Basic properties
| Modulus: | \(24704\) | |
| Conductor: | \(24704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(192\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 24704.st
\(\chi_{24704}(61,\cdot)\) \(\chi_{24704}(405,\cdot)\) \(\chi_{24704}(1269,\cdot)\) \(\chi_{24704}(1589,\cdot)\) \(\chi_{24704}(1685,\cdot)\) \(\chi_{24704}(2373,\cdot)\) \(\chi_{24704}(2685,\cdot)\) \(\chi_{24704}(2781,\cdot)\) \(\chi_{24704}(3629,\cdot)\) \(\chi_{24704}(3813,\cdot)\) \(\chi_{24704}(3845,\cdot)\) \(\chi_{24704}(4413,\cdot)\) \(\chi_{24704}(6005,\cdot)\) \(\chi_{24704}(6213,\cdot)\) \(\chi_{24704}(6413,\cdot)\) \(\chi_{24704}(6421,\cdot)\) \(\chi_{24704}(6765,\cdot)\) \(\chi_{24704}(6821,\cdot)\) \(\chi_{24704}(7221,\cdot)\) \(\chi_{24704}(7461,\cdot)\) \(\chi_{24704}(7701,\cdot)\) \(\chi_{24704}(8197,\cdot)\) \(\chi_{24704}(8413,\cdot)\) \(\chi_{24704}(9341,\cdot)\) \(\chi_{24704}(9933,\cdot)\) \(\chi_{24704}(10469,\cdot)\) \(\chi_{24704}(10581,\cdot)\) \(\chi_{24704}(10605,\cdot)\) \(\chi_{24704}(12189,\cdot)\) \(\chi_{24704}(13197,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((24319,773,23937)\) → \((1,e\left(\frac{19}{32}\right),e\left(\frac{47}{192}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 24704 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{161}{192}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{35}{192}\right)\) | \(e\left(\frac{41}{192}\right)\) | \(e\left(\frac{29}{192}\right)\) | \(e\left(\frac{71}{96}\right)\) |