Basic properties
| Modulus: | \(3969\) | |
| Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1323}(808,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3969.cx
\(\chi_{3969}(73,\cdot)\) \(\chi_{3969}(145,\cdot)\) \(\chi_{3969}(262,\cdot)\) \(\chi_{3969}(334,\cdot)\) \(\chi_{3969}(451,\cdot)\) \(\chi_{3969}(523,\cdot)\) \(\chi_{3969}(640,\cdot)\) \(\chi_{3969}(712,\cdot)\) \(\chi_{3969}(829,\cdot)\) \(\chi_{3969}(1018,\cdot)\) \(\chi_{3969}(1090,\cdot)\) \(\chi_{3969}(1279,\cdot)\) \(\chi_{3969}(1396,\cdot)\) \(\chi_{3969}(1468,\cdot)\) \(\chi_{3969}(1585,\cdot)\) \(\chi_{3969}(1657,\cdot)\) \(\chi_{3969}(1774,\cdot)\) \(\chi_{3969}(1846,\cdot)\) \(\chi_{3969}(1963,\cdot)\) \(\chi_{3969}(2035,\cdot)\) \(\chi_{3969}(2152,\cdot)\) \(\chi_{3969}(2341,\cdot)\) \(\chi_{3969}(2413,\cdot)\) \(\chi_{3969}(2602,\cdot)\) \(\chi_{3969}(2719,\cdot)\) \(\chi_{3969}(2791,\cdot)\) \(\chi_{3969}(2908,\cdot)\) \(\chi_{3969}(2980,\cdot)\) \(\chi_{3969}(3097,\cdot)\) \(\chi_{3969}(3169,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((2108,3727)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{37}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3969 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(-1\) |