Basic properties
| Modulus: | \(3584\) | |
| Conductor: | \(3584\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(384\) | 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 3584.cl
\(\chi_{3584}(37,\cdot)\) \(\chi_{3584}(53,\cdot)\) \(\chi_{3584}(93,\cdot)\) \(\chi_{3584}(109,\cdot)\) \(\chi_{3584}(149,\cdot)\) \(\chi_{3584}(165,\cdot)\) \(\chi_{3584}(205,\cdot)\) \(\chi_{3584}(221,\cdot)\) \(\chi_{3584}(261,\cdot)\) \(\chi_{3584}(277,\cdot)\) \(\chi_{3584}(317,\cdot)\) \(\chi_{3584}(333,\cdot)\) \(\chi_{3584}(373,\cdot)\) \(\chi_{3584}(389,\cdot)\) \(\chi_{3584}(429,\cdot)\) \(\chi_{3584}(445,\cdot)\) \(\chi_{3584}(485,\cdot)\) \(\chi_{3584}(501,\cdot)\) \(\chi_{3584}(541,\cdot)\) \(\chi_{3584}(557,\cdot)\) \(\chi_{3584}(597,\cdot)\) \(\chi_{3584}(613,\cdot)\) \(\chi_{3584}(653,\cdot)\) \(\chi_{3584}(669,\cdot)\) \(\chi_{3584}(709,\cdot)\) \(\chi_{3584}(725,\cdot)\) \(\chi_{3584}(765,\cdot)\) \(\chi_{3584}(781,\cdot)\) \(\chi_{3584}(821,\cdot)\) \(\chi_{3584}(837,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{384})$ |
| Fixed field: | Number field defined by a degree 384 polynomial (not computed) |
Values on generators
\((1023,1541,1025)\) → \((1,e\left(\frac{5}{128}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3584 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{384}\right)\) | \(e\left(\frac{143}{384}\right)\) | \(e\left(\frac{13}{192}\right)\) | \(e\left(\frac{379}{384}\right)\) | \(e\left(\frac{43}{128}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{73}{96}\right)\) | \(e\left(\frac{89}{384}\right)\) | \(e\left(\frac{169}{192}\right)\) | \(e\left(\frac{143}{192}\right)\) |