Basic properties
| Modulus: | \(24704\) | |
| Conductor: | \(6176\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(192\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{6176}(2331,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 24704.sh
\(\chi_{24704}(15,\cdot)\) \(\chi_{24704}(623,\cdot)\) \(\chi_{24704}(1199,\cdot)\) \(\chi_{24704}(1647,\cdot)\) \(\chi_{24704}(1679,\cdot)\) \(\chi_{24704}(1711,\cdot)\) \(\chi_{24704}(1775,\cdot)\) \(\chi_{24704}(2479,\cdot)\) \(\chi_{24704}(2575,\cdot)\) \(\chi_{24704}(3215,\cdot)\) \(\chi_{24704}(4111,\cdot)\) \(\chi_{24704}(4399,\cdot)\) \(\chi_{24704}(5775,\cdot)\) \(\chi_{24704}(5807,\cdot)\) \(\chi_{24704}(6511,\cdot)\) \(\chi_{24704}(6607,\cdot)\) \(\chi_{24704}(7119,\cdot)\) \(\chi_{24704}(7151,\cdot)\) \(\chi_{24704}(7407,\cdot)\) \(\chi_{24704}(9423,\cdot)\) \(\chi_{24704}(9999,\cdot)\) \(\chi_{24704}(10127,\cdot)\) \(\chi_{24704}(10735,\cdot)\) \(\chi_{24704}(10991,\cdot)\) \(\chi_{24704}(11599,\cdot)\) \(\chi_{24704}(11631,\cdot)\) \(\chi_{24704}(11855,\cdot)\) \(\chi_{24704}(11919,\cdot)\) \(\chi_{24704}(12239,\cdot)\) \(\chi_{24704}(12335,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((24319,773,23937)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{85}{192}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 24704 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{109}{192}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{121}{192}\right)\) | \(e\left(\frac{43}{192}\right)\) | \(e\left(\frac{109}{192}\right)\) | \(e\left(\frac{41}{48}\right)\) |