Basic properties
| Modulus: | \(24704\) | |
| Conductor: | \(12352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{12352}(10075,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 24704.na
\(\chi_{24704}(39,\cdot)\) \(\chi_{24704}(1895,\cdot)\) \(\chi_{24704}(2999,\cdot)\) \(\chi_{24704}(3831,\cdot)\) \(\chi_{24704}(3847,\cdot)\) \(\chi_{24704}(4599,\cdot)\) \(\chi_{24704}(5191,\cdot)\) \(\chi_{24704}(5895,\cdot)\) \(\chi_{24704}(9911,\cdot)\) \(\chi_{24704}(10135,\cdot)\) \(\chi_{24704}(11319,\cdot)\) \(\chi_{24704}(11463,\cdot)\) \(\chi_{24704}(12439,\cdot)\) \(\chi_{24704}(13159,\cdot)\) \(\chi_{24704}(14679,\cdot)\) \(\chi_{24704}(14935,\cdot)\) \(\chi_{24704}(15015,\cdot)\) \(\chi_{24704}(15943,\cdot)\) \(\chi_{24704}(16631,\cdot)\) \(\chi_{24704}(17399,\cdot)\) \(\chi_{24704}(18231,\cdot)\) \(\chi_{24704}(18599,\cdot)\) \(\chi_{24704}(18647,\cdot)\) \(\chi_{24704}(18903,\cdot)\) \(\chi_{24704}(19047,\cdot)\) \(\chi_{24704}(20711,\cdot)\) \(\chi_{24704}(21143,\cdot)\) \(\chi_{24704}(21159,\cdot)\) \(\chi_{24704}(21511,\cdot)\) \(\chi_{24704}(22215,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((24319,773,23937)\) → \((-1,e\left(\frac{9}{16}\right),e\left(\frac{11}{64}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 24704 }(39, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{47}{64}\right)\) | \(1\) | \(i\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{5}{8}\right)\) |