Basic properties
Modulus: | \(512\) | |
Conductor: | \(512\) | 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 512.p
\(\chi_{512}(3,\cdot)\) \(\chi_{512}(11,\cdot)\) \(\chi_{512}(19,\cdot)\) \(\chi_{512}(27,\cdot)\) \(\chi_{512}(35,\cdot)\) \(\chi_{512}(43,\cdot)\) \(\chi_{512}(51,\cdot)\) \(\chi_{512}(59,\cdot)\) \(\chi_{512}(67,\cdot)\) \(\chi_{512}(75,\cdot)\) \(\chi_{512}(83,\cdot)\) \(\chi_{512}(91,\cdot)\) \(\chi_{512}(99,\cdot)\) \(\chi_{512}(107,\cdot)\) \(\chi_{512}(115,\cdot)\) \(\chi_{512}(123,\cdot)\) \(\chi_{512}(131,\cdot)\) \(\chi_{512}(139,\cdot)\) \(\chi_{512}(147,\cdot)\) \(\chi_{512}(155,\cdot)\) \(\chi_{512}(163,\cdot)\) \(\chi_{512}(171,\cdot)\) \(\chi_{512}(179,\cdot)\) \(\chi_{512}(187,\cdot)\) \(\chi_{512}(195,\cdot)\) \(\chi_{512}(203,\cdot)\) \(\chi_{512}(211,\cdot)\) \(\chi_{512}(219,\cdot)\) \(\chi_{512}(227,\cdot)\) \(\chi_{512}(235,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{128})$ |
Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((511,5)\) → \((-1,e\left(\frac{85}{128}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 512 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{95}{128}\right)\) | \(e\left(\frac{85}{128}\right)\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{31}{64}\right)\) | \(e\left(\frac{121}{128}\right)\) | \(e\left(\frac{91}{128}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{99}{128}\right)\) | \(e\left(\frac{49}{128}\right)\) |