Basic properties
| Modulus: | \(3072\) | |
| Conductor: | \(3072\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(256\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3072.bg
\(\chi_{3072}(5,\cdot)\) \(\chi_{3072}(29,\cdot)\) \(\chi_{3072}(53,\cdot)\) \(\chi_{3072}(77,\cdot)\) \(\chi_{3072}(101,\cdot)\) \(\chi_{3072}(125,\cdot)\) \(\chi_{3072}(149,\cdot)\) \(\chi_{3072}(173,\cdot)\) \(\chi_{3072}(197,\cdot)\) \(\chi_{3072}(221,\cdot)\) \(\chi_{3072}(245,\cdot)\) \(\chi_{3072}(269,\cdot)\) \(\chi_{3072}(293,\cdot)\) \(\chi_{3072}(317,\cdot)\) \(\chi_{3072}(341,\cdot)\) \(\chi_{3072}(365,\cdot)\) \(\chi_{3072}(389,\cdot)\) \(\chi_{3072}(413,\cdot)\) \(\chi_{3072}(437,\cdot)\) \(\chi_{3072}(461,\cdot)\) \(\chi_{3072}(485,\cdot)\) \(\chi_{3072}(509,\cdot)\) \(\chi_{3072}(533,\cdot)\) \(\chi_{3072}(557,\cdot)\) \(\chi_{3072}(581,\cdot)\) \(\chi_{3072}(605,\cdot)\) \(\chi_{3072}(629,\cdot)\) \(\chi_{3072}(653,\cdot)\) \(\chi_{3072}(677,\cdot)\) \(\chi_{3072}(701,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{256})$ |
| Fixed field: | Number field defined by a degree 256 polynomial (not computed) |
Values on generators
\((2047,2053,1025)\) → \((1,e\left(\frac{1}{256}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3072 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{129}{256}\right)\) | \(e\left(\frac{101}{128}\right)\) | \(e\left(\frac{85}{256}\right)\) | \(e\left(\frac{239}{256}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{151}{256}\right)\) | \(e\left(\frac{7}{128}\right)\) | \(e\left(\frac{1}{128}\right)\) | \(e\left(\frac{251}{256}\right)\) | \(e\left(\frac{17}{32}\right)\) |