Basic properties
Modulus: | \(3968\) | |
Conductor: | \(3968\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(480\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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
\((2047,3845,2049)\) → \((1,e\left(\frac{7}{32}\right),e\left(\frac{2}{15}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 3968 }(1197, a) \) | \(1\) | \(1\) | \(e\left(\frac{379}{480}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{221}{240}\right)\) | \(e\left(\frac{139}{240}\right)\) | \(e\left(\frac{317}{480}\right)\) | \(e\left(\frac{359}{480}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{271}{480}\right)\) | \(e\left(\frac{341}{480}\right)\) |