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.lk
\(\chi_{24704}(13,\cdot)\) \(\chi_{24704}(261,\cdot)\) \(\chi_{24704}(357,\cdot)\) \(\chi_{24704}(733,\cdot)\) \(\chi_{24704}(805,\cdot)\) \(\chi_{24704}(1669,\cdot)\) \(\chi_{24704}(2197,\cdot)\) \(\chi_{24704}(2229,\cdot)\) \(\chi_{24704}(3573,\cdot)\) \(\chi_{24704}(4845,\cdot)\) \(\chi_{24704}(5005,\cdot)\) \(\chi_{24704}(5701,\cdot)\) \(\chi_{24704}(5909,\cdot)\) \(\chi_{24704}(6141,\cdot)\) \(\chi_{24704}(6445,\cdot)\) \(\chi_{24704}(10317,\cdot)\) \(\chi_{24704}(10461,\cdot)\) \(\chi_{24704}(10925,\cdot)\) \(\chi_{24704}(10941,\cdot)\) \(\chi_{24704}(12525,\cdot)\) \(\chi_{24704}(12605,\cdot)\) \(\chi_{24704}(13477,\cdot)\) \(\chi_{24704}(13925,\cdot)\) \(\chi_{24704}(14293,\cdot)\) \(\chi_{24704}(16669,\cdot)\) \(\chi_{24704}(16885,\cdot)\) \(\chi_{24704}(17405,\cdot)\) \(\chi_{24704}(18229,\cdot)\) \(\chi_{24704}(18517,\cdot)\) \(\chi_{24704}(19229,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((24319,773,23937)\) → \((1,e\left(\frac{15}{32}\right),e\left(\frac{47}{64}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 24704 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{5}{32}\right)\) |