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.tb
\(\chi_{24704}(45,\cdot)\) \(\chi_{24704}(349,\cdot)\) \(\chi_{24704}(549,\cdot)\) \(\chi_{24704}(1429,\cdot)\) \(\chi_{24704}(1493,\cdot)\) \(\chi_{24704}(1549,\cdot)\) \(\chi_{24704}(1781,\cdot)\) \(\chi_{24704}(2717,\cdot)\) \(\chi_{24704}(2749,\cdot)\) \(\chi_{24704}(3397,\cdot)\) \(\chi_{24704}(3469,\cdot)\) \(\chi_{24704}(4189,\cdot)\) \(\chi_{24704}(4325,\cdot)\) \(\chi_{24704}(4461,\cdot)\) \(\chi_{24704}(5301,\cdot)\) \(\chi_{24704}(5677,\cdot)\) \(\chi_{24704}(6613,\cdot)\) \(\chi_{24704}(6677,\cdot)\) \(\chi_{24704}(7005,\cdot)\) \(\chi_{24704}(8325,\cdot)\) \(\chi_{24704}(8333,\cdot)\) \(\chi_{24704}(8477,\cdot)\) \(\chi_{24704}(8565,\cdot)\) \(\chi_{24704}(9141,\cdot)\) \(\chi_{24704}(9597,\cdot)\) \(\chi_{24704}(9957,\cdot)\) \(\chi_{24704}(10053,\cdot)\) \(\chi_{24704}(10557,\cdot)\) \(\chi_{24704}(10845,\cdot)\) \(\chi_{24704}(11213,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((24319,773,23937)\) → \((1,e\left(\frac{7}{32}\right),e\left(\frac{169}{192}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 24704 }(45, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{19}{192}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{25}{64}\right)\) | \(e\left(\frac{133}{192}\right)\) | \(e\left(\frac{79}{192}\right)\) | \(e\left(\frac{127}{192}\right)\) | \(e\left(\frac{31}{96}\right)\) |