Basic properties
Modulus: | \(256\) | |
Conductor: | \(256\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(64\) | 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 256.n
\(\chi_{256}(3,\cdot)\) \(\chi_{256}(11,\cdot)\) \(\chi_{256}(19,\cdot)\) \(\chi_{256}(27,\cdot)\) \(\chi_{256}(35,\cdot)\) \(\chi_{256}(43,\cdot)\) \(\chi_{256}(51,\cdot)\) \(\chi_{256}(59,\cdot)\) \(\chi_{256}(67,\cdot)\) \(\chi_{256}(75,\cdot)\) \(\chi_{256}(83,\cdot)\) \(\chi_{256}(91,\cdot)\) \(\chi_{256}(99,\cdot)\) \(\chi_{256}(107,\cdot)\) \(\chi_{256}(115,\cdot)\) \(\chi_{256}(123,\cdot)\) \(\chi_{256}(131,\cdot)\) \(\chi_{256}(139,\cdot)\) \(\chi_{256}(147,\cdot)\) \(\chi_{256}(155,\cdot)\) \(\chi_{256}(163,\cdot)\) \(\chi_{256}(171,\cdot)\) \(\chi_{256}(179,\cdot)\) \(\chi_{256}(187,\cdot)\) \(\chi_{256}(195,\cdot)\) \(\chi_{256}(203,\cdot)\) \(\chi_{256}(211,\cdot)\) \(\chi_{256}(219,\cdot)\) \(\chi_{256}(227,\cdot)\) \(\chi_{256}(235,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((255,5)\) → \((-1,e\left(\frac{23}{64}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 256 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{11}{64}\right)\) |