Basic properties
Modulus: | \(3584\) | |
Conductor: | \(3584\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(128\) | 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 3584.cd
\(\chi_{3584}(13,\cdot)\) \(\chi_{3584}(69,\cdot)\) \(\chi_{3584}(125,\cdot)\) \(\chi_{3584}(181,\cdot)\) \(\chi_{3584}(237,\cdot)\) \(\chi_{3584}(293,\cdot)\) \(\chi_{3584}(349,\cdot)\) \(\chi_{3584}(405,\cdot)\) \(\chi_{3584}(461,\cdot)\) \(\chi_{3584}(517,\cdot)\) \(\chi_{3584}(573,\cdot)\) \(\chi_{3584}(629,\cdot)\) \(\chi_{3584}(685,\cdot)\) \(\chi_{3584}(741,\cdot)\) \(\chi_{3584}(797,\cdot)\) \(\chi_{3584}(853,\cdot)\) \(\chi_{3584}(909,\cdot)\) \(\chi_{3584}(965,\cdot)\) \(\chi_{3584}(1021,\cdot)\) \(\chi_{3584}(1077,\cdot)\) \(\chi_{3584}(1133,\cdot)\) \(\chi_{3584}(1189,\cdot)\) \(\chi_{3584}(1245,\cdot)\) \(\chi_{3584}(1301,\cdot)\) \(\chi_{3584}(1357,\cdot)\) \(\chi_{3584}(1413,\cdot)\) \(\chi_{3584}(1469,\cdot)\) \(\chi_{3584}(1525,\cdot)\) \(\chi_{3584}(1581,\cdot)\) \(\chi_{3584}(1637,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{128})$ |
Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((1023,1541,1025)\) → \((1,e\left(\frac{127}{128}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 3584 }(2253, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{128}\right)\) | \(e\left(\frac{63}{128}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{43}{128}\right)\) | \(e\left(\frac{81}{128}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{41}{128}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{63}{64}\right)\) |