Basic properties
| Modulus: | \(16335\) | |
| Conductor: | \(5445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{5445}(304,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 16335.en
\(\chi_{16335}(19,\cdot)\) \(\chi_{16335}(424,\cdot)\) \(\chi_{16335}(469,\cdot)\) \(\chi_{16335}(739,\cdot)\) \(\chi_{16335}(964,\cdot)\) \(\chi_{16335}(1009,\cdot)\) \(\chi_{16335}(1234,\cdot)\) \(\chi_{16335}(1414,\cdot)\) \(\chi_{16335}(1504,\cdot)\) \(\chi_{16335}(1954,\cdot)\) \(\chi_{16335}(2224,\cdot)\) \(\chi_{16335}(2449,\cdot)\) \(\chi_{16335}(2494,\cdot)\) \(\chi_{16335}(2719,\cdot)\) \(\chi_{16335}(2899,\cdot)\) \(\chi_{16335}(2989,\cdot)\) \(\chi_{16335}(3394,\cdot)\) \(\chi_{16335}(3439,\cdot)\) \(\chi_{16335}(3709,\cdot)\) \(\chi_{16335}(3934,\cdot)\) \(\chi_{16335}(3979,\cdot)\) \(\chi_{16335}(4204,\cdot)\) \(\chi_{16335}(4384,\cdot)\) \(\chi_{16335}(4879,\cdot)\) \(\chi_{16335}(4924,\cdot)\) \(\chi_{16335}(5419,\cdot)\) \(\chi_{16335}(5464,\cdot)\) \(\chi_{16335}(5689,\cdot)\) \(\chi_{16335}(5869,\cdot)\) \(\chi_{16335}(5959,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((3026,9802,3511)\) → \((e\left(\frac{2}{3}\right),-1,e\left(\frac{87}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 16335 }(3934, a) \) | \(-1\) | \(1\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{118}{165}\right)\) | \(e\left(\frac{109}{165}\right)\) | \(e\left(\frac{137}{165}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{13}{66}\right)\) |