Basic properties
| Modulus: | \(6664\) | |
| Conductor: | \(3332\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3332}(927,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6664.fo
\(\chi_{6664}(87,\cdot)\) \(\chi_{6664}(383,\cdot)\) \(\chi_{6664}(495,\cdot)\) \(\chi_{6664}(535,\cdot)\) \(\chi_{6664}(831,\cdot)\) \(\chi_{6664}(927,\cdot)\) \(\chi_{6664}(943,\cdot)\) \(\chi_{6664}(1039,\cdot)\) \(\chi_{6664}(1335,\cdot)\) \(\chi_{6664}(1375,\cdot)\) \(\chi_{6664}(1447,\cdot)\) \(\chi_{6664}(1487,\cdot)\) \(\chi_{6664}(1879,\cdot)\) \(\chi_{6664}(1895,\cdot)\) \(\chi_{6664}(2287,\cdot)\) \(\chi_{6664}(2327,\cdot)\) \(\chi_{6664}(2399,\cdot)\) \(\chi_{6664}(2439,\cdot)\) \(\chi_{6664}(2735,\cdot)\) \(\chi_{6664}(2831,\cdot)\) \(\chi_{6664}(2847,\cdot)\) \(\chi_{6664}(2943,\cdot)\) \(\chi_{6664}(3239,\cdot)\) \(\chi_{6664}(3279,\cdot)\) \(\chi_{6664}(3391,\cdot)\) \(\chi_{6664}(3687,\cdot)\) \(\chi_{6664}(3783,\cdot)\) \(\chi_{6664}(3799,\cdot)\) \(\chi_{6664}(3895,\cdot)\) \(\chi_{6664}(4191,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((4999,3333,4217,785)\) → \((-1,1,e\left(\frac{31}{42}\right),e\left(\frac{1}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 6664 }(927, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{168}\right)\) | \(e\left(\frac{5}{168}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{151}{168}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{71}{168}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{5}{56}\right)\) |