Basic properties
| Modulus: | \(16335\) | |
| Conductor: | \(16335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(396\) | 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.ew
\(\chi_{16335}(43,\cdot)\) \(\chi_{16335}(142,\cdot)\) \(\chi_{16335}(373,\cdot)\) \(\chi_{16335}(472,\cdot)\) \(\chi_{16335}(538,\cdot)\) \(\chi_{16335}(637,\cdot)\) \(\chi_{16335}(868,\cdot)\) \(\chi_{16335}(1033,\cdot)\) \(\chi_{16335}(1132,\cdot)\) \(\chi_{16335}(1363,\cdot)\) \(\chi_{16335}(1462,\cdot)\) \(\chi_{16335}(1528,\cdot)\) \(\chi_{16335}(1627,\cdot)\) \(\chi_{16335}(1858,\cdot)\) \(\chi_{16335}(1957,\cdot)\) \(\chi_{16335}(2023,\cdot)\) \(\chi_{16335}(2122,\cdot)\) \(\chi_{16335}(2353,\cdot)\) \(\chi_{16335}(2452,\cdot)\) \(\chi_{16335}(2518,\cdot)\) \(\chi_{16335}(2617,\cdot)\) \(\chi_{16335}(2848,\cdot)\) \(\chi_{16335}(2947,\cdot)\) \(\chi_{16335}(3013,\cdot)\) \(\chi_{16335}(3112,\cdot)\) \(\chi_{16335}(3343,\cdot)\) \(\chi_{16335}(3442,\cdot)\) \(\chi_{16335}(3607,\cdot)\) \(\chi_{16335}(3838,\cdot)\) \(\chi_{16335}(3937,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{396})$ |
| Fixed field: | Number field defined by a degree 396 polynomial (not computed) |
Values on generators
\((3026,9802,3511)\) → \((e\left(\frac{2}{9}\right),-i,e\left(\frac{5}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 16335 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{396}\right)\) | \(e\left(\frac{79}{198}\right)\) | \(e\left(\frac{355}{396}\right)\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{389}{396}\right)\) | \(e\left(\frac{19}{198}\right)\) | \(e\left(\frac{79}{99}\right)\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{239}{396}\right)\) |