Basic properties
| Modulus: | \(3072\) | |
| Conductor: | \(1024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(256\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1024}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3072.bj
\(\chi_{3072}(19,\cdot)\) \(\chi_{3072}(43,\cdot)\) \(\chi_{3072}(67,\cdot)\) \(\chi_{3072}(91,\cdot)\) \(\chi_{3072}(115,\cdot)\) \(\chi_{3072}(139,\cdot)\) \(\chi_{3072}(163,\cdot)\) \(\chi_{3072}(187,\cdot)\) \(\chi_{3072}(211,\cdot)\) \(\chi_{3072}(235,\cdot)\) \(\chi_{3072}(259,\cdot)\) \(\chi_{3072}(283,\cdot)\) \(\chi_{3072}(307,\cdot)\) \(\chi_{3072}(331,\cdot)\) \(\chi_{3072}(355,\cdot)\) \(\chi_{3072}(379,\cdot)\) \(\chi_{3072}(403,\cdot)\) \(\chi_{3072}(427,\cdot)\) \(\chi_{3072}(451,\cdot)\) \(\chi_{3072}(475,\cdot)\) \(\chi_{3072}(499,\cdot)\) \(\chi_{3072}(523,\cdot)\) \(\chi_{3072}(547,\cdot)\) \(\chi_{3072}(571,\cdot)\) \(\chi_{3072}(595,\cdot)\) \(\chi_{3072}(619,\cdot)\) \(\chi_{3072}(643,\cdot)\) \(\chi_{3072}(667,\cdot)\) \(\chi_{3072}(691,\cdot)\) \(\chi_{3072}(715,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{256})$ |
| Fixed field: | Number field defined by a degree 256 polynomial (not computed) |
Values on generators
\((2047,2053,1025)\) → \((-1,e\left(\frac{243}{256}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3072 }(67, a) \) | \(-1\) | \(1\) | \(e\left(\frac{243}{256}\right)\) | \(e\left(\frac{31}{128}\right)\) | \(e\left(\frac{175}{256}\right)\) | \(e\left(\frac{221}{256}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{213}{256}\right)\) | \(e\left(\frac{37}{128}\right)\) | \(e\left(\frac{115}{128}\right)\) | \(e\left(\frac{193}{256}\right)\) | \(e\left(\frac{19}{32}\right)\) |