Basic properties
| Modulus: | \(3584\) | |
| Conductor: | \(512\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(128\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{512}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3584.cc
\(\chi_{3584}(43,\cdot)\) \(\chi_{3584}(99,\cdot)\) \(\chi_{3584}(155,\cdot)\) \(\chi_{3584}(211,\cdot)\) \(\chi_{3584}(267,\cdot)\) \(\chi_{3584}(323,\cdot)\) \(\chi_{3584}(379,\cdot)\) \(\chi_{3584}(435,\cdot)\) \(\chi_{3584}(491,\cdot)\) \(\chi_{3584}(547,\cdot)\) \(\chi_{3584}(603,\cdot)\) \(\chi_{3584}(659,\cdot)\) \(\chi_{3584}(715,\cdot)\) \(\chi_{3584}(771,\cdot)\) \(\chi_{3584}(827,\cdot)\) \(\chi_{3584}(883,\cdot)\) \(\chi_{3584}(939,\cdot)\) \(\chi_{3584}(995,\cdot)\) \(\chi_{3584}(1051,\cdot)\) \(\chi_{3584}(1107,\cdot)\) \(\chi_{3584}(1163,\cdot)\) \(\chi_{3584}(1219,\cdot)\) \(\chi_{3584}(1275,\cdot)\) \(\chi_{3584}(1331,\cdot)\) \(\chi_{3584}(1387,\cdot)\) \(\chi_{3584}(1443,\cdot)\) \(\chi_{3584}(1499,\cdot)\) \(\chi_{3584}(1555,\cdot)\) \(\chi_{3584}(1611,\cdot)\) \(\chi_{3584}(1667,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((1023,1541,1025)\) → \((-1,e\left(\frac{61}{128}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3584 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{128}\right)\) | \(e\left(\frac{61}{128}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{1}{128}\right)\) | \(e\left(\frac{115}{128}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{59}{128}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{61}{64}\right)\) |