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 \(\chi_{1323}(1220,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3969.cp
\(\chi_{3969}(44,\cdot)\) \(\chi_{3969}(233,\cdot)\) \(\chi_{3969}(305,\cdot)\) \(\chi_{3969}(494,\cdot)\) \(\chi_{3969}(611,\cdot)\) \(\chi_{3969}(683,\cdot)\) \(\chi_{3969}(800,\cdot)\) \(\chi_{3969}(872,\cdot)\) \(\chi_{3969}(989,\cdot)\) \(\chi_{3969}(1061,\cdot)\) \(\chi_{3969}(1178,\cdot)\) \(\chi_{3969}(1250,\cdot)\) \(\chi_{3969}(1367,\cdot)\) \(\chi_{3969}(1556,\cdot)\) \(\chi_{3969}(1628,\cdot)\) \(\chi_{3969}(1817,\cdot)\) \(\chi_{3969}(1934,\cdot)\) \(\chi_{3969}(2006,\cdot)\) \(\chi_{3969}(2123,\cdot)\) \(\chi_{3969}(2195,\cdot)\) \(\chi_{3969}(2312,\cdot)\) \(\chi_{3969}(2384,\cdot)\) \(\chi_{3969}(2501,\cdot)\) \(\chi_{3969}(2573,\cdot)\) \(\chi_{3969}(2690,\cdot)\) \(\chi_{3969}(2879,\cdot)\) \(\chi_{3969}(2951,\cdot)\) \(\chi_{3969}(3140,\cdot)\) \(\chi_{3969}(3257,\cdot)\) \(\chi_{3969}(3329,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((2108,3727)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{4}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3969 }(44, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(1\) |