Basic properties
| Modulus: | \(16335\) | |
| Conductor: | \(3267\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(990\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3267}(211,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 16335.fj
\(\chi_{16335}(61,\cdot)\) \(\chi_{16335}(106,\cdot)\) \(\chi_{16335}(151,\cdot)\) \(\chi_{16335}(211,\cdot)\) \(\chi_{16335}(376,\cdot)\) \(\chi_{16335}(391,\cdot)\) \(\chi_{16335}(436,\cdot)\) \(\chi_{16335}(556,\cdot)\) \(\chi_{16335}(601,\cdot)\) \(\chi_{16335}(646,\cdot)\) \(\chi_{16335}(706,\cdot)\) \(\chi_{16335}(871,\cdot)\) \(\chi_{16335}(886,\cdot)\) \(\chi_{16335}(931,\cdot)\) \(\chi_{16335}(976,\cdot)\) \(\chi_{16335}(1051,\cdot)\) \(\chi_{16335}(1096,\cdot)\) \(\chi_{16335}(1141,\cdot)\) \(\chi_{16335}(1366,\cdot)\) \(\chi_{16335}(1381,\cdot)\) \(\chi_{16335}(1426,\cdot)\) \(\chi_{16335}(1471,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{495})$ |
| Fixed field: | Number field defined by a degree 990 polynomial (not computed) |
Values on generators
\((3026,9802,3511)\) → \((e\left(\frac{7}{9}\right),1,e\left(\frac{31}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 16335 }(211, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{990}\right)\) | \(e\left(\frac{59}{495}\right)\) | \(e\left(\frac{413}{990}\right)\) | \(e\left(\frac{59}{330}\right)\) | \(e\left(\frac{679}{990}\right)\) | \(e\left(\frac{236}{495}\right)\) | \(e\left(\frac{118}{495}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{239}{330}\right)\) | \(e\left(\frac{28}{99}\right)\) |