Basic properties
| Modulus: | \(3969\) | |
| Conductor: | \(3969\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(378\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3969.dj
\(\chi_{3969}(11,\cdot)\) \(\chi_{3969}(23,\cdot)\) \(\chi_{3969}(74,\cdot)\) \(\chi_{3969}(86,\cdot)\) \(\chi_{3969}(137,\cdot)\) \(\chi_{3969}(149,\cdot)\) \(\chi_{3969}(200,\cdot)\) \(\chi_{3969}(212,\cdot)\) \(\chi_{3969}(326,\cdot)\) \(\chi_{3969}(338,\cdot)\) \(\chi_{3969}(389,\cdot)\) \(\chi_{3969}(401,\cdot)\) \(\chi_{3969}(452,\cdot)\) \(\chi_{3969}(464,\cdot)\) \(\chi_{3969}(515,\cdot)\) \(\chi_{3969}(527,\cdot)\) \(\chi_{3969}(578,\cdot)\) \(\chi_{3969}(590,\cdot)\) \(\chi_{3969}(641,\cdot)\) \(\chi_{3969}(653,\cdot)\) \(\chi_{3969}(767,\cdot)\) \(\chi_{3969}(779,\cdot)\) \(\chi_{3969}(830,\cdot)\) \(\chi_{3969}(842,\cdot)\) \(\chi_{3969}(893,\cdot)\) \(\chi_{3969}(905,\cdot)\) \(\chi_{3969}(956,\cdot)\) \(\chi_{3969}(968,\cdot)\) \(\chi_{3969}(1019,\cdot)\) \(\chi_{3969}(1031,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
Values on generators
\((2108,3727)\) → \((e\left(\frac{13}{54}\right),e\left(\frac{20}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3969 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{378}\right)\) | \(e\left(\frac{1}{189}\right)\) | \(e\left(\frac{59}{378}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{85}{378}\right)\) | \(e\left(\frac{67}{189}\right)\) | \(e\left(\frac{2}{189}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{8}{9}\right)\) |