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.de
\(\chi_{3969}(13,\cdot)\) \(\chi_{3969}(34,\cdot)\) \(\chi_{3969}(76,\cdot)\) \(\chi_{3969}(139,\cdot)\) \(\chi_{3969}(160,\cdot)\) \(\chi_{3969}(202,\cdot)\) \(\chi_{3969}(223,\cdot)\) \(\chi_{3969}(265,\cdot)\) \(\chi_{3969}(286,\cdot)\) \(\chi_{3969}(328,\cdot)\) \(\chi_{3969}(349,\cdot)\) \(\chi_{3969}(412,\cdot)\) \(\chi_{3969}(454,\cdot)\) \(\chi_{3969}(475,\cdot)\) \(\chi_{3969}(517,\cdot)\) \(\chi_{3969}(580,\cdot)\) \(\chi_{3969}(601,\cdot)\) \(\chi_{3969}(643,\cdot)\) \(\chi_{3969}(664,\cdot)\) \(\chi_{3969}(706,\cdot)\) \(\chi_{3969}(727,\cdot)\) \(\chi_{3969}(769,\cdot)\) \(\chi_{3969}(790,\cdot)\) \(\chi_{3969}(853,\cdot)\) \(\chi_{3969}(895,\cdot)\) \(\chi_{3969}(916,\cdot)\) \(\chi_{3969}(958,\cdot)\) \(\chi_{3969}(1021,\cdot)\) \(\chi_{3969}(1042,\cdot)\) \(\chi_{3969}(1084,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
Values on generators
\((2108,3727)\) → \((e\left(\frac{10}{27}\right),e\left(\frac{1}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3969 }(517, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{189}\right)\) | \(e\left(\frac{86}{189}\right)\) | \(e\left(\frac{223}{378}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{127}{189}\right)\) | \(e\left(\frac{121}{378}\right)\) | \(e\left(\frac{172}{189}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{5}{18}\right)\) |