Basic properties
| Modulus: | \(3072\) | |
| Conductor: | \(1536\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(128\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1536}(1445,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3072.bf
\(\chi_{3072}(41,\cdot)\) \(\chi_{3072}(89,\cdot)\) \(\chi_{3072}(137,\cdot)\) \(\chi_{3072}(185,\cdot)\) \(\chi_{3072}(233,\cdot)\) \(\chi_{3072}(281,\cdot)\) \(\chi_{3072}(329,\cdot)\) \(\chi_{3072}(377,\cdot)\) \(\chi_{3072}(425,\cdot)\) \(\chi_{3072}(473,\cdot)\) \(\chi_{3072}(521,\cdot)\) \(\chi_{3072}(569,\cdot)\) \(\chi_{3072}(617,\cdot)\) \(\chi_{3072}(665,\cdot)\) \(\chi_{3072}(713,\cdot)\) \(\chi_{3072}(761,\cdot)\) \(\chi_{3072}(809,\cdot)\) \(\chi_{3072}(857,\cdot)\) \(\chi_{3072}(905,\cdot)\) \(\chi_{3072}(953,\cdot)\) \(\chi_{3072}(1001,\cdot)\) \(\chi_{3072}(1049,\cdot)\) \(\chi_{3072}(1097,\cdot)\) \(\chi_{3072}(1145,\cdot)\) \(\chi_{3072}(1193,\cdot)\) \(\chi_{3072}(1241,\cdot)\) \(\chi_{3072}(1289,\cdot)\) \(\chi_{3072}(1337,\cdot)\) \(\chi_{3072}(1385,\cdot)\) \(\chi_{3072}(1433,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((2047,2053,1025)\) → \((1,e\left(\frac{57}{128}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3072 }(89, a) \) | \(-1\) | \(1\) | \(e\left(\frac{121}{128}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{45}{128}\right)\) | \(e\left(\frac{55}{128}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{31}{128}\right)\) | \(e\left(\frac{47}{64}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{35}{128}\right)\) | \(e\left(\frac{9}{16}\right)\) |