Basic properties
| Modulus: | \(5445\) | |
| Conductor: | \(1089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1089}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5445.di
\(\chi_{5445}(41,\cdot)\) \(\chi_{5445}(101,\cdot)\) \(\chi_{5445}(266,\cdot)\) \(\chi_{5445}(281,\cdot)\) \(\chi_{5445}(326,\cdot)\) \(\chi_{5445}(371,\cdot)\) \(\chi_{5445}(446,\cdot)\) \(\chi_{5445}(491,\cdot)\) \(\chi_{5445}(536,\cdot)\) \(\chi_{5445}(761,\cdot)\) \(\chi_{5445}(776,\cdot)\) \(\chi_{5445}(821,\cdot)\) \(\chi_{5445}(866,\cdot)\) \(\chi_{5445}(986,\cdot)\) \(\chi_{5445}(1031,\cdot)\) \(\chi_{5445}(1091,\cdot)\) \(\chi_{5445}(1256,\cdot)\) \(\chi_{5445}(1271,\cdot)\) \(\chi_{5445}(1316,\cdot)\) \(\chi_{5445}(1361,\cdot)\) \(\chi_{5445}(1436,\cdot)\) \(\chi_{5445}(1481,\cdot)\) \(\chi_{5445}(1526,\cdot)\) \(\chi_{5445}(1586,\cdot)\) \(\chi_{5445}(1751,\cdot)\) \(\chi_{5445}(1766,\cdot)\) \(\chi_{5445}(1811,\cdot)\) \(\chi_{5445}(1856,\cdot)\) \(\chi_{5445}(1931,\cdot)\) \(\chi_{5445}(2021,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((3026,4357,3511)\) → \((e\left(\frac{5}{6}\right),1,e\left(\frac{23}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 5445 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{263}{330}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{259}{330}\right)\) | \(e\left(\frac{277}{330}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{53}{66}\right)\) |