Basic properties
| Modulus: | \(512\) | |
| Conductor: | \(256\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{256}(211,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 512.n
\(\chi_{512}(7,\cdot)\) \(\chi_{512}(23,\cdot)\) \(\chi_{512}(39,\cdot)\) \(\chi_{512}(55,\cdot)\) \(\chi_{512}(71,\cdot)\) \(\chi_{512}(87,\cdot)\) \(\chi_{512}(103,\cdot)\) \(\chi_{512}(119,\cdot)\) \(\chi_{512}(135,\cdot)\) \(\chi_{512}(151,\cdot)\) \(\chi_{512}(167,\cdot)\) \(\chi_{512}(183,\cdot)\) \(\chi_{512}(199,\cdot)\) \(\chi_{512}(215,\cdot)\) \(\chi_{512}(231,\cdot)\) \(\chi_{512}(247,\cdot)\) \(\chi_{512}(263,\cdot)\) \(\chi_{512}(279,\cdot)\) \(\chi_{512}(295,\cdot)\) \(\chi_{512}(311,\cdot)\) \(\chi_{512}(327,\cdot)\) \(\chi_{512}(343,\cdot)\) \(\chi_{512}(359,\cdot)\) \(\chi_{512}(375,\cdot)\) \(\chi_{512}(391,\cdot)\) \(\chi_{512}(407,\cdot)\) \(\chi_{512}(423,\cdot)\) \(\chi_{512}(439,\cdot)\) \(\chi_{512}(455,\cdot)\) \(\chi_{512}(471,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,5)\) → \((-1,e\left(\frac{7}{64}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 512 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{21}{64}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{59}{64}\right)\) |