Basic properties
| Modulus: | \(3328\) | |
| Conductor: | \(3328\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(192\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3328.ds
\(\chi_{3328}(37,\cdot)\) \(\chi_{3328}(45,\cdot)\) \(\chi_{3328}(85,\cdot)\) \(\chi_{3328}(93,\cdot)\) \(\chi_{3328}(245,\cdot)\) \(\chi_{3328}(253,\cdot)\) \(\chi_{3328}(293,\cdot)\) \(\chi_{3328}(301,\cdot)\) \(\chi_{3328}(453,\cdot)\) \(\chi_{3328}(461,\cdot)\) \(\chi_{3328}(501,\cdot)\) \(\chi_{3328}(509,\cdot)\) \(\chi_{3328}(661,\cdot)\) \(\chi_{3328}(669,\cdot)\) \(\chi_{3328}(709,\cdot)\) \(\chi_{3328}(717,\cdot)\) \(\chi_{3328}(869,\cdot)\) \(\chi_{3328}(877,\cdot)\) \(\chi_{3328}(917,\cdot)\) \(\chi_{3328}(925,\cdot)\) \(\chi_{3328}(1077,\cdot)\) \(\chi_{3328}(1085,\cdot)\) \(\chi_{3328}(1125,\cdot)\) \(\chi_{3328}(1133,\cdot)\) \(\chi_{3328}(1285,\cdot)\) \(\chi_{3328}(1293,\cdot)\) \(\chi_{3328}(1333,\cdot)\) \(\chi_{3328}(1341,\cdot)\) \(\chi_{3328}(1493,\cdot)\) \(\chi_{3328}(1501,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1535,261,769)\) → \((1,e\left(\frac{25}{64}\right),e\left(\frac{7}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 3328 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{192}\right)\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{31}{96}\right)\) | \(e\left(\frac{1}{96}\right)\) | \(e\left(\frac{55}{192}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{173}{192}\right)\) | \(e\left(\frac{21}{64}\right)\) | \(e\left(\frac{29}{96}\right)\) |