Basic properties
Modulus: | \(1024\) | |
Conductor: | \(1024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(256\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 1024.r
\(\chi_{1024}(3,\cdot)\) \(\chi_{1024}(11,\cdot)\) \(\chi_{1024}(19,\cdot)\) \(\chi_{1024}(27,\cdot)\) \(\chi_{1024}(35,\cdot)\) \(\chi_{1024}(43,\cdot)\) \(\chi_{1024}(51,\cdot)\) \(\chi_{1024}(59,\cdot)\) \(\chi_{1024}(67,\cdot)\) \(\chi_{1024}(75,\cdot)\) \(\chi_{1024}(83,\cdot)\) \(\chi_{1024}(91,\cdot)\) \(\chi_{1024}(99,\cdot)\) \(\chi_{1024}(107,\cdot)\) \(\chi_{1024}(115,\cdot)\) \(\chi_{1024}(123,\cdot)\) \(\chi_{1024}(131,\cdot)\) \(\chi_{1024}(139,\cdot)\) \(\chi_{1024}(147,\cdot)\) \(\chi_{1024}(155,\cdot)\) \(\chi_{1024}(163,\cdot)\) \(\chi_{1024}(171,\cdot)\) \(\chi_{1024}(179,\cdot)\) \(\chi_{1024}(187,\cdot)\) \(\chi_{1024}(195,\cdot)\) \(\chi_{1024}(203,\cdot)\) \(\chi_{1024}(211,\cdot)\) \(\chi_{1024}(219,\cdot)\) \(\chi_{1024}(227,\cdot)\) \(\chi_{1024}(235,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{256})$ |
Fixed field: | Number field defined by a degree 256 polynomial (not computed) |
Values on generators
\((1023,5)\) → \((-1,e\left(\frac{213}{256}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1024 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{256}\right)\) | \(e\left(\frac{213}{256}\right)\) | \(e\left(\frac{73}{128}\right)\) | \(e\left(\frac{31}{128}\right)\) | \(e\left(\frac{185}{256}\right)\) | \(e\left(\frac{219}{256}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{35}{256}\right)\) | \(e\left(\frac{177}{256}\right)\) |