Basic properties
| Modulus: | \(24704\) | |
| Conductor: | \(12352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{12352}(7019,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 24704.ky
\(\chi_{24704}(71,\cdot)\) \(\chi_{24704}(519,\cdot)\) \(\chi_{24704}(2183,\cdot)\) \(\chi_{24704}(2631,\cdot)\) \(\chi_{24704}(2983,\cdot)\) \(\chi_{24704}(3687,\cdot)\) \(\chi_{24704}(3735,\cdot)\) \(\chi_{24704}(3959,\cdot)\) \(\chi_{24704}(5031,\cdot)\) \(\chi_{24704}(5143,\cdot)\) \(\chi_{24704}(6215,\cdot)\) \(\chi_{24704}(6263,\cdot)\) \(\chi_{24704}(8071,\cdot)\) \(\chi_{24704}(8503,\cdot)\) \(\chi_{24704}(8759,\cdot)\) \(\chi_{24704}(10023,\cdot)\) \(\chi_{24704}(10455,\cdot)\) \(\chi_{24704}(11223,\cdot)\) \(\chi_{24704}(11367,\cdot)\) \(\chi_{24704}(12055,\cdot)\) \(\chi_{24704}(12071,\cdot)\) \(\chi_{24704}(12471,\cdot)\) \(\chi_{24704}(12727,\cdot)\) \(\chi_{24704}(14967,\cdot)\) \(\chi_{24704}(17271,\cdot)\) \(\chi_{24704}(17639,\cdot)\) \(\chi_{24704}(19335,\cdot)\) \(\chi_{24704}(21191,\cdot)\) \(\chi_{24704}(21527,\cdot)\) \(\chi_{24704}(22119,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((24319,773,23937)\) → \((-1,e\left(\frac{13}{16}\right),e\left(\frac{59}{64}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 24704 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{47}{64}\right)\) | \(-1\) | \(-i\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{21}{64}\right)\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) |