Basic properties
Modulus: | \(1280\) | |
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 \(\chi_{256}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1280.bv
\(\chi_{1280}(21,\cdot)\) \(\chi_{1280}(61,\cdot)\) \(\chi_{1280}(101,\cdot)\) \(\chi_{1280}(141,\cdot)\) \(\chi_{1280}(181,\cdot)\) \(\chi_{1280}(221,\cdot)\) \(\chi_{1280}(261,\cdot)\) \(\chi_{1280}(301,\cdot)\) \(\chi_{1280}(341,\cdot)\) \(\chi_{1280}(381,\cdot)\) \(\chi_{1280}(421,\cdot)\) \(\chi_{1280}(461,\cdot)\) \(\chi_{1280}(501,\cdot)\) \(\chi_{1280}(541,\cdot)\) \(\chi_{1280}(581,\cdot)\) \(\chi_{1280}(621,\cdot)\) \(\chi_{1280}(661,\cdot)\) \(\chi_{1280}(701,\cdot)\) \(\chi_{1280}(741,\cdot)\) \(\chi_{1280}(781,\cdot)\) \(\chi_{1280}(821,\cdot)\) \(\chi_{1280}(861,\cdot)\) \(\chi_{1280}(901,\cdot)\) \(\chi_{1280}(941,\cdot)\) \(\chi_{1280}(981,\cdot)\) \(\chi_{1280}(1021,\cdot)\) \(\chi_{1280}(1061,\cdot)\) \(\chi_{1280}(1101,\cdot)\) \(\chi_{1280}(1141,\cdot)\) \(\chi_{1280}(1181,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,261,257)\) → \((1,e\left(\frac{19}{64}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 1280 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{64}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{11}{64}\right)\) |