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.sl
\(\chi_{24704}(5,\cdot)\) \(\chi_{24704}(77,\cdot)\) \(\chi_{24704}(725,\cdot)\) \(\chi_{24704}(757,\cdot)\) \(\chi_{24704}(1693,\cdot)\) \(\chi_{24704}(1925,\cdot)\) \(\chi_{24704}(1981,\cdot)\) \(\chi_{24704}(2045,\cdot)\) \(\chi_{24704}(2925,\cdot)\) \(\chi_{24704}(3125,\cdot)\) \(\chi_{24704}(3429,\cdot)\) \(\chi_{24704}(3733,\cdot)\) \(\chi_{24704}(3749,\cdot)\) \(\chi_{24704}(4013,\cdot)\) \(\chi_{24704}(4205,\cdot)\) \(\chi_{24704}(4373,\cdot)\) \(\chi_{24704}(4941,\cdot)\) \(\chi_{24704}(5109,\cdot)\) \(\chi_{24704}(6717,\cdot)\) \(\chi_{24704}(6789,\cdot)\) \(\chi_{24704}(7381,\cdot)\) \(\chi_{24704}(9501,\cdot)\) \(\chi_{24704}(9669,\cdot)\) \(\chi_{24704}(9853,\cdot)\) \(\chi_{24704}(9869,\cdot)\) \(\chi_{24704}(10533,\cdot)\) \(\chi_{24704}(10853,\cdot)\) \(\chi_{24704}(10949,\cdot)\) \(\chi_{24704}(11597,\cdot)\) \(\chi_{24704}(13021,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((24319,773,23937)\) → \((1,e\left(\frac{1}{32}\right),e\left(\frac{1}{192}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 24704 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{7}{192}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{109}{192}\right)\) | \(e\left(\frac{7}{192}\right)\) | \(e\left(\frac{91}{192}\right)\) | \(e\left(\frac{37}{96}\right)\) |