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 \(\chi_{1323}(1039,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3969.cv
\(\chi_{3969}(10,\cdot)\) \(\chi_{3969}(199,\cdot)\) \(\chi_{3969}(208,\cdot)\) \(\chi_{3969}(388,\cdot)\) \(\chi_{3969}(397,\cdot)\) \(\chi_{3969}(577,\cdot)\) \(\chi_{3969}(586,\cdot)\) \(\chi_{3969}(775,\cdot)\) \(\chi_{3969}(955,\cdot)\) \(\chi_{3969}(964,\cdot)\) \(\chi_{3969}(1144,\cdot)\) \(\chi_{3969}(1153,\cdot)\) \(\chi_{3969}(1333,\cdot)\) \(\chi_{3969}(1522,\cdot)\) \(\chi_{3969}(1531,\cdot)\) \(\chi_{3969}(1711,\cdot)\) \(\chi_{3969}(1720,\cdot)\) \(\chi_{3969}(1900,\cdot)\) \(\chi_{3969}(1909,\cdot)\) \(\chi_{3969}(2098,\cdot)\) \(\chi_{3969}(2278,\cdot)\) \(\chi_{3969}(2287,\cdot)\) \(\chi_{3969}(2467,\cdot)\) \(\chi_{3969}(2476,\cdot)\) \(\chi_{3969}(2656,\cdot)\) \(\chi_{3969}(2845,\cdot)\) \(\chi_{3969}(2854,\cdot)\) \(\chi_{3969}(3034,\cdot)\) \(\chi_{3969}(3043,\cdot)\) \(\chi_{3969}(3223,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((2108,3727)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{13}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3969 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) |