Basic properties
| Modulus: | \(24704\) | |
| Conductor: | \(24704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | 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.lw
\(\chi_{24704}(29,\cdot)\) \(\chi_{24704}(117,\cdot)\) \(\chi_{24704}(125,\cdot)\) \(\chi_{24704}(1509,\cdot)\) \(\chi_{24704}(1557,\cdot)\) \(\chi_{24704}(1717,\cdot)\) \(\chi_{24704}(2245,\cdot)\) \(\chi_{24704}(4157,\cdot)\) \(\chi_{24704}(6309,\cdot)\) \(\chi_{24704}(6549,\cdot)\) \(\chi_{24704}(6829,\cdot)\) \(\chi_{24704}(7973,\cdot)\) \(\chi_{24704}(8453,\cdot)\) \(\chi_{24704}(9165,\cdot)\) \(\chi_{24704}(10509,\cdot)\) \(\chi_{24704}(10541,\cdot)\) \(\chi_{24704}(11165,\cdot)\) \(\chi_{24704}(11613,\cdot)\) \(\chi_{24704}(11861,\cdot)\) \(\chi_{24704}(12773,\cdot)\) \(\chi_{24704}(18181,\cdot)\) \(\chi_{24704}(18741,\cdot)\) \(\chi_{24704}(18925,\cdot)\) \(\chi_{24704}(19213,\cdot)\) \(\chi_{24704}(19389,\cdot)\) \(\chi_{24704}(20341,\cdot)\) \(\chi_{24704}(20557,\cdot)\) \(\chi_{24704}(20949,\cdot)\) \(\chi_{24704}(23149,\cdot)\) \(\chi_{24704}(23421,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((24319,773,23937)\) → \((1,e\left(\frac{29}{32}\right),e\left(\frac{63}{64}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 24704 }(20949, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{25}{64}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{27}{32}\right)\) |