Basic properties
| Modulus: | \(5445\) | |
| Conductor: | \(5445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5445.dn
\(\chi_{5445}(4,\cdot)\) \(\chi_{5445}(49,\cdot)\) \(\chi_{5445}(169,\cdot)\) \(\chi_{5445}(214,\cdot)\) \(\chi_{5445}(229,\cdot)\) \(\chi_{5445}(394,\cdot)\) \(\chi_{5445}(454,\cdot)\) \(\chi_{5445}(499,\cdot)\) \(\chi_{5445}(544,\cdot)\) \(\chi_{5445}(619,\cdot)\) \(\chi_{5445}(664,\cdot)\) \(\chi_{5445}(709,\cdot)\) \(\chi_{5445}(724,\cdot)\) \(\chi_{5445}(889,\cdot)\) \(\chi_{5445}(949,\cdot)\) \(\chi_{5445}(994,\cdot)\) \(\chi_{5445}(1039,\cdot)\) \(\chi_{5445}(1114,\cdot)\) \(\chi_{5445}(1159,\cdot)\) \(\chi_{5445}(1204,\cdot)\) \(\chi_{5445}(1384,\cdot)\) \(\chi_{5445}(1444,\cdot)\) \(\chi_{5445}(1489,\cdot)\) \(\chi_{5445}(1534,\cdot)\) \(\chi_{5445}(1609,\cdot)\) \(\chi_{5445}(1699,\cdot)\) \(\chi_{5445}(1714,\cdot)\) \(\chi_{5445}(1879,\cdot)\) \(\chi_{5445}(1984,\cdot)\) \(\chi_{5445}(2029,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((3026,4357,3511)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{7}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 5445 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{317}{330}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{239}{330}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{7}{330}\right)\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{5}{66}\right)\) |