Basic properties
| Modulus: | \(3968\) | |
| Conductor: | \(3968\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(480\) | 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 3968.dr
\(\chi_{3968}(3,\cdot)\) \(\chi_{3968}(11,\cdot)\) \(\chi_{3968}(43,\cdot)\) \(\chi_{3968}(75,\cdot)\) \(\chi_{3968}(83,\cdot)\) \(\chi_{3968}(115,\cdot)\) \(\chi_{3968}(179,\cdot)\) \(\chi_{3968}(203,\cdot)\) \(\chi_{3968}(251,\cdot)\) \(\chi_{3968}(259,\cdot)\) \(\chi_{3968}(291,\cdot)\) \(\chi_{3968}(323,\cdot)\) \(\chi_{3968}(331,\cdot)\) \(\chi_{3968}(363,\cdot)\) \(\chi_{3968}(427,\cdot)\) \(\chi_{3968}(451,\cdot)\) \(\chi_{3968}(499,\cdot)\) \(\chi_{3968}(507,\cdot)\) \(\chi_{3968}(539,\cdot)\) \(\chi_{3968}(571,\cdot)\) \(\chi_{3968}(579,\cdot)\) \(\chi_{3968}(611,\cdot)\) \(\chi_{3968}(675,\cdot)\) \(\chi_{3968}(699,\cdot)\) \(\chi_{3968}(747,\cdot)\) \(\chi_{3968}(755,\cdot)\) \(\chi_{3968}(787,\cdot)\) \(\chi_{3968}(819,\cdot)\) \(\chi_{3968}(827,\cdot)\) \(\chi_{3968}(859,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{480})$ |
| Fixed field: | Number field defined by a degree 480 polynomial (not computed) |
Values on generators
\((2047,3845,2049)\) → \((-1,e\left(\frac{29}{32}\right),e\left(\frac{11}{30}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 3968 }(1067, a) \) | \(1\) | \(1\) | \(e\left(\frac{281}{480}\right)\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{199}{240}\right)\) | \(e\left(\frac{41}{240}\right)\) | \(e\left(\frac{463}{480}\right)\) | \(e\left(\frac{301}{480}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{389}{480}\right)\) | \(e\left(\frac{199}{480}\right)\) |