Basic properties
| Modulus: | \(1024\) | |
| 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 \(\chi_{512}(477,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1024.o
\(\chi_{1024}(9,\cdot)\) \(\chi_{1024}(25,\cdot)\) \(\chi_{1024}(41,\cdot)\) \(\chi_{1024}(57,\cdot)\) \(\chi_{1024}(73,\cdot)\) \(\chi_{1024}(89,\cdot)\) \(\chi_{1024}(105,\cdot)\) \(\chi_{1024}(121,\cdot)\) \(\chi_{1024}(137,\cdot)\) \(\chi_{1024}(153,\cdot)\) \(\chi_{1024}(169,\cdot)\) \(\chi_{1024}(185,\cdot)\) \(\chi_{1024}(201,\cdot)\) \(\chi_{1024}(217,\cdot)\) \(\chi_{1024}(233,\cdot)\) \(\chi_{1024}(249,\cdot)\) \(\chi_{1024}(265,\cdot)\) \(\chi_{1024}(281,\cdot)\) \(\chi_{1024}(297,\cdot)\) \(\chi_{1024}(313,\cdot)\) \(\chi_{1024}(329,\cdot)\) \(\chi_{1024}(345,\cdot)\) \(\chi_{1024}(361,\cdot)\) \(\chi_{1024}(377,\cdot)\) \(\chi_{1024}(393,\cdot)\) \(\chi_{1024}(409,\cdot)\) \(\chi_{1024}(425,\cdot)\) \(\chi_{1024}(441,\cdot)\) \(\chi_{1024}(457,\cdot)\) \(\chi_{1024}(473,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((1023,5)\) → \((1,e\left(\frac{75}{128}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1024 }(201, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{128}\right)\) | \(e\left(\frac{75}{128}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{103}{128}\right)\) | \(e\left(\frac{5}{128}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{61}{128}\right)\) | \(e\left(\frac{111}{128}\right)\) |