Basic properties
| Modulus: | \(8993\) | |
| Conductor: | \(529\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(23\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{529}(392,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8993.o
\(\chi_{8993}(392,\cdot)\) \(\chi_{8993}(783,\cdot)\) \(\chi_{8993}(1174,\cdot)\) \(\chi_{8993}(1565,\cdot)\) \(\chi_{8993}(1956,\cdot)\) \(\chi_{8993}(2347,\cdot)\) \(\chi_{8993}(2738,\cdot)\) \(\chi_{8993}(3129,\cdot)\) \(\chi_{8993}(3520,\cdot)\) \(\chi_{8993}(3911,\cdot)\) \(\chi_{8993}(4302,\cdot)\) \(\chi_{8993}(4693,\cdot)\) \(\chi_{8993}(5084,\cdot)\) \(\chi_{8993}(5475,\cdot)\) \(\chi_{8993}(5866,\cdot)\) \(\chi_{8993}(6257,\cdot)\) \(\chi_{8993}(6648,\cdot)\) \(\chi_{8993}(7039,\cdot)\) \(\chi_{8993}(7430,\cdot)\) \(\chi_{8993}(7821,\cdot)\) \(\chi_{8993}(8212,\cdot)\) \(\chi_{8993}(8603,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{23})\) |
| Fixed field: | Number field defined by a degree 23 polynomial |
Values on generators
\((530,7940)\) → \((1,e\left(\frac{16}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8993 }(392, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) |