Basic properties
| Modulus: | \(1024\) | |
| 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 \(\chi_{256}(181,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1024.m
\(\chi_{1024}(17,\cdot)\) \(\chi_{1024}(49,\cdot)\) \(\chi_{1024}(81,\cdot)\) \(\chi_{1024}(113,\cdot)\) \(\chi_{1024}(145,\cdot)\) \(\chi_{1024}(177,\cdot)\) \(\chi_{1024}(209,\cdot)\) \(\chi_{1024}(241,\cdot)\) \(\chi_{1024}(273,\cdot)\) \(\chi_{1024}(305,\cdot)\) \(\chi_{1024}(337,\cdot)\) \(\chi_{1024}(369,\cdot)\) \(\chi_{1024}(401,\cdot)\) \(\chi_{1024}(433,\cdot)\) \(\chi_{1024}(465,\cdot)\) \(\chi_{1024}(497,\cdot)\) \(\chi_{1024}(529,\cdot)\) \(\chi_{1024}(561,\cdot)\) \(\chi_{1024}(593,\cdot)\) \(\chi_{1024}(625,\cdot)\) \(\chi_{1024}(657,\cdot)\) \(\chi_{1024}(689,\cdot)\) \(\chi_{1024}(721,\cdot)\) \(\chi_{1024}(753,\cdot)\) \(\chi_{1024}(785,\cdot)\) \(\chi_{1024}(817,\cdot)\) \(\chi_{1024}(849,\cdot)\) \(\chi_{1024}(881,\cdot)\) \(\chi_{1024}(913,\cdot)\) \(\chi_{1024}(945,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1023,5)\) → \((1,e\left(\frac{37}{64}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1024 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{1}{64}\right)\) |