Basic properties
| Modulus: | \(3584\) | |
| Conductor: | \(512\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(128\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{512}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3584.ca
\(\chi_{3584}(29,\cdot)\) \(\chi_{3584}(85,\cdot)\) \(\chi_{3584}(141,\cdot)\) \(\chi_{3584}(197,\cdot)\) \(\chi_{3584}(253,\cdot)\) \(\chi_{3584}(309,\cdot)\) \(\chi_{3584}(365,\cdot)\) \(\chi_{3584}(421,\cdot)\) \(\chi_{3584}(477,\cdot)\) \(\chi_{3584}(533,\cdot)\) \(\chi_{3584}(589,\cdot)\) \(\chi_{3584}(645,\cdot)\) \(\chi_{3584}(701,\cdot)\) \(\chi_{3584}(757,\cdot)\) \(\chi_{3584}(813,\cdot)\) \(\chi_{3584}(869,\cdot)\) \(\chi_{3584}(925,\cdot)\) \(\chi_{3584}(981,\cdot)\) \(\chi_{3584}(1037,\cdot)\) \(\chi_{3584}(1093,\cdot)\) \(\chi_{3584}(1149,\cdot)\) \(\chi_{3584}(1205,\cdot)\) \(\chi_{3584}(1261,\cdot)\) \(\chi_{3584}(1317,\cdot)\) \(\chi_{3584}(1373,\cdot)\) \(\chi_{3584}(1429,\cdot)\) \(\chi_{3584}(1485,\cdot)\) \(\chi_{3584}(1541,\cdot)\) \(\chi_{3584}(1597,\cdot)\) \(\chi_{3584}(1653,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((1023,1541,1025)\) → \((1,e\left(\frac{123}{128}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3584 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{81}{128}\right)\) | \(e\left(\frac{123}{128}\right)\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{87}{128}\right)\) | \(e\left(\frac{85}{128}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{13}{128}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{59}{64}\right)\) |