Basic properties
| Modulus: | \(24704\) | |
| Conductor: | \(1544\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1544}(837,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 24704.pt
\(\chi_{24704}(65,\cdot)\) \(\chi_{24704}(321,\cdot)\) \(\chi_{24704}(577,\cdot)\) \(\chi_{24704}(1345,\cdot)\) \(\chi_{24704}(2241,\cdot)\) \(\chi_{24704}(3649,\cdot)\) \(\chi_{24704}(3777,\cdot)\) \(\chi_{24704}(5697,\cdot)\) \(\chi_{24704}(6081,\cdot)\) \(\chi_{24704}(6337,\cdot)\) \(\chi_{24704}(6465,\cdot)\) \(\chi_{24704}(6593,\cdot)\) \(\chi_{24704}(7233,\cdot)\) \(\chi_{24704}(7745,\cdot)\) \(\chi_{24704}(8385,\cdot)\) \(\chi_{24704}(10561,\cdot)\) \(\chi_{24704}(10945,\cdot)\) \(\chi_{24704}(14145,\cdot)\) \(\chi_{24704}(14529,\cdot)\) \(\chi_{24704}(16705,\cdot)\) \(\chi_{24704}(17345,\cdot)\) \(\chi_{24704}(17857,\cdot)\) \(\chi_{24704}(18497,\cdot)\) \(\chi_{24704}(18625,\cdot)\) \(\chi_{24704}(18753,\cdot)\) \(\chi_{24704}(19009,\cdot)\) \(\chi_{24704}(19393,\cdot)\) \(\chi_{24704}(21313,\cdot)\) \(\chi_{24704}(21441,\cdot)\) \(\chi_{24704}(22849,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((24319,773,23937)\) → \((1,-1,e\left(\frac{71}{96}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 24704 }(65, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(i\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{83}{96}\right)\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{71}{96}\right)\) | \(e\left(\frac{13}{24}\right)\) |