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 \(\chi_{256}(101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 512.m
\(\chi_{512}(9,\cdot)\) \(\chi_{512}(25,\cdot)\) \(\chi_{512}(41,\cdot)\) \(\chi_{512}(57,\cdot)\) \(\chi_{512}(73,\cdot)\) \(\chi_{512}(89,\cdot)\) \(\chi_{512}(105,\cdot)\) \(\chi_{512}(121,\cdot)\) \(\chi_{512}(137,\cdot)\) \(\chi_{512}(153,\cdot)\) \(\chi_{512}(169,\cdot)\) \(\chi_{512}(185,\cdot)\) \(\chi_{512}(201,\cdot)\) \(\chi_{512}(217,\cdot)\) \(\chi_{512}(233,\cdot)\) \(\chi_{512}(249,\cdot)\) \(\chi_{512}(265,\cdot)\) \(\chi_{512}(281,\cdot)\) \(\chi_{512}(297,\cdot)\) \(\chi_{512}(313,\cdot)\) \(\chi_{512}(329,\cdot)\) \(\chi_{512}(345,\cdot)\) \(\chi_{512}(361,\cdot)\) \(\chi_{512}(377,\cdot)\) \(\chi_{512}(393,\cdot)\) \(\chi_{512}(409,\cdot)\) \(\chi_{512}(425,\cdot)\) \(\chi_{512}(441,\cdot)\) \(\chi_{512}(457,\cdot)\) \(\chi_{512}(473,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,5)\) → \((1,e\left(\frac{9}{64}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 512 }(473, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{21}{64}\right)\) |