Basic properties
| Modulus: | \(3969\) | |
| Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1323}(1276,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3969.co
\(\chi_{3969}(100,\cdot)\) \(\chi_{3969}(172,\cdot)\) \(\chi_{3969}(289,\cdot)\) \(\chi_{3969}(478,\cdot)\) \(\chi_{3969}(550,\cdot)\) \(\chi_{3969}(739,\cdot)\) \(\chi_{3969}(856,\cdot)\) \(\chi_{3969}(928,\cdot)\) \(\chi_{3969}(1045,\cdot)\) \(\chi_{3969}(1117,\cdot)\) \(\chi_{3969}(1234,\cdot)\) \(\chi_{3969}(1306,\cdot)\) \(\chi_{3969}(1423,\cdot)\) \(\chi_{3969}(1495,\cdot)\) \(\chi_{3969}(1612,\cdot)\) \(\chi_{3969}(1801,\cdot)\) \(\chi_{3969}(1873,\cdot)\) \(\chi_{3969}(2062,\cdot)\) \(\chi_{3969}(2179,\cdot)\) \(\chi_{3969}(2251,\cdot)\) \(\chi_{3969}(2368,\cdot)\) \(\chi_{3969}(2440,\cdot)\) \(\chi_{3969}(2557,\cdot)\) \(\chi_{3969}(2629,\cdot)\) \(\chi_{3969}(2746,\cdot)\) \(\chi_{3969}(2818,\cdot)\) \(\chi_{3969}(2935,\cdot)\) \(\chi_{3969}(3124,\cdot)\) \(\chi_{3969}(3196,\cdot)\) \(\chi_{3969}(3385,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((2108,3727)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{13}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3969 }(100, a) \) | \(1\) | \(1\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) |