\chi_{5054}(1131,\cdot)\) \(\chi_{5054}(1143,\cdot)\) \(\chi_{5054}(1229,\cdot)\) \(\chi_{5054}(1325,\cdot)\) \(\chi_{5054}(1383,\cdot)\) \(\chi_{5054}(1397,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{269}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 5054 }(67, a) \) | \(-1\) | \(1\) | \(e\left(\frac{341}{342}\right)\) | \(e\left(\frac{139}{171}\right)\) | \(e\left(\frac{170}{171}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{265}{342}\right)\) | \(e\left(\frac{277}{342}\right)\) | \(e\left(\frac{73}{171}\right)\) | \(e\left(\frac{29}{171}\right)\) | \(e\left(\frac{107}{171}\right)\) | \(e\left(\frac{113}{114}\right)\) |