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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3969.dg
\(\chi_{3969}(47,\cdot)\) \(\chi_{3969}(59,\cdot)\) \(\chi_{3969}(110,\cdot)\) \(\chi_{3969}(122,\cdot)\) \(\chi_{3969}(173,\cdot)\) \(\chi_{3969}(185,\cdot)\) \(\chi_{3969}(236,\cdot)\) \(\chi_{3969}(248,\cdot)\) \(\chi_{3969}(299,\cdot)\) \(\chi_{3969}(311,\cdot)\) \(\chi_{3969}(425,\cdot)\) \(\chi_{3969}(437,\cdot)\) \(\chi_{3969}(488,\cdot)\) \(\chi_{3969}(500,\cdot)\) \(\chi_{3969}(551,\cdot)\) \(\chi_{3969}(563,\cdot)\) \(\chi_{3969}(614,\cdot)\) \(\chi_{3969}(626,\cdot)\) \(\chi_{3969}(677,\cdot)\) \(\chi_{3969}(689,\cdot)\) \(\chi_{3969}(740,\cdot)\) \(\chi_{3969}(752,\cdot)\) \(\chi_{3969}(866,\cdot)\) \(\chi_{3969}(878,\cdot)\) \(\chi_{3969}(929,\cdot)\) \(\chi_{3969}(941,\cdot)\) \(\chi_{3969}(992,\cdot)\) \(\chi_{3969}(1004,\cdot)\) \(\chi_{3969}(1055,\cdot)\) \(\chi_{3969}(1067,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
Values on generators
\((2108,3727)\) → \((e\left(\frac{7}{54}\right),e\left(\frac{5}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3969 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{378}\right)\) | \(e\left(\frac{85}{189}\right)\) | \(e\left(\frac{82}{189}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{169}{378}\right)\) | \(e\left(\frac{365}{378}\right)\) | \(e\left(\frac{170}{189}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{7}{18}\right)\) |