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 \(\chi_{512}(411,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1024.p
\(\chi_{1024}(7,\cdot)\) \(\chi_{1024}(23,\cdot)\) \(\chi_{1024}(39,\cdot)\) \(\chi_{1024}(55,\cdot)\) \(\chi_{1024}(71,\cdot)\) \(\chi_{1024}(87,\cdot)\) \(\chi_{1024}(103,\cdot)\) \(\chi_{1024}(119,\cdot)\) \(\chi_{1024}(135,\cdot)\) \(\chi_{1024}(151,\cdot)\) \(\chi_{1024}(167,\cdot)\) \(\chi_{1024}(183,\cdot)\) \(\chi_{1024}(199,\cdot)\) \(\chi_{1024}(215,\cdot)\) \(\chi_{1024}(231,\cdot)\) \(\chi_{1024}(247,\cdot)\) \(\chi_{1024}(263,\cdot)\) \(\chi_{1024}(279,\cdot)\) \(\chi_{1024}(295,\cdot)\) \(\chi_{1024}(311,\cdot)\) \(\chi_{1024}(327,\cdot)\) \(\chi_{1024}(343,\cdot)\) \(\chi_{1024}(359,\cdot)\) \(\chi_{1024}(375,\cdot)\) \(\chi_{1024}(391,\cdot)\) \(\chi_{1024}(407,\cdot)\) \(\chi_{1024}(423,\cdot)\) \(\chi_{1024}(439,\cdot)\) \(\chi_{1024}(455,\cdot)\) \(\chi_{1024}(471,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((1023,5)\) → \((-1,e\left(\frac{73}{128}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1024 }(39, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{128}\right)\) | \(e\left(\frac{73}{128}\right)\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{125}{128}\right)\) | \(e\left(\frac{39}{128}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{79}{128}\right)\) | \(e\left(\frac{21}{128}\right)\) |