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 \(\chi_{6176}(3907,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 24704.tc
\(\chi_{24704}(47,\cdot)\) \(\chi_{24704}(111,\cdot)\) \(\chi_{24704}(335,\cdot)\) \(\chi_{24704}(367,\cdot)\) \(\chi_{24704}(975,\cdot)\) \(\chi_{24704}(1231,\cdot)\) \(\chi_{24704}(1839,\cdot)\) \(\chi_{24704}(1967,\cdot)\) \(\chi_{24704}(2543,\cdot)\) \(\chi_{24704}(4559,\cdot)\) \(\chi_{24704}(4815,\cdot)\) \(\chi_{24704}(4847,\cdot)\) \(\chi_{24704}(5359,\cdot)\) \(\chi_{24704}(5455,\cdot)\) \(\chi_{24704}(6159,\cdot)\) \(\chi_{24704}(6191,\cdot)\) \(\chi_{24704}(7567,\cdot)\) \(\chi_{24704}(7855,\cdot)\) \(\chi_{24704}(8751,\cdot)\) \(\chi_{24704}(9391,\cdot)\) \(\chi_{24704}(9487,\cdot)\) \(\chi_{24704}(10191,\cdot)\) \(\chi_{24704}(10255,\cdot)\) \(\chi_{24704}(10287,\cdot)\) \(\chi_{24704}(10319,\cdot)\) \(\chi_{24704}(10767,\cdot)\) \(\chi_{24704}(11343,\cdot)\) \(\chi_{24704}(11951,\cdot)\) \(\chi_{24704}(12431,\cdot)\) \(\chi_{24704}(12623,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((24319,773,23937)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{29}{192}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 24704 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{101}{192}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{161}{192}\right)\) | \(e\left(\frac{35}{192}\right)\) | \(e\left(\frac{5}{192}\right)\) | \(e\left(\frac{13}{48}\right)\) |