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.do
\(\chi_{3968}(45,\cdot)\) \(\chi_{3968}(69,\cdot)\) \(\chi_{3968}(133,\cdot)\) \(\chi_{3968}(165,\cdot)\) \(\chi_{3968}(173,\cdot)\) \(\chi_{3968}(205,\cdot)\) \(\chi_{3968}(237,\cdot)\) \(\chi_{3968}(245,\cdot)\) \(\chi_{3968}(293,\cdot)\) \(\chi_{3968}(317,\cdot)\) \(\chi_{3968}(381,\cdot)\) \(\chi_{3968}(413,\cdot)\) \(\chi_{3968}(421,\cdot)\) \(\chi_{3968}(453,\cdot)\) \(\chi_{3968}(485,\cdot)\) \(\chi_{3968}(493,\cdot)\) \(\chi_{3968}(541,\cdot)\) \(\chi_{3968}(565,\cdot)\) \(\chi_{3968}(629,\cdot)\) \(\chi_{3968}(661,\cdot)\) \(\chi_{3968}(669,\cdot)\) \(\chi_{3968}(701,\cdot)\) \(\chi_{3968}(733,\cdot)\) \(\chi_{3968}(741,\cdot)\) \(\chi_{3968}(789,\cdot)\) \(\chi_{3968}(813,\cdot)\) \(\chi_{3968}(877,\cdot)\) \(\chi_{3968}(909,\cdot)\) \(\chi_{3968}(917,\cdot)\) \(\chi_{3968}(949,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{480})$ |
| Fixed field: | Number field defined by a degree 480 polynomial (not computed) |
Values on generators
\((2047,3845,2049)\) → \((1,e\left(\frac{27}{32}\right),e\left(\frac{14}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 3968 }(1309, a) \) | \(1\) | \(1\) | \(e\left(\frac{223}{480}\right)\) | \(e\left(\frac{49}{96}\right)\) | \(e\left(\frac{137}{240}\right)\) | \(e\left(\frac{223}{240}\right)\) | \(e\left(\frac{89}{480}\right)\) | \(e\left(\frac{443}{480}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{67}{480}\right)\) | \(e\left(\frac{17}{480}\right)\) |