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.df
\(\chi_{3969}(61,\cdot)\) \(\chi_{3969}(94,\cdot)\) \(\chi_{3969}(124,\cdot)\) \(\chi_{3969}(157,\cdot)\) \(\chi_{3969}(187,\cdot)\) \(\chi_{3969}(220,\cdot)\) \(\chi_{3969}(250,\cdot)\) \(\chi_{3969}(283,\cdot)\) \(\chi_{3969}(346,\cdot)\) \(\chi_{3969}(376,\cdot)\) \(\chi_{3969}(409,\cdot)\) \(\chi_{3969}(439,\cdot)\) \(\chi_{3969}(502,\cdot)\) \(\chi_{3969}(535,\cdot)\) \(\chi_{3969}(565,\cdot)\) \(\chi_{3969}(598,\cdot)\) \(\chi_{3969}(628,\cdot)\) \(\chi_{3969}(661,\cdot)\) \(\chi_{3969}(691,\cdot)\) \(\chi_{3969}(724,\cdot)\) \(\chi_{3969}(787,\cdot)\) \(\chi_{3969}(817,\cdot)\) \(\chi_{3969}(850,\cdot)\) \(\chi_{3969}(880,\cdot)\) \(\chi_{3969}(943,\cdot)\) \(\chi_{3969}(976,\cdot)\) \(\chi_{3969}(1006,\cdot)\) \(\chi_{3969}(1039,\cdot)\) \(\chi_{3969}(1069,\cdot)\) \(\chi_{3969}(1102,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
Values on generators
\((2108,3727)\) → \((e\left(\frac{26}{27}\right),e\left(\frac{11}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3969 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{146}{189}\right)\) | \(e\left(\frac{103}{189}\right)\) | \(e\left(\frac{281}{378}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{188}{189}\right)\) | \(e\left(\frac{131}{378}\right)\) | \(e\left(\frac{17}{189}\right)\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{7}{18}\right)\) |