Basic properties
| Modulus: | \(24704\) | |
| Conductor: | \(24704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 24704.md
\(\chi_{24704}(11,\cdot)\) \(\chi_{24704}(35,\cdot)\) \(\chi_{24704}(299,\cdot)\) \(\chi_{24704}(1171,\cdot)\) \(\chi_{24704}(1331,\cdot)\) \(\chi_{24704}(1643,\cdot)\) \(\chi_{24704}(4235,\cdot)\) \(\chi_{24704}(4603,\cdot)\) \(\chi_{24704}(5051,\cdot)\) \(\chi_{24704}(5443,\cdot)\) \(\chi_{24704}(6163,\cdot)\) \(\chi_{24704}(11475,\cdot)\) \(\chi_{24704}(11651,\cdot)\) \(\chi_{24704}(12619,\cdot)\) \(\chi_{24704}(12827,\cdot)\) \(\chi_{24704}(13475,\cdot)\) \(\chi_{24704}(14211,\cdot)\) \(\chi_{24704}(14955,\cdot)\) \(\chi_{24704}(16299,\cdot)\) \(\chi_{24704}(16331,\cdot)\) \(\chi_{24704}(16859,\cdot)\) \(\chi_{24704}(17723,\cdot)\) \(\chi_{24704}(18171,\cdot)\) \(\chi_{24704}(18267,\cdot)\) \(\chi_{24704}(18275,\cdot)\) \(\chi_{24704}(18355,\cdot)\) \(\chi_{24704}(19939,\cdot)\) \(\chi_{24704}(19955,\cdot)\) \(\chi_{24704}(20419,\cdot)\) \(\chi_{24704}(20563,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((24319,773,23937)\) → \((-1,e\left(\frac{21}{32}\right),e\left(\frac{61}{64}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 24704 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) |