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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5445.dj
\(\chi_{5445}(14,\cdot)\) \(\chi_{5445}(59,\cdot)\) \(\chi_{5445}(104,\cdot)\) \(\chi_{5445}(119,\cdot)\) \(\chi_{5445}(284,\cdot)\) \(\chi_{5445}(344,\cdot)\) \(\chi_{5445}(389,\cdot)\) \(\chi_{5445}(434,\cdot)\) \(\chi_{5445}(509,\cdot)\) \(\chi_{5445}(554,\cdot)\) \(\chi_{5445}(599,\cdot)\) \(\chi_{5445}(779,\cdot)\) \(\chi_{5445}(839,\cdot)\) \(\chi_{5445}(884,\cdot)\) \(\chi_{5445}(929,\cdot)\) \(\chi_{5445}(1004,\cdot)\) \(\chi_{5445}(1094,\cdot)\) \(\chi_{5445}(1109,\cdot)\) \(\chi_{5445}(1274,\cdot)\) \(\chi_{5445}(1379,\cdot)\) \(\chi_{5445}(1424,\cdot)\) \(\chi_{5445}(1499,\cdot)\) \(\chi_{5445}(1544,\cdot)\) \(\chi_{5445}(1589,\cdot)\) \(\chi_{5445}(1604,\cdot)\) \(\chi_{5445}(1769,\cdot)\) \(\chi_{5445}(1829,\cdot)\) \(\chi_{5445}(1874,\cdot)\) \(\chi_{5445}(1919,\cdot)\) \(\chi_{5445}(1994,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((3026,4357,3511)\) → \((e\left(\frac{5}{6}\right),-1,e\left(\frac{4}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 5445 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{134}{165}\right)\) | \(e\left(\frac{113}{330}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{169}{330}\right)\) | \(e\left(\frac{247}{330}\right)\) | \(e\left(\frac{103}{165}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{25}{33}\right)\) |