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 \(\chi_{1323}(652,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3969.cn
\(\chi_{3969}(64,\cdot)\) \(\chi_{3969}(127,\cdot)\) \(\chi_{3969}(253,\cdot)\) \(\chi_{3969}(316,\cdot)\) \(\chi_{3969}(505,\cdot)\) \(\chi_{3969}(631,\cdot)\) \(\chi_{3969}(694,\cdot)\) \(\chi_{3969}(820,\cdot)\) \(\chi_{3969}(1009,\cdot)\) \(\chi_{3969}(1072,\cdot)\) \(\chi_{3969}(1198,\cdot)\) \(\chi_{3969}(1261,\cdot)\) \(\chi_{3969}(1387,\cdot)\) \(\chi_{3969}(1450,\cdot)\) \(\chi_{3969}(1576,\cdot)\) \(\chi_{3969}(1639,\cdot)\) \(\chi_{3969}(1828,\cdot)\) \(\chi_{3969}(1954,\cdot)\) \(\chi_{3969}(2017,\cdot)\) \(\chi_{3969}(2143,\cdot)\) \(\chi_{3969}(2332,\cdot)\) \(\chi_{3969}(2395,\cdot)\) \(\chi_{3969}(2521,\cdot)\) \(\chi_{3969}(2584,\cdot)\) \(\chi_{3969}(2710,\cdot)\) \(\chi_{3969}(2773,\cdot)\) \(\chi_{3969}(2899,\cdot)\) \(\chi_{3969}(2962,\cdot)\) \(\chi_{3969}(3151,\cdot)\) \(\chi_{3969}(3277,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((2108,3727)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{5}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3969 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) |