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 \(\chi_{5445}(2644,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 16335.et
\(\chi_{16335}(64,\cdot)\) \(\chi_{16335}(289,\cdot)\) \(\chi_{16335}(334,\cdot)\) \(\chi_{16335}(559,\cdot)\) \(\chi_{16335}(829,\cdot)\) \(\chi_{16335}(1279,\cdot)\) \(\chi_{16335}(1369,\cdot)\) \(\chi_{16335}(1549,\cdot)\) \(\chi_{16335}(1774,\cdot)\) \(\chi_{16335}(1819,\cdot)\) \(\chi_{16335}(2044,\cdot)\) \(\chi_{16335}(2314,\cdot)\) \(\chi_{16335}(2359,\cdot)\) \(\chi_{16335}(2764,\cdot)\) \(\chi_{16335}(2854,\cdot)\) \(\chi_{16335}(3259,\cdot)\) \(\chi_{16335}(3304,\cdot)\) \(\chi_{16335}(3529,\cdot)\) \(\chi_{16335}(3799,\cdot)\) \(\chi_{16335}(3844,\cdot)\) \(\chi_{16335}(4249,\cdot)\) \(\chi_{16335}(4339,\cdot)\) \(\chi_{16335}(4519,\cdot)\) \(\chi_{16335}(4744,\cdot)\) \(\chi_{16335}(4789,\cdot)\) \(\chi_{16335}(5014,\cdot)\) \(\chi_{16335}(5329,\cdot)\) \(\chi_{16335}(5734,\cdot)\) \(\chi_{16335}(5824,\cdot)\) \(\chi_{16335}(6004,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((3026,9802,3511)\) → \((e\left(\frac{2}{3}\right),-1,e\left(\frac{6}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 16335 }(829, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{330}\right)\) | \(e\left(\frac{91}{165}\right)\) | \(e\left(\frac{307}{330}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{281}{330}\right)\) | \(e\left(\frac{34}{165}\right)\) | \(e\left(\frac{17}{165}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{31}{66}\right)\) |