Basic properties
| Modulus: | \(16335\) | |
| Conductor: | \(16335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1980\) | 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 16335.fm
\(\chi_{16335}(38,\cdot)\) \(\chi_{16335}(47,\cdot)\) \(\chi_{16335}(92,\cdot)\) \(\chi_{16335}(113,\cdot)\) \(\chi_{16335}(137,\cdot)\) \(\chi_{16335}(158,\cdot)\) \(\chi_{16335}(203,\cdot)\) \(\chi_{16335}(212,\cdot)\) \(\chi_{16335}(218,\cdot)\) \(\chi_{16335}(257,\cdot)\) \(\chi_{16335}(302,\cdot)\) \(\chi_{16335}(317,\cdot)\) \(\chi_{16335}(383,\cdot)\) \(\chi_{16335}(443,\cdot)\) \(\chi_{16335}(482,\cdot)\) \(\chi_{16335}(488,\cdot)\) \(\chi_{16335}(533,\cdot)\) \(\chi_{16335}(542,\cdot)\) \(\chi_{16335}(587,\cdot)\) \(\chi_{16335}(653,\cdot)\) \(\chi_{16335}(698,\cdot)\) \(\chi_{16335}(707,\cdot)\) \(\chi_{16335}(713,\cdot)\) \(\chi_{16335}(752,\cdot)\) \(\chi_{16335}(797,\cdot)\) \(\chi_{16335}(812,\cdot)\) \(\chi_{16335}(878,\cdot)\) \(\chi_{16335}(938,\cdot)\) \(\chi_{16335}(983,\cdot)\) \(\chi_{16335}(1028,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1980})$ |
| Fixed field: | Number field defined by a degree 1980 polynomial (not computed) |
Values on generators
\((3026,9802,3511)\) → \((e\left(\frac{7}{18}\right),i,e\left(\frac{49}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 16335 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{1049}{1980}\right)\) | \(e\left(\frac{59}{990}\right)\) | \(e\left(\frac{1403}{1980}\right)\) | \(e\left(\frac{389}{660}\right)\) | \(e\left(\frac{1669}{1980}\right)\) | \(e\left(\frac{118}{495}\right)\) | \(e\left(\frac{59}{495}\right)\) | \(e\left(\frac{487}{660}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{155}{396}\right)\) |