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 \(\chi_{1024}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3072.bh
\(\chi_{3072}(13,\cdot)\) \(\chi_{3072}(37,\cdot)\) \(\chi_{3072}(61,\cdot)\) \(\chi_{3072}(85,\cdot)\) \(\chi_{3072}(109,\cdot)\) \(\chi_{3072}(133,\cdot)\) \(\chi_{3072}(157,\cdot)\) \(\chi_{3072}(181,\cdot)\) \(\chi_{3072}(205,\cdot)\) \(\chi_{3072}(229,\cdot)\) \(\chi_{3072}(253,\cdot)\) \(\chi_{3072}(277,\cdot)\) \(\chi_{3072}(301,\cdot)\) \(\chi_{3072}(325,\cdot)\) \(\chi_{3072}(349,\cdot)\) \(\chi_{3072}(373,\cdot)\) \(\chi_{3072}(397,\cdot)\) \(\chi_{3072}(421,\cdot)\) \(\chi_{3072}(445,\cdot)\) \(\chi_{3072}(469,\cdot)\) \(\chi_{3072}(493,\cdot)\) \(\chi_{3072}(517,\cdot)\) \(\chi_{3072}(541,\cdot)\) \(\chi_{3072}(565,\cdot)\) \(\chi_{3072}(589,\cdot)\) \(\chi_{3072}(613,\cdot)\) \(\chi_{3072}(637,\cdot)\) \(\chi_{3072}(661,\cdot)\) \(\chi_{3072}(685,\cdot)\) \(\chi_{3072}(709,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{256})$ |
| Fixed field: | Number field defined by a degree 256 polynomial (not computed) |
Values on generators
\((2047,2053,1025)\) → \((1,e\left(\frac{25}{256}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3072 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{256}\right)\) | \(e\left(\frac{93}{128}\right)\) | \(e\left(\frac{205}{256}\right)\) | \(e\left(\frac{87}{256}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{191}{256}\right)\) | \(e\left(\frac{111}{128}\right)\) | \(e\left(\frac{25}{128}\right)\) | \(e\left(\frac{3}{256}\right)\) | \(e\left(\frac{9}{32}\right)\) |